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Author name code: frisch
ADS astronomy entries on 2022-09-14
author:"Frisch, Helene"
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Title: Effects of Angle-Dependent Partial Frequency Redistribution
on Polarized Line Profiles
Authors: Sampoorna, M.; Nagendra, K. N.; Frisch, H.; Stenflo, J. O.
2019ASPC..519..109S Altcode:
Scattering of the solar limb-darkened radiation field on atoms and
molecules produces linearly polarized spectrum of the Sun (Second Solar
Spectrum). Partial frequency redistribution (PFR) plays a fundamental
role in shaping the wings of linearly polarized profiles of strong
resonance lines. Here we present the effects of the angle-dependent
(AD) PFR on resonance polarization both in the presence and absence
of magnetic fields. We consider scattering on a two-level atom with
unpolarized lower level, and a one-dimensional isothermal atmosphere.
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Title: Non-conservative Rayleigh Scattering. A Perturbation Approach
Authors: Frisch, H.
2019ASPC..519..101F Altcode:
The continuous spectra of stellar and planetary atmospheres may be
linearly polarized by Rayleigh or Thomson scattering. The polarization
rate follows the Chandrasekhar's law for the Milne or diffuse
reflection problems, if scattering processes are the only source
of absorption and emission. Deviations from the Chandrasekhar's law
due to true absorptions by bound-free or free-free transitions are
derived from a perturbation analysis of the polarized radiative
transfer equation, using as expansion parameter the ratio ɛ =
κ<SUB>c</SUB>/(κ<SUB>c</SUB> + σ<SUB>c</SUB>), with κ<SUB>c</SUB>
and σ<SUB>c</SUB> the true absorption and scattering absorption
coefficients. An expansion in powers of ɛ is proposed for the
polarization rate. A comparison with numerical results shows
an excellent fit for ɛ up to 10<SUP>-3</SUP> but a systematic
underestimation above this value.
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Title: Nonconservative Rayleigh scattering. A perturbation approach
Authors: Frisch, H.
2019A&A...625A.125F Altcode:
Context. The continuous spectrum of stellar and planetary atmospheres
can be linearly polarized by Rayleigh or Thomson scattering. The
polarization rate depends on the ratio κ<SUB>c</SUB>/(κ<SUB>c</SUB> +
σ<SUB>c</SUB>), κ<SUB>c</SUB> and σ<SUB>c</SUB> being the absorption
coefficients due to photo-ionizations and scattering processes,
respectively. The scattering process is conservative if κ<SUB>c</SUB>
= 0, and in this case the center-to-limb variation of the polarization
rate follows Chandrasekhar's law. Deviations from this law appear
if the scattering is nonconservative, that is, if photons have a
probability ɛ = κ<SUB>c</SUB>/(κ<SUB>c</SUB> + σ<SUB>c</SUB>)
of being destroyed at each scattering. <BR /> Aims: Nonconservative
Rayleigh scattering is addressed here with a perturbation point of view,
using ɛ, assumed to be a constant, as an expansion parameter. The
goal is to obtain a perturbation expansion of the polarized radiation
field that can be used to measure of the effects of a nonzero ɛ on
the polarization rate of the emergent radiation and to check the
accuracy of numerical codes. <BR /> Methods: The expansion method
is an application to Rayleigh scattering of a general perturbation
approach developed for scalar monochromatic transport equations. The
introduction of a space variable, rescaled by a factor √ɛ, transforms
the radiative transfer equation into a new equation from which one can
extract simpler equations to describe the field in the interior of the
medium and in boundary layers. <BR /> Results: The perturbation method
is applied to a plane-parallel slab with no incident radiation and an
unpolarized primary source of photons. The interior and boundary layer
fields are expanded in powers of √ɛ. The expansion of the interior
radiation field shows that it is unpolarized at leading order, with
an intensity i<SUB>0</SUB>(τ∼) satisfying a diffusion equation,
and that the polarization appears at order ɛ. The emergent radiation
is calculated up to and including order ɛ. The leading term yields
the polarization rate of the Chandrasekhar's law. The following one,
of order √ɛ, accurately predicts the decrease of the polarization
rate for values of ɛ up to 10<SUP>-3</SUP> and shows that it varies
roughly as (1 - μ) for any unpolarized primary source. Methods for
testing the accuracy of numerical schemes are proposed. The perturbation
method is also applied to a slab with an incident radiation field and
a polarized primary source of photons.
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Title: Analytic Results for Rayleigh Scattering and Resonance
Polarization
Authors: Frisch, H.
2019ASPC..526...19F Altcode:
In a plane parallel semi-infinite atmosphere, where the scattering
of photons follows the Rayleigh scattering law and all the absorbed
photons are reemitted (conservative scattering), the polarized radiation
field can be expressed in terms of two functions H<SUB>l</SUB>(μ) and
H<SUB>r</SUB>(μ) introduced by Chandrasekhar. It will be shown how the
vector radiative transfer problem for the polarized radiation field can
be decomposed into two scalar equations leading to exact expressions
for H<SUB>l</SUB>(μ) and H<SUB>r</SUB>(μ). For non conservative
Rayleigh scattering, the radiation field can be expressed in terms of
a matrix H(μ) satisfying a numerically solvable nonlinear integral
equation. The method of construction of this nonlinear equation and
its generalization to resonance scattering of spectral lines formed
with complete frequency redistribution is outlined.
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Title: Large Area Flat Panel Imaging Detectors for Astronomy and
Night Time Sensing
Authors: Siegmund, O.; McPhate, J.; Frisch, H.; Elam, J.; Mane, A.;
Wagner, R.; Varner, G.
2013amos.confE.105S Altcode:
Sealed tube photo-sensing detectors for optical/IR detection have
applications in astronomy, nighttime remote reconnaissance, and
airborne/space situational awareness. The potential development
of large area photon counting, imaging, timing detectors has
significance for these applications and a number of other areas
(High energy particle detection (RICH), biological single-molecule
fluorescence lifetime imaging microscopy, neutron imaging, time of
flight mass spectroscopy, diffraction imaging). We will present details
of progress towards the development of a 20 cm sealed tube optical
detector with nanoengineered microchannel plates for photon counting,
imaging and sub-ns event time stamping. In the operational scheme of
the photodetector incoming light passes through an entrance window
and interacts with a semitransparent photocathode on the inside of the
window. The photoelectrons emitted are accelerated across a proximity
gap and are detected by an MCP pair. The pair of novel borosilicate
substrate MCPs are functionalized by atomic layer deposition (ALD),
and amplify the signal and the resulting electron cloud is detected
by a conductive strip line anode for determination of the event
positions and the time of arrival. The physical package is ~ 25 x 25
cm but only 1.5 cm thick. Development of such a device in a square 20
cm format presents challenges: hermetic sealing to a large entrance
window, a 20 cm semitransparent photocathode with good efficiency
and uniformity, 20 cm MCPs with reasonable cost and performance,
robust construction to preserve high vacuum and withstand an atmosphere
pressure differential. We will discuss the schemes developed to address
these issues and present the results for the first test devices. The
novel microchannel plates employing borosilicate micro-capillary arrays
provide many performance characteristics typical of conventional MCPs,
but have been made in sizes up to 20 cm, have low intrinsic background
(0.08 events cm2 s-1) and have very stable gain behavior over >
7 C cm2 of charge extracted. They are high temperature compatible
and have minimal outgassing, which shortens and simplifies the sealed
tube production process and should improve overall lifetimes. Bialkali
(NaKSb) semitransparent photocathodes with > 20% quantum efficiency
have also been made on 20 cm borosilicate windows compatible with the
window seals for the large sealed tube device. The photocathodes have
good response uniformity and have been stable for > 5 months in
testing. Tests with a 20 cm detector with a cross delay line readout
have achieved ~50µm FWHM imaging with single photon sub-ns timing and
MHz event rates, and tests with a 10 x 10cm detector with cross strip
readout has achieved ~20µm FWHM imaging with >4 MHz event rates
with ~10% deadtime. We will discuss the details and implications of
these novel detector implementations and their potential applications.
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Title: Performance characteristics of atomic layer functionalized
microchannel plates
Authors: Siegmund, O. H. W.; Richner, N.; Gunjala, G.; McPhate, J. B.;
Tremsin, A. S.; Frisch, H. J.; Elam, J.; Mane, A.; Wagner, R.; Craven,
C. A.; Minot, M. J.
2013SPIE.8859E..0YS Altcode:
Microchannel plates that have been constructed by atomic layer
deposition of resistive and secondary emissive layers, onto
borosilicate glass microcapillary arrays provide a novel alternative
to conventional microchannel plates for detection of radiation and
particles. Conventional microchannel plates can also benefit from
atomic layer deposition of highly efficient secondary emissive
layers. Our evaluations of these techniques have revealed unique
features of atomic layer functionalized microchannel plates, including
enhanced stability and lifetime, low background rates, and low levels of
adsorbed gas. In addition borosilicate glass microcapillary arrays show
enhanced physical and thermal robustness, which makes it possible to
successfully fabricate large area devices (20 cm) with good uniformity
of operational characteristics.
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Title: Latest Advancements in Microchannel Plate Detectors
Authors: Vallerga, John; Siegmund, O.; McPhate, J. B.; Tremsin, A.;
Welsh, B.; Frisch, H.; Wagner, R. G.; Elam, J.; Mane, A.; Varner, G.
2013HEAD...1312315V Altcode:
Microchannel plate (MCP) detectors have been used in space-based
astronomical detectors for decades (e.g. EUVE, ROSAT, Chandra, COS on
Hubble) and their performance continues to improve. We will present
the latest technological developments in MCP detectors, including
very large format MCPs made from low background borosilicate glass
(20cm x 20cm MCPs); functionalized by atomic layer deposition of
semiconductor layers and high electron emission coefficient layers
which substantially increase the lifetime of the output gain; high
speed cross strip readouts (> 4MHz count rate at 10% deadtime); and
photocathode development for increased QE in the UV and x-ray bands. We
will also present our efforts to raise the technology readiness level
of our cross-strip electronics to level 6 by developing low power and
low mass ASICs that can be space qualified. This work is supported by
NASA Grants NNX12AF46A, NNG11AD54G and DOE grant #DE-AC02-06CH11357.
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Title: Large Area and High Efficiency Photon Counting Imaging
Detectors with High Time and Spatial Resolution for Night Time
Sensing and Astronomy
Authors: Siegmund, O.; Vallerga, J.; Tremsin, A.; McPhate, J.; Frisch,
H.; Elam, J.; Mane, A.; Wagner, R.; Varner, G.
2012amos.confE..92S Altcode:
The development of large area photon counting, imaging, timing detectors
with high performance has significance for applications in astronomy
(such as our sensor on the SAAO SALT 10m telescope), night time remote
reconnaissance, airborne/space situational awareness, and high-speed
adaptive optics. Sealed tube configurations for optical/IR sensing also
have applications in detection of Cherenkov light (RICH), biological
single-molecule fluorescence lifetime imaging microscopy and neutron
imaging applications. In open faced configurations these devices are
important for UV and particle detection in space astrophysics, mass
spectroscopy and many time-of flight applications. Currently available
devices are limited to sizes of about 5 cm and use either conventional
microchannel plates, or dynode multipliers for amplification, coupled
coarse pad array readouts. Extension of these schemes to devices
as large as 20 cm with high spatial resolution presents significant
problems and potentially considerable cost. A collaboration (Large
Area Picosecond Photon Detector) of the U. Chicago, Argonne National
Laboratory, U.C. Berkeley, U. Hawaii and a number of other institutions
has developed novel technologies to realize 20 cm format detectors
in open face or sealed tube configurations. One critical component of
this development is novel microchannel plates employing borosilicate
micro-capillary arrays. The microchannel plates are based on a
novel concept where the substrate is constructed from a borosilicate
micro-capillary array that is made to function as a microchannel plate
by deposition of resistive and secondary emissive layers using atomic
layer deposition. The process is relatively inexpensive compared with
conventional microchannel plates and allows very large microchannel
plates to be produced with pore sizes as small as 10 microns. These
provide many performance characteristics typical of conventional
microchannel plates, but have been made in sizes up to 20 cm, have
low intrinsic background (<0.1 events/sq-cm/sec) and high stability
with no observed gain degradation behavior over at least 5 Coul/sq-cm
of charge extraction. Initial tests in a 20 cm detector with a cross
strip electronic readout have achieved 4k x 4k pixel imaging with
single photon sub-ns timing and MHz event rates. In concert with this
effort we have made stable, uniform 20 cm bialkali photocathodes with
>20% quantum efficiency on borosilicate windows compatible with
a large sealed tube device. Other related efforts have also produced
small sealed tubes with 30% quantum efficiency GaAs sealed tubes with
high resolution imaging and timing that are immediately applicable
to current applications, and opaque GaN UV photocathodes directly
deposited onto these novel microchannel plates. We will discuss the
details and implications of these novel microchannel plates with
respect to the realization of novel detectors up to 20 cm format with
reasonable cost and performance, robust construction, high flexibility
of format and readout, reduction of fabrication effort, dramatically
increased lifetime and stability, and their potential applications.
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Title: Forward-scattering Hanle effect in the solar Ca I 4227 Å line
Authors: Frisch, H.; Anusha, L. S.; Bianda, M.; Holzreuter, R.;
Nagendra, K. N.; Ramelli, R.; Sampoorna, M.; Smitha, H. N.; Stenflo,
J. O.
2012EAS....55...59F Altcode:
High sensitivity spectropolarimetric observations of the four Stokes
parameters of the solar Ca I 4227 Å line have been performed in
October 2010 at IRSOL with the ZIMPOL polarimeter, near the disk center,
outside an active region (Bianda et al. 2011). They were analyzed in
Anusha et al. 2011 with a combination of detailed radiative transfer
modelling of the Hanle effect for the linear polarization and weak
field Zeeman approximation for the circular polarization. This approach
made possible a unique determination of the magnetic field vector at
various positions along the slit of the spectrograph. A summary of
the observations and of their analysis is presented here.
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Title: Search for anomalous production of multiple leptons in
association with W and Z bosons at CDF
Authors: Aaltonen, T.; Álvarez González, B.; Amerio, S.; Amidei, D.;
Anastassov, A.; Annovi, A.; Antos, J.; Apollinari, G.; Appel, J. A.;
Arisawa, T.; Artikov, A.; Asaadi, J.; Ashmanskas, W.; Auerbach, B.;
Aurisano, A.; Azfar, F.; Badgett, W.; Bae, T.; Barbaro-Galtieri, A.;
Barnes, V. E.; Barnett, B. A.; Barria, P.; Bartos, P.; Bauce, M.;
Bedeschi, F.; Behari, S.; Bellettini, G.; Bellinger, J.; Benjamin,
D.; Beretvas, A.; Bhatti, A.; Bisello, D.; Bizjak, I.; Bland, K. R.;
Blumenfeld, B.; Bocci, A.; Bodek, A.; Bortoletto, D.; Boudreau, J.;
Boveia, A.; Brigliadori, L.; Bromberg, C.; Brucken, E.; Budagov,
J.; Budd, H. S.; Burkett, K.; Busetto, G.; Bussey, P.; Buzatu, A.;
Calamba, A.; Calancha, C.; Camarda, S.; Campanelli, M.; Campbell,
M.; Canelli, F.; Carls, B.; Carlsmith, D.; Carosi, R.; Carrillo, S.;
Carron, S.; Casal, B.; Casarsa, M.; Castro, A.; Catastini, P.; Cauz,
D.; Cavaliere, V.; Cavalli-Sforza, M.; Cerri, A.; Cerrito, L.; Chen,
Y. C.; Chertok, M.; Chiarelli, G.; Chlachidze, G.; Chlebana, F.; Cho,
K.; Chokheli, D.; Chung, W. H.; Chung, Y. S.; Ciocci, M. A.; Clark,
A.; Clarke, C.; Compostella, G.; Convery, M. E.; Conway, J.; Corbo,
M.; Cordelli, M.; Cox, C. A.; Cox, D. J.; Crescioli, F.; Cuevas, J.;
Culbertson, R.; Dagenhart, D.; d'Ascenzo, N.; Datta, M.; de Barbaro,
P.; Dell'Orso, M.; Demortier, L.; Deninno, M.; Devoto, F.; d'Errico,
M.; Di Canto, A.; Di Ruzza, B.; Dittmann, J. R.; D'Onofrio, M.; Donati,
S.; Dong, P.; Dorigo, M.; Dorigo, T.; Ebina, K.; Elagin, A.; Eppig,
A.; Erbacher, R.; Errede, S.; Ershaidat, N.; Eusebi, R.; Farrington,
S.; Feindt, M.; Fernandez, J. P.; Field, R.; Flanagan, G.; Forrest, R.;
Frank, M. J.; Franklin, M.; Freeman, J. C.; Frisch, H.; Funakoshi, Y.;
Furic, I.; Gallinaro, M.; Garcia, J. E.; Garfinkel, A. F.; Garosi, P.;
Gerberich, H.; Gerchtein, E.; Giagu, S.; Giakoumopoulou, V.; Giannetti,
P.; Gibson, K.; Ginsburg, C. M.; Giokaris, N.; Giromini, P.; Giurgiu,
G.; Glagolev, V.; Glenzinski, D.; Gold, M.; Goldin, D.; Goldschmidt,
N.; Golossanov, A.; Gomez, G.; Gomez-Ceballos, G.; Goncharov, M.;
González, O.; Gorelov, I.; Goshaw, A. T.; Goulianos, K.; Grinstein,
S.; Grosso-Pilcher, C.; Group, R. C.; Guimaraes da Costa, J.; Hahn,
S. R.; Halkiadakis, E.; Hamaguchi, A.; Han, J. Y.; Happacher, F.; Hara,
K.; Hare, D.; Hare, M.; Harr, R. F.; Hatakeyama, K.; Hays, C.; Heck,
M.; Heinrich, J.; Herndon, M.; Hewamanage, S.; Hocker, A.; Hopkins,
W.; Horn, D.; Hou, S.; Hughes, R. E.; Hurwitz, M.; Husemann, U.;
Hussain, N.; Hussein, M.; Huston, J.; Introzzi, G.; Iori, M.; Ivanov,
A.; James, E.; Jang, D.; Jayatilaka, B.; Jeon, E. J.; Jindariani, S.;
Jones, M.; Joo, K. K.; Jun, S. Y.; Junk, T. R.; Kamon, T.; Karchin,
P. E.; Kasmi, A.; Kato, Y.; Ketchum, W.; Keung, J.; Khotilovich, V.;
Kilminster, B.; Kim, D. H.; Kim, H. S.; Kim, J. E.; Kim, M. J.; Kim,
S. B.; Kim, S. H.; Kim, Y. K.; Kim, Y. J.; Kimura, N.; Kirby, M.;
Klimenko, S.; Knoepfel, K.; Kondo, K.; Kong, D. J.; Konigsberg, J.;
Kotwal, A. V.; Kreps, M.; Kroll, J.; Krop, D.; Kruse, M.; Krutelyov,
V.; Kuhr, T.; Kurata, M.; Kwang, S.; Laasanen, A. T.; Lami, S.; Lammel,
S.; Lancaster, M.; Lander, R. L.; Lannon, K.; Lath, A.; Latino, G.;
LeCompte, T.; Lee, E.; Lee, H. S.; Lee, J. S.; Lee, S. W.; Leo, S.;
Leone, S.; Lewis, J. D.; Limosani, A.; Lin, C. -J.; Lindgren, M.;
Lipeles, E.; Lister, A.; Litvintsev, D. O.; Liu, C.; Liu, H.; Liu, Q.;
Liu, T.; Lockwitz, S.; Loginov, A.; Lucchesi, D.; Lueck, J.; Lujan,
P.; Lukens, P.; Lungu, G.; Lys, J.; Lysak, R.; Madrak, R.; Maeshima,
K.; Maestro, P.; Malik, S.; Manca, G.; Manousakis-Katsikakis, A.;
Margaroli, F.; Marino, C.; Martínez, M.; Mastrandrea, P.; Matera,
K.; Mattson, M. E.; Mazzacane, A.; Mazzanti, P.; McFarland, K. S.;
McIntyre, P.; McNulty, R.; Mehta, A.; Mehtala, P.; Mesropian, C.;
Miao, T.; Mietlicki, D.; Mitra, A.; Miyake, H.; Moed, S.; Moggi, N.;
Mondragon, M. N.; Moon, C. S.; Moore, R.; Morello, M. J.; Morlock, J.;
Movilla Fernandez, P.; Mukherjee, A.; Muller, Th.; Murat, P.; Mussini,
M.; Nachtman, J.; Nagai, Y.; Naganoma, J.; Nakano, I.; Napier, A.;
Nett, J.; Neu, C.; Neubauer, M. S.; Nielsen, J.; Nodulman, L.; Noh,
S. Y.; Norniella, O.; Oakes, L.; Oh, S. H.; Oh, Y. D.; Oksuzian, I.;
Okusawa, T.; Orava, R.; Ortolan, L.; Pagan Griso, S.; Pagliarone,
C.; Palencia, E.; Papadimitriou, V.; Paramonov, A. A.; Patrick,
J.; Pauletta, G.; Paulini, M.; Paus, C.; Pellett, D. E.; Penzo, A.;
Phillips, T. J.; Piacentino, G.; Pianori, E.; Pilot, J.; Pitts, K.;
Plager, C.; Pondrom, L.; Poprocki, S.; Potamianos, K.; Prokoshin,
F.; Pranko, A.; Ptohos, F.; Punzi, G.; Rahaman, A.; Ramakrishnan,
V.; Ranjan, N.; Redondo, I.; Renton, P.; Rescigno, M.; Riddick, T.;
Rimondi, F.; Ristori, L.; Robson, A.; Rodrigo, T.; Rodriguez, T.;
Rogers, E.; Rolli, S.; Roser, R.; Ruffini, F.; Ruiz, A.; Russ, J.;
Rusu, V.; Safonov, A.; Sakumoto, W. K.; Sakurai, Y.; Santi, L.; Sato,
K.; Saveliev, V.; Savoy-Navarro, A.; Schlabach, P.; Schmidt, A.;
Schmidt, E. E.; Schwarz, T.; Scodellaro, L.; Scribano, A.; Scuri,
F.; Seidel, S.; Seiya, Y.; Semenov, A.; Sforza, F.; Shalhout,
S. Z.; Shears, T.; Shepard, P. F.; Shimojima, M.; Shochet, M.;
Shreyber-Tecker, I.; Simonenko, A.; Sinervo, P.; Sliwa, K.; Smith,
J. R.; Snider, F. D.; Soha, A.; Sorin, V.; Song, H.; Squillacioti,
P.; Stancari, M.; St. Denis, R.; Stelzer, B.; Stelzer-Chilton, O.;
Stentz, D.; Strologas, J.; Strycker, G. L.; Sudo, Y.; Sukhanov, A.;
Suslov, I.; Takemasa, K.; Takeuchi, Y.; Tang, J.; Tecchio, M.; Teng,
P. K.; Thom, J.; Thome, J.; Thompson, G. A.; Thomson, E.; Toback,
D.; Tokar, S.; Tollefson, K.; Tomura, T.; Tonelli, D.; Torre, S.;
Torretta, D.; Totaro, P.; Trovato, M.; Ukegawa, F.; Uozumi, S.;
Varganov, A.; Vázquez, F.; Velev, G.; Vellidis, C.; Vidal, M.; Vila,
I.; Vilar, R.; Vizán, J.; Vogel, M.; Volpi, G.; Wagner, P.; Wagner,
R. L.; Wakisaka, T.; Wallny, R.; Wang, S. M.; Warburton, A.; Waters,
D.; Wester, W. C., III; Whiteson, D.; Wicklund, A. B.; Wicklund, E.;
Wilbur, S.; Wick, F.; Williams, H. H.; Wilson, J. S.; Wilson, P.;
Winer, B. L.; Wittich, P.; Wolbers, S.; Wolfe, H.; Wright, T.; Wu,
X.; Wu, Z.; Yamamoto, K.; Yamato, D.; Yang, T.; Yang, U. K.; Yang,
Y. C.; Yao, W. -M.; Yeh, G. P.; Yi, K.; Yoh, J.; Yorita, K.; Yoshida,
T.; Yu, G. B.; Yu, I.; Yu, S. S.; Yun, J. C.; Zanetti, A.; Zeng, Y.;
Zucchelli, S.
2012PhRvD..85i2001A Altcode: 2012arXiv1202.1260T
This paper presents a search for anomalous production of multiple
low-energy leptons in association with a W or Z boson using events
collected at the CDF experiment corresponding to 5.1fb<SUP>-1</SUP>
of integrated luminosity. This search is sensitive to a wide range
of topologies with low-momentum leptons, including those with
the leptons near one another. The observed rates of production of
additional electrons and muons are compared with the standard model
predictions. No indications of phenomena beyond the standard model are
found. A 95% confidence level limit is presented on the production cross
section for a benchmark model of supersymmetric hidden-valley Higgs
production. Particle identification efficiencies are also provided to
enable the calculation of limits on additional models.
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Title: Advances in microchannel plates and photocathodes for
ultraviolet photon counting detectors
Authors: Siegmund, O. H. W.; Fujiwara, K.; Hemphill, R.; Jelinsky,
S. R.; McPhate, J. B.; Tremsin, A. S.; Vallerga, J. V.; Frisch, H. J.;
Elam, J.; Mane, A.; Bennis, D. C.; Craven, C. A.; Deterando, M. A.;
Escolas, J. R.; Minot, M. J.; Renaud, J. M.
2011SPIE.8145E..0JS Altcode: 2011SPIE.8145E.251S
A new method of fabricating microchannel plates has been investigated,
employing microcapillary arrays of borosilicate glass that are
deposited with resistive and secondary emissive layers using atomic
layer deposition. Microchannel plates of this kind have been made in
sizes from 33 mm to 200 mm, with pore sizes of 40 μm and 20 μm, pore
length to diameter ratios of 60:1, bias angles of 8°, and open areas
from 60% to 83%. Tests with single MCPs and MCP pairs have been done
and show good imaging quality, gain comparable to conventional MCPs, low
background rates (~ 0.085 events sec<SUP>-1</SUP> cm<SUP>-2</SUP>), fast
pulse response, and good ageing characteristics. The quantum efficiency
for bare and alkali halide coated MCPs is similar to conventional MCPs,
and we have also been able to deposit opaque GaN(Mg) cathodes directly
onto these MCPs.
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Title: Analysis of the Forward-scattering Hanle Effect in the Ca I
4227 Å Line
Authors: Anusha, L. S.; Nagendra, K. N.; Bianda, M.; Stenflo, J. O.;
Holzreuter, R.; Sampoorna, M.; Frisch, H.; Ramelli, R.; Smitha, H. N.
2011ApJ...737...95A Altcode:
Coherent scattering of limb-darkened radiation is responsible for the
generation of the linearly polarized spectrum of the Sun (the Second
Solar Spectrum). This Second Solar Spectrum is usually observed near the
limb of the Sun, where the polarization amplitudes are largest. At the
center of the solar disk the linear polarization is zero for an axially
symmetric atmosphere. Any mechanism that breaks the axial symmetry (like
the presence of an oriented magnetic field, or resolved inhomogeneities
in the atmosphere) can generate a non-zero linear polarization. In the
present paper we study the linear polarization near the disk center
in a weakly magnetized region, where the axisymmetry is broken. We
present polarimetric (I, Q/I, U/I, and V/I) observations of the Ca
I 4227 Å line recorded around μ = cos θ = 0.9 (where θ is the
heliocentric angle) and a modeling of these observations. The high
sensitivity of the instrument (ZIMPOL-3) makes it possible to measure
the weak polarimetric signals with great accuracy. The modeling of
these high-quality observations requires the solution of the polarized
radiative transfer equation in the presence of a magnetic field. For
this we use standard one-dimensional model atmospheres. We show that the
linear polarization is mainly produced by the Hanle effect (rather than
by the transverse Zeeman effect), while the circular polarization is due
to the longitudinal Zeeman effect. A unique determination of the full
\bm {B} vector may be achieved when both effects are accounted for. The
field strengths required for the simultaneous fitting of Q/I, U/I, and
V/I are in the range 10-50 G. The shapes and signs of the Q/I and U/I
profiles are highly sensitive to the orientation of the magnetic field.
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Title: Observations of the forward scattering Hanle effect in the
Ca I 4227 Å line
Authors: Bianda, M.; Ramelli, R.; Anusha, L. S.; Stenflo, J. O.;
Nagendra, K. N.; Holzreuter, R.; Sampoorna, M.; Frisch, H.; Smitha,
H. N.
2011A&A...530L..13B Altcode: 2011arXiv1105.2157B
Chromospheric magnetic fields are notoriously difficult to measure. The
chromospheric lines are broad, while the fields are producing
a minuscule Zeeman-effect polarization. A promising diagnostic
alternative is provided by the forward-scattering Hanle effect, which
can be recorded in chromospheric lines such as the He i 10 830 Å
and the Ca i 4227 Å lines. We present a set of spectropolarimetric
observations of the full Stokes vector obtained near the center of the
solar disk in the Ca i 4227 Å line with the ZIMPOL polarimeter at the
IRSOL observatory. We detect a number of interesting forward-scattering
Hanle effect signatures, which we model successfully using polarized
radiative transfer. Here we focus on the observational aspects, while
a separate companion paper deals with the theoretical modeling.
---------------------------------------------------------
Title: Linear Polarization of the Solar Ca I 4227 Å Line: Modeling
with Radiative Transfer and Last Scattering Approximation
Authors: Anusha, L. S.; Stenflo, J. O.; Frisch, H.; Bianda, M.;
Holzreuter, R.; Nagendra, K. N.; Sampoorna, M.; Ramelli, R.
2011ASPC..437...57A Altcode:
To model the Ca I 4227 Å line polarization, radiative transfer
effects with partial frequency redistribution (PRD) must be taken into
account. The numerical solution of the relevant polarized radiative
transfer (RT) equations is computationally very demanding. The
“last scattering approximation” (LSA) is a concept allowing
faster methods to be devised. It is based on the remark that a single
scattering of the radiation field is sufficient for creating most
of the polarization. Its key ingredient is the anisotropy of the
radiation field. If the anisotropy is extracted from the observed
center to limb variation of the intensity profile, only the wings
of the Q/I spectrum can be modeled (Sampoorna et al. 2009). We show
here that the core region may be modeled as well if one takes into
account the depth variation of the anisotropy which is obtained from
an unpolarized multilevel RT (Anusha et al. 2010). After a validation
of the LSA approach by comparison with a polarized RT calculation, we
apply both approaches to model recent observations of the Ca I 4227 Å
line polarization taken on the quiet Sun. Apart from a global scaling
factor, both approaches give a very good fit to the Q/I spectrum for
all the wavelengths. As the LSA is 8 times faster than the RT approach,
we can recommend it as an efficient method to analyze other strong
resonance lines in the second solar spectrum.
---------------------------------------------------------
Title: Observations of the Solar Ca I 4227 Å Line
Authors: Bianda, M.; Ramelli, R.; Stenflo, J. O.; Anusha, L. S.;
Nagendra, K. N.; Sampoorna, M.; Holzreuter, R.; Frisch, H.
2011ASPC..437...67B Altcode:
Our aim is to understand some interesting polarization features
observed in the solar Ca I 4277 Å line. Here we only discuss the
observational aspects. Observations have also been made in other
chromospheric lines within a few hours of those in the Ca I 4227 Å
line, in the same region near the north solar limb, to illustrate the
potential of simultaneous observations in different lines.
---------------------------------------------------------
Title: Spectral line polarization with angle-dependent partial
frequency redistribution. II. Accelerated lambda iteration and
scattering expansion methods for the Rayleigh scattering
Authors: Sampoorna, M.; Nagendra, K. N.; Frisch, H.
2011A&A...527A..89S Altcode:
Context. The linear polarization of strong resonance lines observed in
the solar spectrum is created by the scattering of the photospheric
radiation field. This polarization is sensitive to the form of
the partial frequency redistribution (PRD) function used in the
line radiative transfer equation. Observations have been analyzed
until now with angle-averaged PRD functions. With an increase in
the polarimetric sensitivity and resolving power of the present-day
telescopes, it will become possible to detect finer effects caused
by the angle dependence of the PRD functions. <BR /> Aims: We devise
new efficient numerical methods to solve the polarized line transfer
equation with angle-dependent PRD, in plane-parallel cylindrically
symmetrical media. We try to bring out the essential differences
between the polarized spectra formed under angle-averaged and the
more realistic case of angle-dependent PRD functions. <BR /> Methods:
We use a recently developed Stokes vector decomposition technique to
formulate three different iterative methods tailored for angle-dependent
PRD functions. Two of them are of the accelerated lambda iteration
type, one is based on the core-wing approach, and the other one on
the frequency by frequency approach suitably generalized to handle
angle-dependent PRD. The third one is based on a series expansion in
the mean number of scattering events (Neumann series expansion). <BR />
Results: We show that all these methods work well on this difficult
problem of polarized line formation with angle-dependent PRD. We
present several benchmark solutions with isothermal atmospheres to
show the performance of the three numerical methods and to analyze the
role of the angle-dependent PRD effects. For weak lines, we find no
significant effects when the angle-dependence of the PRD functions is
taken into account. For strong lines, we find a significant decrease in
the polarization, the largest effect occurring in the near wing maxima.
---------------------------------------------------------
Title: Polymers in Constrained Ceramic Environments
Authors: Frisch, H. L.; Huang, L.
2011emst.book.7684F Altcode:
There is a great deal of interest in the preparation and
characterization of organic-inorganic nanocomposites, particularly in
those materials in which an organic phase is ceramic constrained in
such a way as to produce novel structures, frequently at the molecular
level. Such ceramic-constrained environments include zeolites, clay
galleries, and mesoporous silica. In some cases, a polymer is directly
introduced into a constraining structure (clay galleries), while in
others a constrained monomer is polymerized subsequently, for example
in pores, to obtain the final composite material. This review focuses
on some specific aspects of the morphology of organic-inorganic
nanocomposites and how the confinement affects the properties of
the polymer.
---------------------------------------------------------
Title: Spectral line polarization with angle-dependent partial
frequency redistribution. I. A Stokes parameters decomposition for
Rayleigh scattering
Authors: Frisch, H.
2010A&A...522A..41F Altcode:
Context. The linear polarization of a strong resonance lines observed
near the solar limb is created by a multiple-scattering process. Partial
frequency redistribution (PRD) effects must be accounted for to explain
the polarization profiles. The redistribution matrix describing the
scattering process is a sum of terms, each containing a PRD function
multiplied by a Rayleigh type phase matrix. A standard approximation
made in calculating the polarization is to average the PRD functions
over all the scattering angles, because the numerical work needed to
take the angle-dependence of the PRD functions into account is large and
not always needed for reasonable evaluations of the polarization. <BR />
Aims: This paper describes a Stokes parameters decomposition method,
that is applicable in plane-parallel cylindrically symmetrical media,
which aims at simplifying the numerical work needed to overcome
the angle-average approximation. <BR /> Methods: The decomposition
method relies on an azimuthal Fourier expansion of the PRD functions
associated to a decomposition of the phase matrices in terms of the
Landi Degl'Innocenti irreducible spherical tensors for polarimetry
T^K_Q(i, Ω) (i Stokes parameter index, Ω ray direction). The terms
that depend on the azimuth of the scattering angle are retained in the
phase matrices. <BR /> Results: It is shown that the Stokes parameters
I and Q, which have the same cylindrical symmetry as the medium, can be
expressed in terms of four cylindrically symmetrical components I_Q^K (K
= Q = 0, K = 2, Q = 0, 1, 2). The components with Q = 1, 2 are created
by the angular dependence of the PRD functions. They go to zero at
disk center, ensuring that Stokes Q also goes to zero. Each component
I_Q^K is a solution to a standard radiative transfer equation. The
source term S_Q^K are significantly simpler than the source terms
corresponding to I and Q. They satisfy a set of integral equations
that can be solved by an accelerated lambda iteration (ALI) method.
---------------------------------------------------------
Title: Generalization of the Last Scattering Approximation for the
Second Solar Spectrum Modeling: The Ca I 4227 Å Line as a Case Study
Authors: Anusha, L. S.; Nagendra, K. N.; Stenflo, J. O.; Bianda, M.;
Sampoorna, M.; Frisch, H.; Holzreuter, R.; Ramelli, R.
2010ApJ...718..988A Altcode:
To model the second solar spectrum (the linearly polarized spectrum
of the Sun that is due to coherent scattering processes), one needs
to solve the polarized radiative transfer (RT) equation. For strong
resonance lines, partial frequency redistribution (PRD) effects must be
accounted for, which make the problem computationally demanding. The
"last scattering approximation" (LSA) is a concept that has been
introduced to make this highly complex problem more tractable. An
earlier application of a simple LSA version could successfully model
the wings of the strong Ca I 4227 Å resonance line in Stokes Q/I
(fractional linear polarization), but completely failed to reproduce
the observed Q/I peak in the line core. Since the magnetic field
signatures from the Hanle effect only occur in the line core, we need
to generalize the existing LSA approach if it is to be useful for the
diagnostics of chromospheric and turbulent magnetic fields. In this
paper, we explore three different approximation levels for LSA and
compare each of them with the benchmark represented by the solution of
the full polarized RT, including PRD effects. The simplest approximation
level is LSA-1, which uses the observed center-to-limb variation of
the intensity profile to obtain the anisotropy of the radiation field
at the surface, without solving any transfer equation. In contrast,
the next two approximation levels use the solution of the unpolarized
transfer equation to derive the anisotropy of the incident radiation
field and use it as an input. In the case of LSA-2, the anisotropy
at level τ<SUB>λ</SUB> = μ, the atmospheric level from which an
observed photon is most likely to originate, is used. LSA-3, on the
other hand, makes use of the full depth dependence of the radiation
anisotropy. The Q/I formula for LSA-3 is obtained by keeping the
first term in a series expansion of the Q-source function in powers
of the mean number of scattering events. Computationally, LSA-1 is 21
times faster than LSA-2, which is 5 times faster than the more general
LSA-3, which itself is 8 times faster than the polarized RT approach. A
comparison of the calculated Q/I spectra with the RT benchmark shows
excellent agreement for LSA-3, including good modeling of the Q/I
core region with its PRD effects. In contrast, both LSA-1 and LSA-2
fail to model the core region. The RT and LSA-3 approaches are then
applied to model the recently observed Q/I profile of the Ca I 4227
Å line in quiet regions of the Sun. Apart from a global scale factor
both give a very good fit to the Q/I spectra for all the wavelengths,
including the core peak and blend line depolarizations. We conclude
that LSA-3 is an excellent substitute for the full polarized RT and
can be used to interpret the second solar spectrum, including the
Hanle effect with PRD. It also allows the techniques developed for
unpolarized three-dimensional RT to be applied to the modeling of the
second solar spectrum.
---------------------------------------------------------
Title: The Hanle Effect as Diagnostic Tool for Turbulent Magnetic
Fields
Authors: Anusha, L. S.; Sampoorna, M.; Frisch, H.; Nagendra, K. N.
2010ASSP...19..390A Altcode: 2010mcia.conf..390A
The Hanle effect is calculated for a random magnetic field characterized
by a finite correlation length and a probability density function
of the magnetic field vector. It is shown that linear polarization
is essentially independent of the magnetic field correlation length,
but strongly depends on the distribution of the field strength.
---------------------------------------------------------
Title: The quiet Sun magnetic field observed with ZIMPOL on
THEMIS. I. The probability density function
Authors: Bommier, V.; Martínez González, M.; Bianda, M.; Frisch,
H.; Asensio Ramos, A.; Gelly, B.; Landi Degl'Innocenti, E.
2009A&A...506.1415B Altcode:
Context: The quiet Sun magnetic field probability density function (PDF)
remains poorly known. Modeling this field also introduces a magnetic
filling factor that is also poorly known. With these two quantities,
PDF and filling factor, the statistical description of the quiet Sun
magnetic field is complex and needs to be clarified. <BR />Aims:
In the present paper, we propose a procedure that combines direct
determinations and inversion results to derive the magnetic field
vector and filling factor, and their PDFs. <BR />Methods: We used
spectro-polarimetric observations taken with the ZIMPOL polarimeter
mounted on the THEMIS telescope. The target was a quiet region at disk
center. We analyzed the data by means of the UNNOFIT inversion code,
with which we inferred the distribution of the mean magnetic field α
B, α being the magnetic filling factor. The distribution of α was
derived by an independent method, directly from the spectro-polarimetric
data. The magnetic field PDF p(B) could then be inferred. By introducing
a joint PDF for the filling factor and the magnetic field strength, we
have clarified the definition of the PDF of the quiet Sun magnetic field
when the latter is assumed not to be volume-filling. <BR />Results: The
most frequent local average magnetic field strength is found to be 13
G. We find that the magnetic filling factor is related to the magnetic
field strength by the simple law α = B_1/B with B<SUB>1</SUB> = 15
G. This result is compatible with the Hanle weak-field determinations,
as well as with the stronger field determinations from the Zeeman effect
(kGauss field filling 1-2% of space). From linear fits, we obtain the
analytical dependence of the magnetic field PDF. Our analysis has also
revealed that the magnetic field in the quiet Sun is isotropically
distributed in direction. <BR />Conclusions: We conclude that the
quiet Sun is a complex medium where magnetic fields having different
field strengths and filling factors coexist. Further observations
with a better polarimetric accuracy are, however, needed to confirm
the results obtained in the present work. <P />Based on observations
made with the French-Italian telescope THEMIS operated by the CNRS
and CNR on the island of Tenerife in the Spanish Observatorio del
Teide of the Instituto de Astrofísica de Canarias. Present address:
Instituto de Astrofísica de Canarias, vía Láctea s/n, 38205 La
Laguna, Tenerife, Spain.
---------------------------------------------------------
Title: The Hanle effect in a random magnetic field. Dependence of
the polarization on statistical properties of the magnetic field
Authors: Frisch, H.; Anusha, L. S.; Sampoorna, M.; Nagendra, K. N.
2009A&A...501..335F Altcode:
Context: The Hanle effect is used to determine weak turbulent magnetic
fields in the solar atmosphere, usually assuming that the angular
distribution is isotropic, the magnetic field strength constant, and
that micro-turbulence holds, i.e. that the magnetic field correlation
length is much less than a photon mean free path. <BR />Aims: To
examine the sensitivity of turbulent magnetic field measurements
to these assumptions, we study the dependence of Hanle effect on
the magnetic field correlation length, its angular, and strength
distributions. <BR />Methods: We introduce a fairly general random
magnetic field model characterized by a correlation length and a
magnetic field vector distribution. Micro-turbulence is recovered
when the correlation length goes to zero and macro-turbulence when it
goes to infinity. Radiative transfer equations are established for
the calculation of the mean Stokes parameters and they are solved
numerically by a polarized approximate lambda iteration method. <BR
/>Results: We show that optically thin spectral lines and optically
very thick ones are insensitive to the correlation length of the
magnetic field, while spectral lines with intermediate optical depths
(around 10-100) show some sensitivity to this parameter. The result is
interpreted in terms of the mean number of scattering events needed to
create the surface polarization. It is shown that the single-scattering
approximation holds good for thin and thick lines but may fail for lines
with intermediate thickness. The dependence of the polarization on the
magnetic field vector probability density function (PDF) is examined
in the micro-turbulent limit. A few PDFs with different angular and
strength distributions, but equal mean value of the magnetic field,
are considered. It is found that the polarization is in general quite
sensitive to the shape of the magnetic field strength PDF and somewhat
to the angular distribution. <BR />Conclusions: The mean field derived
from Hanle effect analysis of polarimetric data strongly depends on
the choice of the field strength distribution used in the analysis. It
is shown that micro-turbulence is in general a safe approximation.
---------------------------------------------------------
Title: The Hanle Effect. Angle-dependent Frequency Redistribution
Function. Decomposition of the Stokes Parameters in Irreducible
Components.
Authors: Frisch, H.
2009ASPC..405...87F Altcode:
We show that the spherical tensor decomposition of the Stokes
parameters developed for angle-averaged frequency redistribution
functions can be extended to angle-dependent frequency redistribution
functions. The irreducible components of the Stokes parameters loose
their cylindrical symmetry but one can still write an integral equation
for the irreducible components of the source vector. Numerical solution
of this equation may be simplified by the introduction of an azimuthal
Fourier expansion of the frequency redistribution function.
---------------------------------------------------------
Title: The CDF level 2 calorimetric trigger upgrade
Authors: Bhatti, A.; Canepa, A.; Casarsa, M.; Convery, M.; Cortiana,
G.; Dell'Orso, M.; Donati, S.; Flanagan, G.; Frisch, H.; Fukun, T.;
Krop, D.; Giannetti, P.; Greco, V.; Jones, M.; Liu, T.; Lucchesi, D.;
Pagan-Griso, S.; Pantano, D.; Pianori, E.; Piendibene, M.; Pilcher,
C.; Ristori, L.; Rogondino, L.; Rusu, V.; Sartori, L.; Schmidt, M.;
Veszpremi, V.; Vidal, M.; Zhou, L.
2009NIMPA.598..331B Altcode:
CDF II upgraded the calorimeter trigger to cope with the higher detector
occupancy due to the increased Tevatron instantaneous luminosity
(∼2.8×10<SUP></SUP>cm<SUP></SUP>s<SUP></SUP>). While the original
system was implemented in custom hardware and provided to the L2 trigger
a limited-quality jet clustering performed using a reduced resolution
measurement of the transverse energy in the calorimeter trigger towers,
the upgraded system provides offline-quality jet reconstruction of the
full resolution calorimeter data. This allows to keep better under
control the dependence of the trigger rates on the instantaneous
luminosity and to improve the efficiency and purity of the trigger
selections. The upgraded calorimeter trigger uses the general purpose
VME board Pulsar, developed at CDF II and already widely used to
upgrade the L2 tracking and L2 decision systems. A battery of Pulsars
is used to merge and send the calorimeter data to the L2 CPUs, where
software-implemented algorithms perform offline-like clustering. In this
paper we review the design and the performance of the upgraded system.
---------------------------------------------------------
Title: Zeeman line formation in solar magnetic fields. Studies with
empirical probability distribution functions
Authors: Sampoorna, M.; Nagendra, K. N.; Frisch, H.; Stenflo, J. O.
2008A&A...485..275S Altcode:
Context: Numerical simulations of magneto-convection and analysis
of solar magnetograms provide probability distribution functions
(PDFs) for the magnetic field strength. <BR />Aims: In the paper,
we explore the effects of these PDFs on Zeeman line formation. <BR
/>Methods: We calculate the mean Stokes parameters for a Milne-Eddington
atmosphere in the limit of optically thin (micro-turbulent) and thick
(macro-turbulent) magnetic structures and also the dispersion around
the mean profiles in the optically thick limit. Several types of PDFs
are considered: (a) Voigt function and stretched exponential type
PDFs for fields with fixed direction but fluctuating strength; (b)
a cylindrically symmetrical power law for the angular distribution of
magnetic fields with given field strength; (c) composite PDFs accounting
for randomness in both strength and direction obtained by combining a
Voigt function or a stretched exponential with an angular power law. For
optically thin structures, explicit expressions are given for the mean
values of the Zeeman absorption matrix elements. We also describe how
the averaging technique for a normal Zeeman triplet may be generalized
to the more common case of anomalous Zeeman splitting patterns. <BR
/>Results: We show that, for magnetic field rms fluctuations of
the order of 6 G, consistent with observational data, Stokes I is
essentially independent of the shapes of the PDFs but Stokes Q, U, and
V and also the dispersion around the mean values are quite sensitive
to the tail behavior of the PDF. We confirm a previous result that
Stokes V is less sensitive to the scale of the magnetic structures
than Stokes Q and U. The composite PDF proposed for the fluctuations of
the magnetic field vector has an angular distribution peaked about the
vertical direction for strong fields, and is isotropically distributed
for weak fields; it can be used to mimic solar surface random fields.
---------------------------------------------------------
Title: Some aspects of polarized line formation in magneto-turbulent
media
Authors: Sampoorna, M.; Frisch, H.; Nagendra, K. N.
2008NewA...13..233S Altcode:
Observations and numerical simulations of magneto-convection show a
highly variable solar magnetic field. Using a statistical approach,
we analyze the effects of random magnetic fields on Stokes profiles of
spectral lines. We consider the micro and macro-turbulent regimes,
which provide bounds for more general random fields with finite
scales of variations. The mean Stokes parameters are obtained in the
micro-turbulent regime, by first averaging the Zeeman propagation
matrix Φ^ over the probability distribution function P( B) of the
magnetic field and then solving the concerned radiative transfer
equation. In the macro-turbulent regime, the mean solution is obtained
by averaging the emergent solution over P( B). It is assumed that B has
a Gaussian distribution defined by its mean field B<SUB>0</SUB>, angular
distribution and dispersion. Fluctuations parallel and perpendicular
to B<SUB>0</SUB> are considered. Spectral lines are parameterized by
their strength β, which is varied over the range 1-10 <SUP>4</SUP>. A
detailed comparison of micro and macro-turbulent limit with mean field
solution shows that differences are important for β ⩾ 10. When β
increases, the saturation behavior of micro-turbulent profiles are
significantly different from that of mean field profiles. The Stokes
profiles shapes are explained in terms of the non-linear β-dependence
of the Unno-Rachkovsky solution using approximate expressions for the
mean absorption coefficients. These expressions when inserted in the
Unno-Rachkovsky solution can predict Stokes profiles that match with
the numerical result to a good approximation.
---------------------------------------------------------
Title: The Hanle effect. Decomposition of the Stokes parameters into
irreducible components
Authors: Frisch, H.
2007A&A...476..665F Altcode:
Context: It has been shown for the weak-field Hanle effect that the
Stokes parameters I, Q, and U can be represented by a set of six
cylindrically symmetrical functions. The proof relies on azimuthal
Fourier expansions of the radiation field and of the Hanle phase
matrix. It holds for a plane-parallel atmosphere and scattering
processes that can be described by a redistribution matrix where
redistribution in frequency is decoupled from angle redistribution and
polarization. <BR />Aims: We give a simpler and more general proof of
the Stokes parameter decomposition using powerful new tools introduced
for polarimetry, in particular the Landi Degl'Innocenti spherical
tensors T^K_Q(i,Ω). <BR />Methods: The elements of the Hanle phase
matrix are written as a sum of terms that depend separately on the
magnetic field vector and the directions Ω and Ω' of the incoming and
scattered beams. The dependence on Ω and Ω' is expressed in terms
of the spherical tensors T^K_Q(i,Ω) where i refers to the Stokes
parameters (i=0,ldots,3). A multipolar expansion in terms of the
T^K_Q(i,Ω) is then established for the source term in the transfer
equation for the Stokes parameters. <BR />Results: We show that the
Stokes parameters have a multipolar expansion that can be written
as I_i(ν,Ω)= sum<SUB>KQ</SUB>T^K_Q(i,Ω)I_Q^K(ν,θ) (K=0,1,2,
-K≤ Q≤ +K) where the I_Q<SUP>K</SUP> are nine cylindrically
symmetrical, irreducible tensors, θ being the inclination of Ω with
respect to the vertical in the atmosphere. The proof is generalized
to frequency-dependent phase matrices. It is applied both to partial
frequency redistribution with angle-averaged scalar frequency
redistribution functions and to complete frequency redistribution
with the Hanle effect in the line core and Rayleigh scattering in the
wings. Non-LTE transfer equations for the I_Q<SUP>K</SUP> and integral
equations for the associated source functions S_Q<SUP>K</SUP> are
established. Formal vectors and matrices constructed with I_Q^K, S_Q^K,
and T_Q<SUP>K</SUP> are introduced in order to present the results in
a compact matrix notation. In particular, a simple factorized form is
proposed for the Hanle phase matrix.
---------------------------------------------------------
Title: Turbulent magnetic field averages for the Zeeman effect .
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
2007MmSAI..78..142F Altcode:
Stokes parameters measured in the Solar atmosphere are in general
time or space averages over a magnetic field probability distribution
function. Here we show how to write the Zeeman propagation matrix in a
reference frame defined with respect to the direction of a mean magnetic
field and how to average over a random magnetic field distribution. We
concentrate on the case of a normal Zeeman triplet but indicate how
to treat general Zeeman patterns. Numerical results are presented
for Gaussian distributions having cylindrical symmetry about a mean
field. Different models of probability distribution functions (PDF),
are compared.
---------------------------------------------------------
Title: Polarized Spectral Line Formation in Turbulent Magnetic Fields:
The Zeeman and Hanle Effects
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
2006ASPC..358..126F Altcode:
We present a short summary of work carried out on the effects of
random magnetic fields with finite correlation length on spectral line
polarization. The magnetic field is modeled by a step-wise Markovian
random process defined by a probability distribution and a correlation
length. Micro- and macro-turbulent limits are recovered when this
length goes to zero and infinity, respectively. For the Zeeman effect,
explicit expressions have been obtained for the mean emergent Stokes
parameters and for their r.m.s. fluctuations. Examples illustrate the
dependence of the mean Zeeman propagation matrix on the magnetic field
distribution, and the dependence of mean Stokes parameters and their
r.m.s. fluctuations on the correlation length of the magnetic field. For
the Hanle effect, explicit expressions have also been obtained for the
mean Stokes parameters. We outline the approach and give an explicit
expression for the mean value of Stokes Q.
---------------------------------------------------------
Title: Stochastic polarized line formation. II. Zeeman line transfer
in a random magnetic field
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
2006A&A...453.1095F Altcode:
Context: .The Zeeman effect produced by a turbulent magnetic field
or a random distribution of flux tubes is usually treated in the
microturbulent or macroturbulent limits where the Zeeman propagation
matrix or the Stokes parameters, respectively, are averaged over
the probability distribution function of the magnetic field when
computing polarized line profiles.<BR /> Aims: .To overcome these
simplifying assumptions we consider the Zeeman effect from a random
magnetic field which has a finite correlation length that can be
varied from zero to infinity and thus made comparable to the photon
mean free-path.<BR /> Methods: .The vector magnetic field is modeled
by a Kubo-Anderson process, a piecewise constant Markov process
characterized by a correlation length and a probability distribution
function for the random values of the magnetic field. The micro and
macro turbulent limits are recovered when the correlation goes to zero
or infinity.<BR /> Results: .An integral equation is constructed for
the mean propagation operator and explicit expressions are obtained
for the mean values and second-order moments of the Stokes parameters
at the surface of a Milne-Eddington type atmosphere. The expression
given by Landi Degl'Innocenti (1994) for the mean Stokes parameters
is recovered. Mean values and rms fluctuations around the mean values
are calculated numerically for a random magnetic field with isotropic
Gaussian fluctuations. The effects of a finite correlation length
are discussed in detail. Various extensions of the Milne-Eddington
and magnetic field model are considered and the corresponding
integral equations for the mean propagation operator are given.<BR
/> Conclusions: .The rms fluctuations of the Stokes parameters are
shown to be very sensitive to the correlation length of the magnetic
field. It is suggested to use them as a diagnostic tool to determine
the scale of unresolved features in the solar atmosphere.
---------------------------------------------------------
Title: The Hanle effect in a random medium
Authors: Frisch, H.
2006A&A...446..403F Altcode:
This paper considers the Hanle effect produced by a turbulent magnetic
field. To overcome the simplified microturbulent treatment whereby
the Hanle phase matrix is locally averaged over some magnetic field
distribution, we consider a turbulent magnetic field with a finite
correlation length. We assume that the magnetic field along each
individual photon path can be represented by a Kubo-Anderson process
(KAP) and study the stationary solution as time goes to infinity. A
KAP is a discontinuous Markov process. The random magnetic field is
characterized by a correlation length and a distribution function
of the magnetic field vector; both can be chosen arbitrarily. The
microturbulent limit is recovered when the correlation length goes to
zero. A non-stochastic integral equation of the Wiener-Hopf type is
obtained for a mean conditional source vector. This integral equation
yields explicit expressions for the mean Stokes parameters, provided
one makes physically realistic approximations, namely neglect the
effect of the magnetic field on Stokes I, keep only the contributions
from I and Q in the source terms for Stokes Q and Stokes U and solve
the integral equation for Q with a two-scattering approximation. The
final expressions involve mean values and correlation functions of
some of the elements of the Hanle phase matrix and show the dependence
on the correlation length of the random magnetic field. The combined
effects of a turbulent velocity field and a turbulent magnetic field
with finite correlation lengths is also studied. The velocity field
is represented by a KAP with the same correlation length as the
magnetic field. Some of the velocity field effects are treated with
an effective medium approximation as in Frisch & Frisch (1976,
MNRAS, 175, 157). Explicit expressions are obtained for the mean Stokes
parameters. They can account for correlations between velocity field
and magnetic field fluctuations.
---------------------------------------------------------
Title: Stochastic polarized line formation. I. Zeeman propagation
matrix in a random magnetic field
Authors: Frisch, H.; Sampoorna, M.; Nagendra, K. N.
2005A&A...442...11F Altcode:
This paper considers the effect of a random magnetic field on Zeeman
line transfer, assuming that the scales of fluctuations of the random
field are much smaller than photon mean free paths associated to
the line formation (micro-turbulent limit). The mean absorption and
anomalous dispersion coefficients are calculated for random fields with
a given mean value, isotropic or anisotropic Gaussian distributions
azimuthally invariant about the direction of the mean field. Following
Domke & Pavlov (1979, Ap&SS, 66, 47), the averaging process
is carried out in a reference frame defined by the direction of the
mean field. The main steps are described in detail. They involve the
writing of the Zeeman matrix in the polarization matrix representation
of the radiation field and a rotation of the line of sight reference
frame. Three types of fluctuations are considered : fluctuations along
the direction of the mean field, fluctuations perpendicular to the
mean field, and isotropic fluctuations. In each case, the averaging
method is described in detail and fairly explicit expressions for the
mean coefficients are established, most of which were given in Dolginov
& Pavlov (1972, Soviet Ast., 16, 450) or Domke & Pavlov (1979,
Ap&SS, 66, 47). They include the effect of a microturbulent velocity
field with zero mean and a Gaussian distribution. A detailed numerical
investigation of the mean coefficients illustrates the two effects
of magnetic field fluctuations: broadening of the σ-components by
fluctuations of the magnetic field intensity, leaving the π-components
unchanged, and averaging over the angular dependence of the π and σ
components. For longitudinal fluctuations only the first effect is at
play. For isotropic and perpendicular fluctuations, angular averaging
can modify the frequency profiles of the mean coefficients quite
drastically with the appearance of an unpolarized central component
in the diagonal absorption coefficient, even when the mean field is in
direction of the line of sight. A detailed comparison of the effects of
the three types of fluctuation coefficients is performed. In general
the magnetic field fluctuations induce a broadening of the absorption
and anomalous dispersion coefficients together with a decrease of their
values. Two different regimes can be distinguished depending on whether
the broadening is larger or smaller than the Zeeman shift by the mean
magnetic field. For isotropic fluctuations, the mean coefficients can
be expressed in terms of generalized Voigt and Faraday-Voigt functions
H<SUP>(n)</SUP> and F<SUP>(n)</SUP> introduced by Dolginov &
Pavlov (1972, Soviet Ast., 16, 450). These functions are related to
the derivatives of the Voigt and Faraday-Voigt functions. A recursion
relation is given in an Appendix for their calculation. A detailed
analysis is carried out of the dependence of the mean coefficients
on the intensity and direction of the mean magnetic field, on its
root mean square fluctuations and on the Landé factor and damping
parameter of the line.
---------------------------------------------------------
Title: An operator perturbation method for polarized line
transfer. VI. Generalized PALI method for Hanle effect with partial
frequency redistribution and collisions
Authors: Fluri, D. M.; Nagendra, K. N.; Frisch, H.
2003A&A...400..303F Altcode:
A generalized iteration method is presented to solve the polarized line
transfer equation for a two-level-atom in an arbitrarily oriented,
weak magnetic field. The polarized redistribution matrix employed
accounts self-consistently for collisions as well as the presence of
a weak magnetic field responsible for the Hanle effect. The proposed
numerical method of solution is based on a Polarized Approximate Lambda
Iteration (PALI) method. A Fourier decomposition of the radiation field
and of the phase matrix with respect to the azimuthal angle reduces
the complexity of the problem. A generalized core-wing technique is
proposed, which permits an efficient implementation of the frequency
domain structure inherent in the polarized redistribution matrix. The
numerical method is tested for its accuracy and efficiency by comparing
with the existing methods.
---------------------------------------------------------
Title: Numerical Methods for Solving the Polarized Line Transfer
Equations with Partial Frequency Redistribution
Authors: Nagendra, K. N.; Frisch, H.; Fluri, D. M.
2003ASPC..307..227N Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Hanle effect with angle-dependent partial redistribution
Authors: Nagendra, K. N.; Frisch, H.; Faurobert, M.
2002A&A...395..305N Altcode:
The polarized line transfer equation for the Hanle effect is solved in
the framework of an exact partial frequency redistribution (PRD) theory
developed by Bommier (1997a,b). In that theory the effect of collisions
on the Hanle effect is considered self-consistently. We follow that
approach in the line transfer computations presented here. The theory
formulated by Bommier clearly recognizes two levels of approximations
for exact PRD, in order to facilitate the solution of the line transfer
equation. The second level employs angle-dependent redistribution
functions, and numerically represents a more difficult problem compared
to the third level, which involves only the use of angle-averaged
frequency redistribution functions. We present a method which can
solve the problem in both the levels of approximation. The method
is based on a perturbative approach to line polarization. Although
computationally expensive, it offers the only practical means of solving
the angle-dependent Hanle PRD problem. We discuss the numerical aspects
of assembling the so called “frequency domain dependent redistribution
matrices”, and also an efficient way of computing the scattering
integral. Some examples are presented to illustrate the interesting
aspects of the Hanle-PRD problem with angle-dependent frequency
redistribution. A comparison of the emergent profiles computed under
angle-averaged and angle-dependent redistribution is carried out, and
the effect of collisions is investigated. We show that it is necessary
to incorporate an angle-dependent redistribution mechanism especially
in the computation of the Stokes U parameter. We demonstrate that the
use of simple frequency domains is good enough in practical applications
of the Hanle PRD theory.
---------------------------------------------------------
Title: Investigation of weak solar magnetic fields. New observational
results for the SrI 460.7 nm linear polarization and radiative
transfer modeling
Authors: Faurobert, M.; Arnaud, J.; Vigneau, J.; Frisch, H.
2001A&A...378..627F Altcode:
Scattering polarization measurements were obtained with THEMIS in July
2000, close to the solar south Pole and to the east Equator and in
a period of maximum solar activity. Using the THEMIS multi-lines
spectro-polarimetric mode (MTR), we observed simultaneously
four spectral domains containing the 460.7 nm Sr i line, several
molecular lines around 515.9 nm and the Na i D<SUB>1</SUB> and Na i
D<SUB>2</SUB> lines. This allows us to scan different altitudes in the
solar atmosphere at the same time and provides us with a large set
of constraints to study the behaviour of the magnetic field. This
paper is devoted to the Sr i line which exhibits quite a strong
linear polarization peak outside active regions. A detailed radiative
transfer modeling is performed in order to interpret the observed
center-to-limb variations of the line intensity and polarization. It
was shown previously (Faurobert-Scholl \cite{Faurobert-Scholl1})
that this line, which is sensitive to the Hanle effect, can be used
as a diagnostic tool for the presence of weak turbulent magnetic
fields in the solar photosphere outside active regions. The line
polarization rates that we measured in July 2000 are 25% lower
than what has been reported previously, for observations near the
minimum, or in the increasing phase, of the activity cycle (Stenflo
et al. \cite{Stenflo1}). They are in agreement with other observations
performed with a different observational set-up in August 2000 (Bommier
& Molodij \cite{Bommier4}). We show that they are consistent with
the presence of a weak turbulent magnetic field with an average strength
between 20 G and 30 G in the upper solar photosphere. This is about
twice the value which was derived from previous observations. This
result raises the possiblity of a long-term variation of the turbulent
photospheric magnetic field with the activity cycle.
---------------------------------------------------------
Title: Scattering Polarization and Hanle Effect: On the Importance
of Angle-Dependent Frequency Redistribution
Authors: Faurobert, M.; Frisch, H.; Nagendra, K. N.
2001ASPC..248..145F Altcode: 2001mfah.conf..145F
No abstract at ADS
---------------------------------------------------------
Title: The Hanle Effect with Angle Dependent Redistribution Functions
Authors: Frisch, H.; Faurobert, M.; Nagendra, K. N.
2001ASPC..236..197F Altcode: 2001aspt.conf..197F
No abstract at ADS
---------------------------------------------------------
Title: An Operator Perturbation Method of Polarized Line Transfer
V. Diagnosis of Solar Weak Magnetic Fields
Authors: Nagendra, K. N.; Frisch, H.; Faurobeet-Scholl, M.; Paletou, F.
2000JApA...21..255N Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Fast Numerical Methods for Polarized Line Radiative Transfer
in the Presence of Hanle Effect
Authors: Faurobert, M.; Frisch, H.; Nagendra, K. N.
1999ASPC..184...28F Altcode:
The Hanle effect provides a diagnostic tool for weak magnetic fields
which do not give rise to a measurable Zeeman effect, such as turbulent
fields or magnetic canopies. The lines which are sensitive to the
Hanle effect are formed under non-LTE conditions, by scattering of
photons. Inversion methods for such diagnostics require to solve the
non-LTE polarized transfer equation for a large number of magnetic
configurations. Fast numerical methods are thus highly required. We
present an Approximate Lambda Iteration method to treat the Hanle effect
for lines formed with complete frequency redistribution. Referred to
as PALI-H, this method is an extension of ALI methods first developed
for non polarized line transfer. The starting point is to recast the
polarized transfer equation into a vectorial integral equation for a
6-component source function. We show that the convergence of the method
is independent of the strength and direction of the magnetic field. The
method is very fast and allows to handle any type of depth-dependent
magnetic field.
---------------------------------------------------------
Title: An operator perturbation method for polarized line transfer IV:
Applications to the Hanle effect with partial frequency redistribution
Authors: Nagendra, K. N.; Paletou, F.; Frisch, H.; Faurobert-Scholl, M.
1999ASSL..243..127N Altcode: 1999sopo.conf..127N
No abstract at ADS
---------------------------------------------------------
Title: Resonance polarization and Hanle effect: The integral equation
formulation and some applications
Authors: Frisch, H.
1999ASSL..243...97F Altcode: 1999sopo.conf...97F
No abstract at ADS
---------------------------------------------------------
Title: The Hanle effect. The density matrix and scattering approaches
to the protect sqrt epsilon -law
Authors: Frisch, H.
1998A&A...338..683F Altcode:
A sqrt epsilon -law was demonstrated by Landi Degl'Innocenti &
Bommier (1994) for resonance polarization in a magnetic atmosphere
where the primary source of photons is of thermal origin (isotropic and
unpolarized). In this paper we propose a generalized form of this law by
dropping the hypothesis on the primary source of photons. We restrict
ourselves to the case of weak magnetic fields (Hanle effect). For
spectral lines formed with complete redistribution, it has been shown
by Landi Degl'Innocenti et al (1990), using the density matrix theory
in its irreducible tensorial operator version, that the Hanle effect
can be reduced to an integral equation of the convolution type for
a six-component source vector. As shown by Faurobert-Scholl (1991),
a similar equation can be obtained by performing an azimuthal Fourier
decomposition of the transfer equation for the Stokes parameters. In the
first part of the paper we recall the main steps of the two methods and
establish the correspondence between the convolution equations that
they provide. In the second part we use these equations to obtain
a generalized sqrt epsilon -law. For the equation coming from the
density matrix formalism, we essentially follow the original proof of
Landi Degl'Innocenti & Bommier (1994). For the equation coming from
the Fourier decomposition, because of a lack of symmetry in operator
describing the action of the magnetic field, we use as intermediate
step the Hopf-Bronstein-Rybicki relation established by Ivanov (1995)
for transport operators which are not self-adjoint.
---------------------------------------------------------
Title: An operator perturbation method for polarized line
transfer. III. Applications to the Hanle effect in 1D media
Authors: Nagendra, K. N.; Frisch, H.; Faurobert-Scholl, M.
1998A&A...332..610N Altcode:
In this paper we present an Approximate Lambda Iteration method to
treat the Hanle effect (resonance scattering in the presence of
a weak magnetic field) for lines formed with complete frequency
redistribution. The Hanle effect is maximum in the line core and
goes to zero in the line wings. Referred to as PALI-H, this method is
an extension to non-axisymmetric radiative transfer problems of the
PALI method presented in Faurobert-Scholl et al. (1997), hereafter
referred to as Paper I. It makes use of a Fourier decomposition of the
radiation field with respect to the azimuthal angle which is somewhat
more general than the decomposition introduced in Faurobert-Scholl
(1991, hereafter referred to as FS91). The starting point of the
method is a vector integral equation for a six-component source vector
representing the non-axisymmetric polarized radiation field. As
in Paper I, the Approximate Lambda operator is a block diagonal
matrix. The convergence rate of the PALI-H method is independent
of the polarization rate and hence of the strength and direction
of the magnetic field. Also this method is more reliable than the
perturbation method used in FS91. The PALI-H method can handle any
type of depth-dependent magnetic field. Here it is used to examine
the dependence of the six-component source vector on the co-latitude,
azimuthal angle and strength of the magnetic field. The dependence of
the surface polarization on the direction of the line-of-sight and on
the magnetic field is illustrated with polarization diagrams showing
Q/I versus U/I at line center. The analysis of the results show that
the full six-dimension problem can be approximated by a two-component
modified resonance polarization problem, producing errors of at most
20% on the surface polarization at line center.
---------------------------------------------------------
Title: An operator perturbation method for polarized line
transfer. I. Non-magnetic regime in 1D media.
Authors: Faurobert-Scholl, M.; Frisch, H.; Nagendra, K. N.
1997A&A...322..896F Altcode:
In this paper we generalize an Approximate Lambda Iteration (ALI)
technique developed for scalar transfer problems to a vectorial transfer
problem for polarized radiation. Scalar ALI techniques are based on a
suitable decomposition of the Lambda operator governing the integral
form of the transfer equation. Lambda operators for scalar transfer
equations are diagonally dominant, offering thus the possibility to
use iterative methods of the Jacobi type where the iteration process
is based on the diagonal of the Lambda operator (Olson et al., 1986,
JQSRT 35, 431). Here we consider resonance polarization, created by
the scattering of an anisotropic radiation field, for spectral lines
formed with complete frequency redistribution in a 1D axisymmetric
medium. The problem can be formulated as an integral equation for a
2-component vector (Rees, 1978PASJ...30..455R) or, as shown by Ivanov
(1995A&A...303..621I), as an integral equation for a (2x2) matrix
source function which involves the same generalized Lambda operator as
the vector integral equation. We find that this equation holds also in
the presence of a weak turbulent magnetic field. The generalized Lambda
operator is a (2x2) matrix operator. The element {11} describes the
propagation of the intensity and is identical to the Lambda operator of
non-polarized problems. The element {22} describes the propagation of
the polarization. The off-diagonal terms weakly couple the intensity and
the polarization. We propose a block Jacobi iterative method and show
that its convergence properties are controlled by the propagator for
the intensity. We also show that convergence can be accelerated by an
Ng acceleration method applied to each element of the source matrix. We
extend to polarized transfer a convergence criterion introduced by
Auer et al. (1994A&A...292..599A) based on the grid truncation
error of the converged solution.
---------------------------------------------------------
Title: Transfert de rayonnement hors-ETL et applications en physique
solaire.
Authors: Faurobert-Scholl, M.; Paletou, F.; Frisch, H.
1996JAF....53...24F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Partial Frequency Redistribution of Polarized Radiation
Authors: Frisch, H.
1996SoPh..164...49F Altcode:
Resonance polarization, which is created by the scattering of an
anisotropic radiation field in regions of zero or weak magnetic
fields, is strongly dependent on the frequency redistribution
taking place during the scatterings. Here we discuss the frequency
redistribution matrix relevant to resonance lines, concentrating on
linear polarization. First we analyze in detail the redistribution
matrix in a zero magnetic field given by the theory of Omont, Smith
and Cooper (1972), revisited by Domke and Hubeny (1988). We explain
that the linear polarization maxima which may appear in the wings
of the Stokes Q profiles of strong resonances lines such as the Ca I
4227 Å line are coherent frequency redistribution effects. Various
approximate forms of the frequency redistribution matrix are also
examined. For resonance polarization in a weak magnetic field, we
suggest a new expression for the redistribution matrix which can be
used at all line frequencies, and is consistent with the condition
that the Hanle effect acts only in the line core.
---------------------------------------------------------
Title: CDF Results on the W Mass and the Search for the Top
Authors: Frisch, H. J.
1995psc..conf...81F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Monte-Carlo simulation of a radiative transfer problem in a
random medium: application to a binary mixture.
Authors: Audic, S.; Frisch, H.
1993JQSRT..50..127A Altcode:
This paper considers monochromatic radiative transfer in a diffusive
three dimensional random binary mixture. The absorption coefficient,
along any line-of-sight is a homogeneous Markoy process, which is
described by a three-dimensional Kubo-Anderson process. The transfer
equation is solved numerically by Monte-Carlo simulations on a massively
parallel computer (a Connection Machine) by attaching one or several
photons to each processor. The implementation of the simulations on
the machine is discussed in detail, in particular the association
between photons and processors and the storage of the data concerning
the photons and the realizations of the statistics.
---------------------------------------------------------
Title: Quelques problèmes de transfert en physique solaire.
Authors: Frisch, H.; Faurobert-Scholl, M.
1991sed..conf..151F Altcode:
(1) Introduction. (2) Formation ETL des raies: (2.1) Intensité
du rayonnement et équation de transfert. (2.2) Approximation
de diffusion. (2.3) Equation de transfert ETL pour les raies. (3)
Formation non-ETL des raies: (3.1) Fonction source d'un atome à deux
niveaux. (3.2) Fonction de redistribution. (3.3) Equation de transfert
non-ETL. (3.4) Analyse asymptotique. (3.5) Transfert non-ETL dans
une couche plane. (3.6) Probabilité d'échappement. (3.7) Méthodes
numériques en transfert non-ETL. (3.8) Construction de modèles
d'atmosphères. (4) Transfert de rayonnement polarisé. (4.1)
Les paramètres de Stokes. (4.2) Mécanismes de polarisation des
raies spectrales. (4.3) Equation de transfert d'un rayonnement
polarisé. (4.4) Effet Hanle. (4.5) Effet Zeeman.
---------------------------------------------------------
Title: An exact analytical solution of a radiative transfer problem
in a binary mixture.
Authors: Frisch, H.; Pomraning, G. C.; Zweifel, P. F.
1990JQSRT..43..271F Altcode:
The authors give an exact analytical solution of a statistical
radiative transfer problem. This problem consists of time-independent,
non-scattering transport in a binary statistical mixture. The mixing
statistics are taken as homogeneous. The chord-length distribution
of each constituent is assumed to be representable as a Laplace
transform. Markov statistics are a special (degenerate) case of
the class of statistics the authors are able to treat. Two different
techniques, a singular eigenfunction analysis and an integral equation
method, are applied to the problem.
---------------------------------------------------------
Title: Asymptotic analysis of resonance polarization and escape
probability approximations
Authors: Faurobert-Scholl, M.; Frisch, H.
1989A&A...219..338F Altcode:
Polarized transfer asymptotic and first order escape probability methods
developed for the nonpolarized case are generalized to include linear
polarization produced by the scattering of anisotropic radiation in
the absence of magnetic fields. The analyses are based on a coupled
integral equation for two-angle-dependent source functions. Some general
properties, such as the order of magnitude of the surface polarization
and approximations for the source functions, are deduced. The escape
probability approximations are compared with exact solutions and found
to be more accurate than first order perturbation techniques for lines
of moderate optical thickness in solar isothermal prominences.
---------------------------------------------------------
Title: A Model for the Penetration of Lyman Alpha in the Solar
Chromosphere
Authors: Faurobert, M.; Frisch, H.; Skumanich, A.
1988ApJ...328..856F Altcode:
A multilevel calculation of the hydrogen spectrum by Skumanich and
Lites, followed by a two-level representation of each transition, shows
that all the solar Lyα photons are created in an optically thick layer
in the high chromosphere above τ<SUB>0</SUB> ≈ 10<SUP>2</SUP>. The
authors give a simplified model that demonstrates the penetration of
Lyα into the lower chromosphere below the creation region, i.e., for
τ<SUB>0</SUB> > 10<SUP>2</SUP>. A second-order escape probability
approximation yields a simple analytical expression which accurately
reproduces the behavior of the Lyα source function for 10<SUP>2</SUP>
⪉ τ<SUB>0</SUB> ⪉ 5×10<SUP>6</SUP> provided the destruction
probability, ɛ is set close to 10<SUP>-6</SUP>.
---------------------------------------------------------
Title: A Cauchy integral equation method for analytic solutions of
half-space convolution equations.
Authors: Frisch, H.
1988JQSRT..39..149F Altcode:
This paper is devoted to a method of Cauchy integral equation for
the solution of half-space convolution equations. It was introduced
by Frisch and Frisch to solve Wiener-Hopf integral equations with
algebraically decreasing kernels, arising in non-coherent transfer with
complete frequency redistribution. The author shows here that coherent
transfer may also be treated by the Cauchy integral method. Various
examples chosen among standard problems are used to illustrate the
method.
---------------------------------------------------------
Title: Radiation in moving gaseous media : eighteenth Advanced Course
of the Swiss Society of Astrophysics and Astronomy
Authors: Kudritzki, R. P.; Yorke, H. W.; Frisch, Helene
1988rmgm.book.....K Altcode: 1988STIA...8950499K
The propagation of EM radiation in gaseous media is characterized
in chapters based on lectures presented at Leysin, Switzerland, on
March 6-12, 1988. The emphases are on the fundamental astrophysics
and the experimental and observational methods employed. Topics
addressed include hot-star atmosphere models and their application
to observations, radiation in diffuse matter (dust properties, gas
microphysics, static nebula models, radiation hydrodynamics, and the
formation and evolution of H II regions), and radiative transfer
with frequency redistribution (asymptotic methods, scaling laws,
and approximate solutions).
---------------------------------------------------------
Title: Radiative Transfer with Frequency Redistribution - Asymptotic
methods scaling laws and approximate solutions
Authors: Frisch, Hélène
1988rmgm.conf..339F Altcode: 1988SAAS...18..339F
General Introduction Asymptotic methods. Some general ideas Outline
of the lectures Diffusive and Non-Diffusive Large Scale Behaviour
Introduction Asymptotic analysis of the integral equation for the source
function Specific intensity in the interior Transfer with Partial
Frequency Redistribution Introduction The ingredients of a partial
redistribution problem The redistribution function The Asymptotic of
Partial Redistribution Introduction R<SUB>I</SUB> and R<SUB>III</SUB>
partial redistribution R<SUB>IV</SUB> partial redistribution Coherent
scattering and R<SUB>II</SUB> partial redistribution Hints for
the calculation of subordinate and resonance lines Boundary Layers
Introduction Complete redistribution Diffusive type processes Transport
of continuous radiation in stars Scaling Laws for Spectral Line
Formation. A Summary Introduction Complete redistribution R<SUB>II</SUB>
redistribution and coherent scattering Time-dependent transfer Escape
Probabilties for Static and Moving Media Introduction Escape probability
approximation procedures in a static medium Line formation in moving
media Numerical Methods Introduction Iterative methods with exact
operators Operator perturbation methods Preconditioning; necessity
and technique Analytic Solutions of Half-Space Transport Equations
Introduction A Cauchy integral equation method of solution Utilizations
of exact analytical solutions Monochromatic scattering The H-function
in the Wiener-Hopf type methods References
---------------------------------------------------------
Title: The Lyman α line in the solar chromosphere: penetrative
model andapproximations.
Authors: Faurobert, M.; Frisch, H.; Skumanich, A.
1987PAICz..66..205F Altcode: 1987eram....1..205F
The authors present a model for the formation of Lyman α in the
chromosphere below the creation region. The hydrogen atom is treated
as a two-level atom and the chromosphere as a semi-infinite medium
free of primary sources and illuminated by an isotropic and frequency
independent radiation field at r<SUB>0</SUB> ≅ 10<SUP>2</SUP>.
---------------------------------------------------------
Title: First results from a 1.1-m-diameter superconducting monopole
detector
Authors: Incandela, J.; Frisch, H.; Somalwar, S.; Kuchnir, M.;
Gustafson, H. R.
1986PhRvD..34.2637I Altcode:
We present the design and performance of a superconducting induction
magnetic-monopole detector with 1.1-m-diameter gradiometer loops. The
detector demonstrates that gradiometers can be overlapped with no
mutual inductance to yield high redundancy without increasing shield
volume. One of two detector units was sensitive to the passage of
monopoles through two overlapped gradiometers with 98% coincidence
efficiency for 161 hours. The unit has a coincident sensitive area
averaged over 4π sr of 4400 cm<SUP>2</SUP>. No candidate events were
observed, setting an upper limit on the flux of cosmic-ray magnetic
monopoles of f<~7.1×10<SUP>-11</SUP> cm<SUP>-2</SUP> sr<SUP>-1</SUP>
sec<SUP>-1</SUP> (90% C.L.). The detector was operated in ambient
magnetic fields of ~5-125 mG.
---------------------------------------------------------
Title: The status of searches for magnetic monopoles
Authors: Frisch, H. J.
1986NYASA.461..652F Altcode: 1986awph.conf..652F
The fundamental principles, apparatus, procedures, and results of
ongoing terrestrial searches for the superheavy magnetic monopoles
(MMs) predicted by GUTs are reviewed. Approaches examined include
methods based on the MM magnetic charge (Faraday induction experiments
and the Parker bound from Galactic magnetic fields), MM ionization
properties (MM velocity estimates; detection in scintillation and
gas detectors), and the ability of MMs to catalyze nucleon decay
(proton-decay experiments and cosmic-ray-shower hadronic cross section
measurements). Diagrams, drawings, graphs, and tables of numerical
data are provided, and plans for future MM detectors are indicated.
---------------------------------------------------------
Title: Line transfer with complete frequency redistribution in an
absorbing medium - Scaling laws and approximation
Authors: Faurobert, M.; Frisch, H.
1985A&A...149..372F Altcode:
This paper discusses the influence of a continuous absorption
produced by dust grains or photoionization on subordinate or weak
resonance lines. The lines are being formed with complete Doppler or
Voigt frequency redistribution in a one dimensional slab of finite
thickness. An asymptotic analysis in the limit of small β (ratio
of continuum to line opacity coefficient) shows that the large scale
behaviour of the radiation field is described by a singular integral
equation identical to that obtained by Frisch and Frisch (1977) for
collisional destruction, but with an exponentially decreasing kernel
in the case of the Voigt profile. Asymptotic scaling laws for the mean
path length, the mean number of scatterings and the fraction of created
photons which escapes the medium are given in the limits of weak and
strong absorption. A first order escape probability method is used to
evaluate net radiative brackets and line cooling rates, taking into
account a possible emission by the continuum in the frequency domain
of the line. Finally, a definition of the mean number of scatterings
properly incorporating this emission term is proposed.
---------------------------------------------------------
Title: Asymptotic properties of complete and partial frequency
redistribution.
Authors: Frisch, H.
1985ASIC..152...87F Altcode: 1985pssl.proc...87F
Radiative transfer problems with frequency redistribution may be
investigated by asymptotic methods when the mean number of scatterings
undergone by photons is very large. These methods provide scaling laws
for characteristic parameters of the line radiation field. These methods
also provide asymptotic transfer equations which describe the large
scale behaviour of the radiation field away from boundaries. Complete
redistribution and the four standard types of partial redistribution
is discussed. Implications for numerical calculations are briefly
considered.
---------------------------------------------------------
Title: Pannel discussion on partial redistribution.
Authors: Freire Ferrero, R.; Frisch, H.; Linsky, J.; Oxenius, J.;
Simonneau, E.
1985ASIC..152..143F Altcode: 1985pssl.proc..143F
No abstract at ADS
---------------------------------------------------------
Title: Flux limit on cosmic-ray magnetic monopoles from a large area
induction detector
Authors: Incandela, J.; Campbell, M.; Frisch, H.; Somalwar, S.;
Kuchnir, M.; Gustafson, H. R.
1984PhRvL..53.2067I Altcode:
The design and performance of a superconducting induction detector
with two 60-cm-diameter superconducting loops is presented. During
eight months of data taking, no candidate events were observed,
and an upper limit on the flux of cosmic-ray magnetic monopoles of
about 6.7 x 10 to the -12th/sq cm sr sec (90-percent confidence level)
is set. The detector demonstrates the possibility of operating large
induction detectors in ambient magnetic fields greater than 1 mG.
---------------------------------------------------------
Title: Boundary layer conditions for the transport of radiation
in stars
Authors: Frisch, H.; Faurobert, M.
1984A&A...140...57F Altcode:
An expansion technique used by Larsen et al. (1983) for
describing coherent scattering is applied to characterizing an
outer thermal boundary condition for radiation transport in stellar
interiors. Modifications are introduced to cover conditions of non-gray
radiative equilibrium, which is analyzed asymptotically. An expansion
parameter is defined in terms of coupled transfer and energy equations
and carried out to first order to obtain a ratio of the photon free
path to the stellar characteristic dimension. The ratio provides a
scale for the space variable with which a singular perturbation problem
is solved for interior and boundary conditions, the latter being in
the stellar atmosphere and the sum of the interior solution and the
boundary layer correction. A Robin boundary condition results which
is only 5 percent higher in temperature than the interior in the case
of a gray opacity coefficient.
---------------------------------------------------------
Title: Mean Escape Probabilities and Mean Numbers of Scatterings
for Resonance Lines
Authors: Frisch, H.
1984mrt..book...25F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: First results from the Chicago-Fermilab-Michigan cosmic ray
magnetic monopole detector.
Authors: Incandela, J. R.; Campbell, M.; Frisch, H.; Somalwar, S.;
Kuchnir, M.; Gustafson, H. R.
1984mono.conf..461I Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Scaling laws for the scattering of resonance line photons.
Authors: Frisch, H.
1984PhST....7..110F Altcode: 1984PhyS....7..110F
Resonance lines of ions with a large Z are broadened essentially by
natural damping, and therefore photons with frequencies larger than a
few Doppler widths are scattered almost coherently. This "coherent"
scattering of resonance-line photons can be described by a space
and frequency diffusion process when the mean number of scatterings
undergone by the photons is sufficiently large.
---------------------------------------------------------
Title: Mean escape probabilities and mean numbers of scatterings
for resonance lines.
Authors: Frisch, H.
1984mrt..book...65F Altcode: 1984mrt..conf...65F
A mean escape-probability approximation for resonance lines, which
encompasses both the effectively thin and the effectively thick
limits, is described. Global conservation of photons and the large
scale diffusive behavior of the radiation field are reasonably well
preserved in this approximation. This approximation is tested on a
two-level atom by comparison with accurate numerical results.
---------------------------------------------------------
Title: Dust-driven winds. I - A two-fluid model and its numerical
solution
Authors: Berruyer, N.; Frisch, H.
1983A&A...126..269B Altcode:
A model of dust-driven wind relevant to red giant stars is investigated,
in which the usual hypothesis of 'momentum coupling' (amounting to
neglect of grain particle mass) is relaxed. When the momentum coupling
approximation is abandoned, the sonic point is shifted outwards, and the
gas and grain expansion velocities are reduced. In the supersonic part
of the wind the diminution is of the order of 30 percent, but it may
reach several orders of magnitude below the sonic point. An asymptotic
analysis of the flow at the base of the wind shows the existence of
a boundary layer where the grains suffer a very strong acceleration,
the gas velocity staying almost constant. The coupling between the
grains and the gas is maximum just outside the boundary layer, and
decreases gradually outwards. Beyond a thousand inner envelope radii
the grains and the gas are fully uncoupled. The coupling is still very
strong when the velocities have saturated the almost constant values.
---------------------------------------------------------
Title: Escape probabilities, mean number of scatterings and net
radiative bracket for resonance lines
Authors: Frisch, H.
1982A&A...114..119F Altcode:
An examination of the multiple scattering of resonance-line photons
in nonconservative media, where the photons have a small probability
of destruction at each scattering, yields an approximation for the
mean number of scatterings on the basis of scaling arguments which
takes into account both the destruction of photons and escape through
boundaries. The approximation is used to show that the fraction of
the emitted energy escaping from the medium, known as the mean escape
probability, is nearly independent of the value of the destruction
probability. Analytical solutions which are valid deep within the
medium, and accurate numerical solutions of the transfer problem,
are used to check the validity of the stated results and examine the
errors made when scaling laws for the mean escape probability are
transformed into depth variation scaling laws.
---------------------------------------------------------
Title: A method of Cauchy integral equation for noncoherent tranfer
in half-space.
Authors: Frisch, H.; Frisch, U.
1982JQSRT..28..361F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Non-LTE transfer with complete redistribution. Scaling laws
for a slab.
Authors: Frisch, H.
1982JQSRT..28..377F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Hydrogen line spectrum in quasars. I - Approximation procedures
for line transfer versus an exact treatment
Authors: Collin-Souffrin, S.; Delache, Ph.; Frisch, H.; Dumont, S.
1981A&A...104..264C Altcode:
Approximation procedures frequently used in handling self-absorption
effects in the hydrogen emission lines of quasars are discussed and
compared with an exact numerical treatment of line transfer. The model
here is a finite slab with prescribed density and temperature. It
is noted that if a medium has finite thickness and is such that
subordinate lines are not thermalized, then a semi-infinite
'local escape probability,' which implicitly assumes that photons
emerge from only one surface of the slab, will overestimate the line
fluxes. In this way, the intensity ratio H-alpha/H-beta can be greatly
underestimated. A modified form of the 'local escape probability'
is proposed which allows for the possibility of photons escaping from
both sides of the medium. With this probability, it becomes possible
to obtain much more accurate line ratios and fluxes. It is also found
that natural broadening effects (representable by a Voigt profile)
may be important in subordinate lines.
---------------------------------------------------------
Title: Diffusion approximations for the scattering of resonance-line
photons: interior and boundary layer solutions.
Authors: Frisch, H.; Bardos, C.
1981JQSRT..26..119F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Broadening of non-LTE lines by a turbulent velocity field
with a finite correlation length
Authors: Froeschle, Ch.; Frisch, H.
1980A&A....91..202F Altcode:
Profiles of non-LTE lines broadened by a turbulent velocity field
with a finite correlation length are computed by the 'effective source
function' technique. This method can reformulate stochastic transfer
as a standard non-LTE problem with an effective escape probability
determined by averaging all realizations of velocity fields. Effective
source functions and mean emergent profiles were calculated for a
two-level atom with two choices of a thermal source, and choices between
the Doppler and Voigt line profiles. It is concluded from correlations
between the macroturbulent limit, the thermalization length, and
variations of emergent profiles in isothermal and chromospheric
atmospheres, that a micro-macroturbulent model cannot reproduce a
turbulent velocity field with a finite correlation length.
---------------------------------------------------------
Title: Scaling laws for resonance line photons in an absorbing medium
Authors: Frisch, H.
1980A&A....87..357F Altcode:
Resonance line scattering in the presence of a source of continuous
absorption is studied for very small values of the ratio of the
continuous to line opacity, beta. Scaling laws for the thermalization
length, the thermalization frequency, the mean number of scatterings
and the mean path length are extracted from an asymptotic analysis
of the equation of transfer in the limit as beta approaches 0. An
interpretation is given for asymptotic scaling laws inferred from
numerical data by Hummer and Kunasz (1978) and Bonilha et al. (1979).
---------------------------------------------------------
Title: Non-LTE transfer. V - The asymptotics of partial redistribution
Authors: Frisch, H.
1980A&A....83..166F Altcode:
The large-scale behavior of noncoherent radiative transfer with
partial frequency redistribution is examined. Scaling laws for four
basic scattering processes are extracted from an asymptotic analysis
of the integral equation for the source function in the limit, epsilon
approaches zero (where epsilon is the probability of photon destruction)
to describe the dependence of characteristic lengths and frequencies on
epsilon. It is shown that partial frequency redistribution simplifies
drastically for small epsilon and angular redistribution is irrelevant
in all cases. For all scattering processes the source function,
after the rescaling of optical depths and frequencies, depends on
fewer variables than the original source functions. The main results
are discussed with reference to implications for numerical methods
currently used in the astrophysical literature.
---------------------------------------------------------
Title: Renormalization-group approach to noncoherent radiative
transfer
Authors: Bell, Thomas L.; Frisch, U.; Frisch, H.
1978PhRvA..17.1049B Altcode:
In noncoherent transfer, a photon undergoes multiple scattering
with frequency changes, the frequency profile φ (0<=φ<=Λ)
after each scattering is prescribed, the mean free path varies like
φ<SUP>-1</SUP>, and there is a small probability of destruction ɛ. In
contrast with the coherent (monochromatic) case, diffusive behavior is
not obtained as ɛ-->0. The scaling law of the intensity of radiation
can be obtained with a technique suggested by the renormalization-group
approach to critical phenomena. The equation of transfer for "core"
photons (say, Λ>=φ>12Λ) is solved in terms of "wing" photons
(Λ2>=φ>0). The solution is substituted wherever core photons
appear in the equation for the wing photons. A closed equation for
wing photons is thus obtained. After rescaling of the variables (wave
number and φ) it resembles the original equation (φ again runs from
0 to Λ) but has a nonlocal scattering operator. The procedure is
iterated and the successive equations are found to approach a fixed
form with suitable choice of the rescaling factors. This choice fixes
the scaling law. It depends only on the asymptotic behavior of the
profile at large frequencies. Known results for the dependence of the
"thermalization length" on ɛ are recovered.
---------------------------------------------------------
Title: Rapport d'activité de l'A.D.I.O.N. par le Secrétaire
Général et rapport financier. Report 1975 and 1976.
Authors: Delache, P.; Schatzman, E.; Frisch, H.
1978BONic..13...33D Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Non-LTE transfer - III. Asymptotic expansion for small
epsilon .
Authors: Frisch, U.; Frisch, H.
1977MNRAS.181..273F Altcode:
Radiative transfer with complete frequency redistribution in a
one-dimensional full- or half-space with no incoming radiation
is analyzed in the limit of small epsilon. It is shown that an
asymptotic expansion can be performed in the case of complete frequency
redistribution. The coherent-scattering problem is also discussed for
purposes of comparison. An asymptotic expansion for specific intensity
is derived from an asymptotic expansion for the source function.
---------------------------------------------------------
Title: Non-LTE transfer - IV. A rapidly convergent iterative method
for the Wiener-Hopf integral equations.
Authors: Frisch, H.; Froeschle, C.
1977MNRAS.181..281F Altcode:
It is shown that a simple approximation previously derived for the
source function in the isothermal case of non-LTE line transfer with
complete frequency redistribution can be extended into a rapidly
convergent iterative scheme for solving Wiener-Hopf integral
equations. The convergence of the method and its numerization
are discussed, and the iterative scheme is used for the singular
integral equation of the interior asymptotic expansion as well as the
homogeneous Wiener-Hopf equation for the boundary layer. Analogs for
these equations based on the approximation for the source function
are presented. Consideration is given to the extent to which the
leading terms of the asymptotic expansions arising when epsilon tends
to zero may be employed in practice to determine the source function
for finite epsilon.
---------------------------------------------------------
Title: Applications of Fourier analysis to broadening of stellar
line profiles. V: Effects of finite sized eddies on solar lines.
Authors: Smith, M. A.; Frisch, H.
1976SoPh...47..461S Altcode:
Turbulence dominated by eddies of a finite size produces effects on
a line profile which are similar to both macro- and micro-turbulence
but which are at the same time neither. It is suggested that one of
these effects in the Fourier transform domain, namely the narrowing
of the first natural sidelobe relative to the width of the main lobe,
can be used as an indicator of the dominance of finite-sized eddies
(`mesoturbulence'). An examination of some existing solar data shows
that finitesized eddy models fit the observed sidelobe widths better
than do models computed with any reasonable combination of micro-
and macro-turbulent broadenings (Paper III).
---------------------------------------------------------
Title: Non-LTE transfer-11. Two-level atoms with stochastic velocity
field
Authors: Frisch, H.; Frisch, U.
1976MNRAS.175..157F Altcode:
Following previous work on LTE stochastic transfer (Auvergne et aL;
sFrisch), transfer with incoherent scattering is considered for
two-level satoms in the presence of turbulent velocity fields with
finite seddy-size. Assuming that the velocity along each individual
photon path smay be represented by a Markov Process in time, we
obtain a snon-stochastic equation of transfer for the `mean conditional
sintensity', from which the mean (observable) intensity may be recovered
sby integration over the velocity distribution. An integral equation
of sthe Wiener-Hopf type is obtained for the `mean conditional source
sfunction' from which it is shown by techniques introduced in Paper I
s(Frisch & Frisch) that the rms surface source function assumes
the susual value EB for uniform thermal source B. An `effective
kernel and ssource function' approximation is introduced by which a
standard stransfer problem is recovered and worked out explicitly in
a special scase. It is shown that finite eddy-size effects can change
the effective ssource function and the emergent profile by a factor
z or more.
---------------------------------------------------------
Title: LTE and non-LTE formation with turbulent velocity fields
Authors: Frisch, H.; Frisch, U.
1976pmas.conf..113F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: On the inverse problem in statistical mechanics
Authors: Frisch, H. L.; Fesciyan, S.
1976GReGr...7...83F Altcode:
We review briefly the status of some inverse problems in classical
equilibrium statistical mechanics.
---------------------------------------------------------
Title: Non-LTE transfer. V C revisited
Authors: Frisch, U.; Frisch, H.
1975MNRAS.173..167F Altcode:
Assuming a semi-infinite atmosphere, a two-level atom and complete
frequency redistribution, we give, in the isothermal case, a new
derivation of the surface value of the source function based only
on the integral equation for the source function. This derivation
has a straightforward extension to the case where a uniform velocity
gradient is included, to the time-dependent case (thermal source B
switched on at time t = o) and to the determination of the mean number
of scatterings undergone by an escaping photon (with Ambartsumian's
definition). Our derivation suggests also a simple approximate
differential equation for the complete source function = /2 B/ r where
P = +(i- )K2(r) and K2(r) is the direct escape probability for outwards
emitted photons. This approximation is tested both for isothermal and
exponential atmosphere. As long as the scale of B is large compared to
the photon mean free-path at the centre of the line, our approximation
reproduces all the qualitative features and is usually slightly in
excess of the exact solution. The approximation is easily extended to
non-uniform E and multilevel atoms.
---------------------------------------------------------
Title: Finite eddy-size effects on centre-to-limb variations; an
alternative to anisotropic microturbulence.
Authors: Frisch, H.
1975A&A....40..267F Altcode:
An attempt is presented to explain the center-to-limb increase in
width of solar lines on the basis of the theory of line formation in a
turbulent medium where finite eddy-size is taken into account (Auvergne
et al., 1973). Hydrodynamic velocities along the line of sight are
represented by a step-wise constant stochastic process (Kubo-Anderson
Process), with Gaussian isotropic velocity distribution and an arbitrary
variation of the eddy-size with the continuum optical depth. For the
simplest case of constant geometrical eddy-size, the profiles are found
to be wider at the limb than at the center; this is because the optical
size of the eddies decreases towards the limb, bringing us closer to
the microturbulent limit. An application to the forbidden Mg I 4571 A
line shows that this effect accounts for much of the observed widening,
without recourse to ad-hoc assumptions such as depth variation of the
microturbulent velocity or anisotropic microturbulence.
---------------------------------------------------------
Title: Spectral Line Formation in a Tur- bulent Atmosphere
Authors: Auvergne, M.; Frisch, H.; Frisch, U.; Froeschle, Ch.;
Pouquet, A.
1973A&A....29...93A Altcode:
. In order to bridge the gap between the usual microturbulent and
macroturbulent approximations, we study the formation of spectral lines
in a turbulent medium in which the eddies have a finite scale. The
variation of the velocity along the line of sight is represented by a
Kubo-Anderson process for which the probability distribution and the
correlation length, or its inverse the eddy density n, can be adjusted
arbitrarily. Exact analytical expressions are obtained for the mean
line profile, its statistical dispersion, and also for the mean curve
of growth. The macro- and microturbulent approximations are recovered
respectively for n =0 and n = . It is found that in the far wings the
mean profile becomes independent of the eddy density. It is shown that
the position of the plateau of the curve of growth depends both on the
eddy density and on the r.m.s. turbulent velocity a unique determination
of the latter is therefore not possible. Key words: spectral line
formation - turbulence - stochastic processes - radiative transfer
---------------------------------------------------------
Title: Coupling between Thermal Conduction and Radiative Transfer
in a Moving Atmosphere
Authors: Frisch, H.
1973A&A....27..223F Altcode:
Summary. A singular perturbation expansion method commonly used in
boundary layer analysis is applied to the study of the coupling between
thermal conduction and radiative transfer in a moving atmosphere. The
expansion parameter is the conduction coefficient assumed to be small
in suitable dimensionless units. The model consists of a plane slab of
finite thickness heated by thermal conduction and loosing energy through
emission of radiation. Boundary temperatures, incoming intensities
and matter flux are given. In order to bring out the essential ideas
the asymptotic expansion is performed on a linearized version of the
equations. This restriction is however not essential. Conditions under
which the equations may be linearized are discussed. It is shown that
thermal conduction is essentially limited to a boundary layer near the
hot end. A separate equation is obtained for the exterior region which
is then used to find the conditions under which convection dominates
over radiative transfer. Matched interior and exterior asymptotic
expansions are give in special cases. Key words: radiative transfer -
thermal conduction - chromosphere - singular perturbation expansion
---------------------------------------------------------
Title: The Solar Chromosphere and Its Transition to the Corona
Authors: Frisch, H.
1972SSRv...13..455F Altcode:
Our present knowledge on the average physical properties of the
chromosphere and of the transition region between chromosphere and
corona is reviewed. It is recalled that shock wave dissipation is
responsible for the high temperatures observed in the chromosphere and
corona and that, due to the non-linear character of the dissipation
mechanism, no satisfactory explanation of the structure of the outer
solar layers has yet been given. In this paper, the main emphasis
is on the observations and their interpretation. Evidence for the
non-spherically symmetric structure of the atmosphere is given;
the validity of interpreting the observations with the help of
a fictitious spherically symmetric atmosphere is discussed. The
chromosphere and the transition region are studied separately: for
each region, the energy balance is considered and recent homogeneous
models derived from ultra-violet, infrared and radio observations are
discussed. It is stressed that although in the chromosphere, a study
of the radiative losses may lead to the determination, as function of
height, of the amount of mechanical energy dissipated as function of
height, a more detailed analysis of the velocity field is necessary
to find the periods and the wavelengths of the waves responsible for
the heating. The methods used for wave detection and some results
are presented. Observational and theoretical evidence is given for
the non-validity of the assumption of hydrostatic equilibrium which
is commonly used in modeling the transition region. We conclude that
a better understanding of the heating mechanism will come through
a higher spatial resolution (less than 0.2″) and more accurate
absolute measurements, rather than from sophisticated hydrodynamical
calculations.
---------------------------------------------------------
Title: Ultraviolet effects on the chemical composition and optical
properties of interstellar grains.
Authors: Greenberg, J. M.; Yencha, A. J.; Corbett, J. W.; Frisch, H. L.
1972saim.conf..425G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Non-linear Coupling between Thermal Conduction and Radiative
Transfer
Authors: Frisch, H.
1971A&A....13..359F Altcode:
The problem of coupled thermal conduction and radiative transfer is
solved numerically for a plane slab, of finite thickness, heated by
thermal conduction, the temperatures at the boundaries and the radiation
entering the slab being given. The absorption coefficient is taken of
the form T , where T is the temperature and n a positive number. An
iterative method is used to solve this non-linear differential
problem. Th the optically thick case a simple physical interpretation
of the solution can be given in terms of a region of pure radiative
equilibrium and transition regions where absorption (but not emission)
of radiative energy is negligible. Key words: radiative transfer -
thermal conduction - solar chromosphere.
---------------------------------------------------------
Title: Growth, Distribution, and Chemical Composition of Interstellar
Dust.
Authors: Greenberg, J. M.; Yencha, A. J.; Corbett, J.; Frisch, H. L.
1971BAAS....3Q.250G Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Coupling between Radiative Transfer and Thermal Conduction
in the Chromosphere
Authors: Frisch, H.
1970A&A.....9..269F Altcode:
The influence of the transfer of radiative energy on the temperature
structure of a plane slab of finite thickness heated by thermal
conduction is studied. The temperatures at the boundaries and
the radiation entering the slab are given. In some cases, constant
absorption coefficient per cm and coefficient of thermal conductivity
proportional to the third power of the temperature, the problem
can be solved analytically. When the absorption coefficient goes
to zero or infinity the temperature distribution in the slab becomes
asymptotically identical to that of a slab heated by thermal conduction
only. In intermediate cases the temperature inside the slab may become
greatly inferior to that of the boundaries with very rapid variations
in the vicinity of those boundaries. A generalization of the results
to the case of a non-constant absorption coefficient is outlined.
---------------------------------------------------------
Title: Couplage du transfert radiatif et de la conduction thermique
dans la chromosphère solaire.
Authors: Frisch, H.
1970CRASB.270..918F Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Contribution à l'étude de la température du surface du
soleil et de la remontée chomosphérique de température Title:
Contribution à l'étude de la température du surface du soleil et
de la remontée chomosphérique de température
---------------------------------------------------------
Title: Contribution
to the study of solar surface temperature and chomospheric temperature
rise;
Authors: Frisch, Hélène
1966PhDT........52F Altcode:
No abstract at ADS
