Author name code: hoyng ADS astronomy entries on 2022-09-14 author:"Hoyng, Peter" ------------------------------------------------------------------------ Title: Mode analysis of numerical geodynamo models Authors: Schrinner, M.; Schmitt, D.; Hoyng, P. Bibcode: 2011PEPI..188..185S Altcode: 2011arXiv1101.3022S It has been suggested in Hoyng (2009) that dynamo action can be analysed by expansion of the magnetic field into dynamo modes and statistical evaluation of the mode coefficients. We here validate this method by analysing a numerical geodynamo model and comparing the numerically derived mean mode coefficients with the theoretical predictions. The model belongs to the class of kinematically stable dynamos with a dominating axisymmetric, dipolar and non-periodic fundamental dynamo mode. Our present study supports that contributions from higher order modes to the magnetic field result from the deformation of the fundamental mode by the turbulent flow. The analysis requires a number of steps: the computation of the so-called dynamo coefficients, the derivation of the temporally and azimuthally averaged dynamo eigenmodes and the decomposition of the magnetic field of the numerical geodynamo model into the eigenmodes. For the determination of the theoretical mode excitation levels the turbulent velocity field needs to be projected on the dynamo eigenmodes. We compare the theoretically and numerically derived mean mode coefficients and find reasonably good agreement for most of the modes. Some deviation might be attributable to the approximation involved in the theory. Since the dynamo eigenmodes are not self-adjoint, a spectral interpretation of the eigenmodes is not possible. Title: An efficient method for computing the eigenfunctions of the dynamo equation Authors: Schrinner, M.; Schmitt, D.; Jiang, J.; Hoyng, P. Bibcode: 2010A&A...519A..80S Altcode: 2009arXiv0911.3279S
Aims: We present an elegant method of determining the eigensolutions of the induction and dynamo equations in a fluid embedded in a vacuum.
Methods: The magnetic field is expanded in a complete set of functions. The new method is based on the biorthogonality of the adjoint electric current and the vector potential with an inner product defined by a volume integral over the fluid domain. The advantage of this method is that the velocity and the dynamo coefficients of the induction and the dynamo equation do not have to be differentiated and thus even numerically determined tabulated values of the coefficients produce reasonable results.
Results: We provide test calculations and compare with published results obtained by the classical treatment based on the biorthogonality of the magnetic field and its adjoint. We especially consider dynamos with mean-field coefficients determined from direct numerical simulations of the geodynamo and compare with initial value calculations and the full MHD simulations. Title: Saturation and time dependence of geodynamo models Authors: Schrinner, M.; Schmitt, D.; Cameron, R.; Hoyng, P. Bibcode: 2010GeoJI.182..675S Altcode: 2009arXiv0909.2181S In this study we address the question under which conditions a saturated velocity field stemming from geodynamo simulations leads to an exponential growth of the magnetic field in a corresponding kinematic calculation. We perform global self-consistent geodynamo simulations and calculate the evolution of a kinematically advanced tracer field. The self-consistent velocity field enters the induction equation in each time step, but the tracer field does not contribute to the Lorentz force. This experiment has been performed by Cattaneo and Tobias and is closely related to the test field method by Schrinner et al. We find two dynamo regimes in which the tracer field either grows exponentially or approaches a state aligned with the actual self-consistent magnetic field after an initial transition period. Both regimes can be distinguished by the Rossby number and coincide with the dipolar and multipolar dynamo regimes identified by Christensen and Aubert. Dipolar dynamos with low Rossby number are kinematically stable whereas the tracer field grows exponentially in the multipolar dynamo regime. This difference in the saturation process for dynamos in both regimes comes along with differences in their time variability. Within our sample of 20 models, solely kinematically unstable dynamos show dipole reversals and large excursions. The complicated time behaviour of these dynamos presumably relates to the alternating growth of several competing dynamo modes. On the other hand, dynamos in the low Rossby number regime exhibit a rather simple time dependence and their saturation merely results in a fluctuation of the fundamental dynamo mode about its critical state. Title: Statistical dynamo theory: Mode excitation Authors: Hoyng, P. Bibcode: 2009PhRvE..79d6320H Altcode: 2009arXiv0903.3844H We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B=∑kak(t)bk(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients ak is governed by a stochastic differential equation from which we infer their averages ⟨ak⟩ , autocorrelation functions ⟨ak(t)ak∗(t+τ)⟩ , and an equation for the cross correlations ⟨akaℓ∗⟩ . The eigenfunctions of the dynamo equation (with eigenvalues λk ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Iλk and -1/Rλk , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for ⟨|ak|2⟩/⟨|a0|2⟩ in case the fundamental mode b0 has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that ⟨|ak|2⟩/⟨|a0|2⟩∼1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rλk<0 . Title: Analysis of the variability of the axial dipole moment of a numerical geodynamo model Authors: Kuipers, J.; Hoyng, P.; Wicht, J.; Barkema, G. T. Bibcode: 2009PEPI..173..228K Altcode: We have analysed the time evolution of the axial dipole moments (ADMs) from three numerical geodynamo models by relating it to the Fokker-Planck equation governing the systematic and random ADM motion. We have determined the effective growth rate of the ADM and the diffusion coefficient D characterising its random fluctuations. We find that the numerical ADM data exhibit a nonlinear quenching that is not significantly different from that of the Sint-2000 data. The quenching is only partly due to a reduction of the r.m.s. convective flow speed with increasing ADM. Our results suggest that in these numerical models similar mechanisms may be at work as in the earth's core, and that the results of Brendel et al. [Brendel, K., Kuipers, J., Barkema, G.T., Hoyng, P., 2007. An analysis of the fluctuations of the geomagnetic dipole. Phys. Earth Planet. Inter. 162, 249-255] are unlikely to be an artifact caused by the restricted length of the dataset. They also suggest that the dynamics of the ADM is that of a Brownian particle (i.e. driven by additive noise) in a bistable potential, and we illustrate some consequences of this idea. Title: An analysis of the fluctuations of the geomagnetic dipole Authors: Brendel, K.; Kuipers, J.; Barkema, G. T.; Hoyng, P. Bibcode: 2007PEPI..162..249B Altcode: 2007arXiv0707.0623B The time evolution of the strength of the Earth's virtual axial dipole moment (VADM) is analyzed by relating it to the Fokker-Planck equation, which describes a random walk with VADM-dependent drift and diffusion coefficients. We demonstrate first that our method is able to retrieve the correct shape of the drift and diffusion coefficients from a time series generated by a test model. Analysis of the Sint-2000 data shows that the geomagnetic dipole mode has a linear growth time of 20-7+13 kyear, and that the nonlinear quenching of the growth rate follows a quadratic function of the type [1-(]. On theoretical grounds, the diffusive motion of the VADM is expected to be driven by multiplicative noise, and the corresponding diffusion coefficient to scale quadratically with dipole strength. However, analysis of the Sint-2000 VADM data reveals a diffusion which depends only very weakly on the dipole strength. This may indicate that the magnetic field quenches the amplitude of the turbulent velocity in the Earth's outer core. Title: Relativistic astrophysics and cosmology : a primer Authors: Hoyng, Peter Bibcode: 2006racp.book.....H Altcode: No abstract at ADS Title: Relativistic Astrophysics and Cosmology Authors: Hoyng, Peter Bibcode: 2006rac..book.....H Altcode: No abstract at ADS Title: End-to-end simulations for the LISA Technology Package Authors: Hannen, V. M.; Smit, M.; Hoyng, P.; Selig, A.; Schleicher, A. Bibcode: 2003CQGra..20S.261H Altcode: We present an end-to-end simulation facility which has been developed in the framework of the LISA Technology Package (LTP) architect study for SMART-2, the technology demonstration mission that precedes LISA. The simulator evolves positions and orientations of the spacecraft and two test masses contained in the inertial sensors of LTP under the influence of external and internal forces and torques and under the influence of control loops for satellite drag-free control (DFC) and electrostatic test mass suspension. Altogether, a coupled system with 18 degrees of freedom is solved numerically. A series of test runs has been performed to verify the correct functioning of the various models contained in the end-to-end simulator and to provide a preliminary assessment of the performance of DFC algorithms and control laws for test mass suspension, which are currently foreseen for use in the basic operation mode of LTP. Title: The field, the mean and the meaning Authors: Hoyng, Peter Bibcode: 2003and..book....1H Altcode: 2003eclm.book....1H No abstract at ADS Title: Solar Cycle Authors: Ossendrijver, M.; Hoyng, P. Bibcode: 2002eaa..bookE1980O Altcode: The term solar cycle refers to a quasi-periodic variation with a period of about 11 years, visible in many of the Sun's observables. The solar cycle is most easily observed in indices directly related to the Sun's magnetic field, such as SUNSPOTS. During the last decades, solar-cycle variations have also been found in many other aspects of the Sun (irradiance, surface flows, coronal shape, oscil... Title: A theoretical analysis of the observed variability of the geomagnetic dipole field Authors: Hoyng, P.; Schmitt, D.; Ossendrijver, M. A. J. H. Bibcode: 2002PEPI..130..143H Altcode: We present a detailed analysis of the Sint-800 virtual axial dipole moment (VADM) data in terms of an αΩ mean field model of the geodynamo that features a non-steady generation of poloidal from toroidal magnetic field. The result is a variable excitation of the dipole mode and the overtones, and there are occasional dipole reversals. The model permits a theoretical evaluation of the statistical properties of the dipole mode. We show that the model correctly predicts the distribution of the VADM and the autocorrelation function inferred from the Sint-800 data. The autocorrelation technique allows us to determine the turbulent diffusion time τd= R2/ β of the geodynamo. We find that τd is about 10-15 kyr. The model is able to reproduce the observed secular variation of the dipole mode, and the mean time between successive dipole reversals. On the other hand, the duration of a reversal is a factor ∼2 too long. This could be due to imperfections in the model or to unknown systematics in the Sint-800 data. The use of mean field theory is shown to be selfconsistent. Title: Magnetic field reversals and secular variation in a bistable geodynamo model Authors: Schmitt, D.; Ossendrijver, M. A. J. H.; Hoyng, P. Bibcode: 2001PEPI..125..119S Altcode: A method is described which enables the calculation of statistical properties of geodynamo models. The result is a Fokker-Planck equation for the probability distribution of the dipole moment. The method only requires a non-oscillatory, predominantly dipolar magnetic field and helicity fluctuations. The fluctuations perturb the fundamental dynamo mode and lead to the excitation of higher modes. This results in stochastic oscillations of the dipole field amplitude in a bistable potential with minima representing normal and reversed polarity, and occasional jumps between them. The shape of the potential is determined by supercritical dynamo excitation and nonlinear limitation of field growth. Application of the method to a mean-field dynamo model with random fluctuations of the helicity parameter α reproduces the observed relation between the secular variation and the reversal rate of the geomagnetic field, as well as the amplitude distribution of the dipole field inferred from the Sint-800 record. Title: The geodynamo as a bistable oscillator Authors: Hoyng, P.; Ossendrijver, M. A. J. H.; Schmitt, D. Bibcode: 2001GApFD..94..263H Altcode: Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating alpha reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ~(1-a^2)^2, subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2-3)x10^5years, is shown to imply a secular variation of the dipole moment of ~15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data. Title: Cyclic Evolution of Sunspots: Gleaning New Results from Old Data Authors: Solanki, S. K.; Fligge, M.; Pulkkinen, P.; Hoyng, P. Bibcode: 2000JApA...21..163S Altcode: No abstract at ADS Title: Book Review: The little book of the big bang : a cosmic primer / Copernicus, 1998/Springer, 1998 Authors: Hoyng, P. Bibcode: 1999SSRv...88..608H Altcode: No abstract at ADS Title: The geodynamo as a bistable oscillator Authors: Ossendrijver, M. A. J. H.; Hoyng, P.; Schmitt, D. Bibcode: 1999AGAb...15...73O Altcode: 1999AGM....15..J13O Paleomagnetism has convincingly shown that the Earth has reversed the polarity of its almost dipolar magnetic field many times in the past. The origin of the field is generally ascribed to dynamo action in the liquid outer core. Numerical simulation of a mean-field model demonstrates that random fluctuations of the dynamo alpha-effect cause occasional rapid magnetic reversals, like those of the Earth's field. The fluctuations perturb the fundamental stationary dipolar mode and lead to the excitation of higher oscillatory dynamo modes. This results in stochastic oscillations of the dipole field amplitude in a bistable potential with minima representing normal and reversed polarity, and occasional jumps between them. The shape of the potential is determined by supercritical dynamo excitation and nonlinear limitation of field growth. A statistical analysis shows that the model reproduces the essential features of the geomagnetic secular variation and reversal record. Title: Op zoek naar de grens van het heelal. Authors: Hoyng, P. Bibcode: 1998Zenit..25..340H Altcode: No abstract at ADS Title: Book Review: SCORe '96 / Kluwer, 1997 & 1998 Authors: Hoyng, P. Bibcode: 1998SSRv...85..552H Altcode: No abstract at ADS Title: Chromospheric and Photospheric Activity of the Sun as a Star Using SOLSTICE Data Authors: Catalano, S.; Lanza, A. F.; Brekke, P.; Rottman, Gary J.; Hoyng, P. Bibcode: 1998ASPC..154..584C Altcode: 1998csss...10..584C The distribution of photospheric and chromospheric active regions (spots and plages) on the surface of stars is mainly recovered from the deconvolution of light or line flux curves. Here we check the reliability of the maximum entropy technique to derive surface maps from the rotational modulation of the continuum and line fluxes observed in active stars. We compare the solar chromospheric map obtained from the deconvolution of daily average of the C 2 line flux at 133.5 nm measured by SOLSTICE, and solar Hα images contemporaneously obtained at Catania observatory. Hα plages may not exactly overlay C 2 plages, however the agreement between the reconstructed and the direct images is strikingly good. Only small (<20circ-30circ in diameter) or low contrast (Delta I/I < 0.3) structures are not recovered. We use also the Wolf sunspot number to study the longitude distribution of the active regions in photosphere and chromosphere, contrasting the solar behaviour with that of other active stars. Title: A Model for a Thin Magnetised Disc in LMC X-3 Authors: Hoyng, P. Bibcode: 1998IAUS..188..379H Altcode: Dynamo action in turbulent accretion discs will generate randomly oriented magnetic fields. The mean field <! !B ! !> can be assumed to be zero. We have determined the radial distribution of the r.m.s. magnetic field (i.e. the six quantities < ! !B theta 2 ! !>, < ! !B theta Br ! !>, etc.). The disc structure is determined with the help of the standard thin disc equations by allowing for the influence of the magnetic field on temperature and angular momentum. This work is an extension of that of Schramkowski et al. (1996) who considered only vertical turbulent transport of magnetic energy. We include also radial transport, energetically unimportant, but essential in that it fixes the radial distribution of the r.m.s. field. Our approach is still kinematic. It is found that a magnetic disc is thinner and hotter than its non-magnetised counterpart. If the escaping magnetic energy heats a disc corona, the radial distribution of the r.m.s. magnetic field may be inferred from the `ratio' of the thermal emission of the disc and the nonthermal emission of the corona. From the X-ray spectrum of black hole candidate LMC X-3 we confirm values in the range of 106 - 107G found by Schramkowski et al. (1996). Schramkowski G.P. et al.: 1996, A&A 315, 638. Title: Mean magnetic field and energy balance of Parker's surface-wave dynamo. Authors: Ossendrijver, A. J. H.; Hoyng, P. Bibcode: 1997A&A...324..329O Altcode: We study the surface-wave dynamo proposed by Parker (1993) as a model for the solar dynamo, by solving equations for the mean magnetic field {vec}(B)_0_, as well as for the mean 'magnetic energy tensor' ((T))=<{vec}(BB)>/8π. This tensor provides information about the energy balance, rms field strengths and correlation coefficients between field components. The main goal of this paper is to check whether the equations for {vec}(B)_0_ and ((T)) are compatible, i.e. whether both have "reasonable" solutions for a set of "reasonable" parameters. We apply the following constraints: {vec}(B)_0_ has a period of 22 years and, taking into account the effect of period variations, a decay time of 10 dynamo periods, and ((T)) is marginally stable. We find that under these constraints, the equations for {vec}(B)_0_ and ((T)) are compatible only if, apart from turbulent transport out of the dynamo region, an additional energy sink is introduced. If this extra term is omitted, then marginal stability of ((T)) requires a turbulent diffusion in the convection zone of the order β_2_>3x10^14^cm^2^/s, whereas the conditions on {vec}(B)_0_ require β_2_=~10^12^cm^2^/s. Furthermore, the rms surface field strength, the maximum rms field strength and the magnetic energy flux through the upper surface of the convection zone cannot simultaneously assume solar values. We explore the possibility that the extra energy sink is provided by resistive dissipation, hitherto not accounted for in the equation for ((T)), by considering various cases. We demonstrate that with a heuristically modified equation for ((T)), the inconsistencies can be removed. Our results suggest that resistive dissipation is the dominant sink of magnetic energy, and that resistive heating may amount to several percent of the solar luminosity. Title: GRB 960720 and GRB 970111 Authors: in 't Zand, J.; Heise, J.; Hoyng, P.; Jager, R.; Piro, L.; Costa, E.; Feroci, M.; Frontera, F.; dal Fiume, D.; Orlandini, M.; Pizzichini, G.; Nicastro, L.; Muller, J. Bibcode: 1997IAUC.6569....1I Altcode: 1997IAUC.6569Q...1I J. in 't Zand, J. Heise, P. Hoyng, and R. Jager, Space Research Organization of the Netherlands (SRON), Utrecht; L. Piro, E. Costa, and M. Feroci, Istituto Astrofisica Spaziale, CNR, Frascati; F. Frontera, D. Dal Fiume, M. Orlandini, G. Pizzichini, and L. Nicastro, Istituto Tecnologie e Studio delle Radiazioni Extraterrestri, CNR, Bologna; and J. Muller, BeppoSAX, Rome, and SRON, Utrecht, write: "The positions of the x-ray counterparts to GRB 960720 and GRB 970111 as determined with the BeppoSAX Wide Field Cameras (cf. IAUC 6467 and 6533, respectively) have been refined through an improvement of the spatial calibration of the instruments. The calibration concerns small misalignments between both cameras and between the cameras and the satellite coordinate system, the image scales of both WFCs, and the modeling of the point spread function. The calibration was tested with 123 detections of catalogued x-ray sources with accurately known positions, as found in 15 SAX WFC observations with a variety of orientation angles. These sources have a representative range of intensities and off-axis angles. None of the detections has a difference between catalogue and measured source positions > 3'.9, and 97 percent have a difference of < 3'. In a subset of fourteen sources having significance levels that are within a factor of 2 of the levels of GRB 960720 and GRB 970111, one source shows a difference of > 3' from the catalogue position. For GRB 960720, we find a 3'-radius error circle centered on R.A. = 17h30m37s, Decl. = +49o05'.8 (equinox 2000.0). This position is 10'.5 from the previously reported position, for which a 10' error circle radius was reported. Neither the previously reported SAX NFI source (IAUC 6480) nor the optical source (IAUC 6526) lies within the error circle. The new error circle does include the radio-loud quasar 4C 49.29 (z = 1.038). The error circle for GRB 970111 is centered on R.A. = 15h28m15s, Decl. = +19o36'.3. This center is 4'.2 from the previously reported position, and the circle overlaps the IPN annulus reported by Hurley et al. (IAUC 6545). None of the previously reported SAX NFI sources (Butler et al., IAUC 6539), RASS sources (Voges et al., IAUC 6539), radio source (Frail et al., IAUC 6545), and ROSAT HRI source (IAUC 6567) lies within the 3'- radius error circle." Title: Is the Solar Cycle Timed by a Clock? Authors: Hoyng, P. Bibcode: 1996SoPh..169..253H Altcode: Dicke (1978) has argued that the phase of the solar cycle appears to be coupled to an internal clock: shorter cycles are usually followed by longer ones, as if the Sun remembers the correct phase. The data set is really too short to demonstrate the presence of a phase memory, but phase and amplitude of the cycle are strongly correlated for 300 yr or more. It is shown that this memory effect can be explained by mean field theory in terms of fluctuations in α, which induce coherent changes in the frequency and amplitude of a dynamo wave. It is concluded that there is neither a strong observational indication nor a theoretical need for an extra timing device, in addition to the one provided by dynamo wave physics. Title: Does the sun have a memory? Authors: Ossendrijver, A. J. H.; Hoyng, P.; Schmitt, D. Bibcode: 1996NAWG.1996..247O Altcode: The authors study the effect of stochastic fluctuations in α using a simple axisymmetric mean field dynamo model. There are two main features: Firstly, the excitation of higher eigenmodes of the dynamo equation, providing a possible explanation of asymmetries between the two hemispheres and, close to the equator, the formation of small regions of the "wrong" polarity. Secondly, a correlation between fluctuations in phase and amplitude of the dipole field. Phase and amplitude are not locked onto one another, i.e. the dynamo has no "memory". The authors use the phase-amplitude correlation to compare the model with sunspot data, where a similar correlation is observed. This provides a rough estimate of the required strength of the α-fluctuations. It is found that α, defined as an azimuthal average, has fluctuations of the order δα/α0 ≍ 3 at mid latitudes. Title: Flow and distribution of magnetic energy in accretion disks: a kinematic approach. Authors: Schramkowski, G. P.; van Niekerk, E. C. M.; Hoyng, P.; Achterberg, A. Bibcode: 1996A&A...315..638S Altcode: By taking account of the statistical nature of kinematic mean field dynamo theory, it is pointed out that the mean magnetic field <B> should always vanish. A more fruitful approach therefore seems to be to study the dynamics of the second moment <BB> of magnetic field which contains information on mean magnetic energy and statistical correlations between the various components of the magnetic field. The general dynamics of this tensor are discussed. As an application a stationary solution for zero helicity is presented in a local approximation. It is found that such a dynamo can only be maintained by compressible turbulence. The implications of this non-helical solution for the structure and emission of stationary thin accretion disks are discussed. The limits of applicability of the kinematic approach are briefly discussed. We apply our model to the inner region of the accretion disk around the black hole candidate LMC X-3. We find typical rms magnetic field strength values in the range 4x10^6^-4x10^7^Gauss. Title: Book reviews Authors: Shore, Steven N.; van der Kruit, P. C.; Achterberg, A.; Hoyng, P.; de Jager, Cornelis Bibcode: 1996SSRv...78..557S Altcode: No abstract at ADS Title: Stochastic and nonlinear fluctuations in a mean field dynamo. Authors: Ossendrijver, A. J. H.; Hoyng, P. Bibcode: 1996A&A...313..959O Altcode: We study the effect of rapid stochastic fluctuations in the kinetic helicity in a plane parallel mean field dynamo model for the Sun. The α-parameter has a fluctuating component δα=α-α_0_, which is modelled as a random forcing term. The fluctuations give rise to variations in the amplitude and phase of the dynamo wave, such that shorter cycles have higher amplitudes, as is observed in the solar cycle. By making a second order expansion close to the unperturbed marginally stable dynamo wave we are able to go beyond the weak forcing limit studied by Hoyng. We show that with increasing strength of the forcing the effective dynamo frequency decreases. We introduce a simple non-linearity to model α-quenching and derive a set of linear equations for the mean field, valid in the weak forcing case. With α-quenching, phase and amplitude fluctuations are bounded, but still correlated. The strength of the α-quenching is measured by a parameter q=-(T_e_/α_0_)(dα/dT)|_T_e__, where T_e_ is the equilibrium value of the toroidal field. We make a comparison with sunspot data, and conclude that these are well explained by the model if δα/α_0_=~2.2 and q=~0.7. Finally we briefly consider the alternative possibility of fluctuations caused by nonlinear dynamics, without external forcing (δα=0). We show that the resulting phase-amplitude diagram does not agree with observations. Although this is no proof that the phase-amplitude correlation cannot be reproduced by nonlinear chaos, we conclude that stochastic noise provides a more natural explanation. Title: Stochastic excitation and memory of the solar dynamo. Authors: Ossendrijver, A. J. H.; Hoyng, P.; Schmitt, D. Bibcode: 1996A&A...313..938O Altcode: We consider a simple axisymmetric mean field dynamo model for the Sun in the α{OMEGA}-limit and study the effect of rapid, latitude dependent stochastic fluctuations in α. The fluctuations excite overtones of the fundamental mode of the mean magnetic field. We decompose the mean field into eigenmodes and derive an equation for the mode coefficients. Transient mode excitation gives rise to a mean field with spatial and temporal variability, and may provide an explanation for grand minima, the observed phase-amplitude correlation, North-South asymmetries and, close to the equator, reverse polarity regions in the solar butterfly diagram. We find that the North-South asymmetry often peaks near the activity minimum, in agreement with the observations. The most likely candidate for the origin of the fluctuations are giant cells. Sunspot data are well reproduced if α, defined as an azimuthal average, has fluctuations δα of the order δα/α_0_=~3 at colatitude θ=60deg, assuming that there are 20 giant cells from pole to pole, with a coherence time of 1 month. The model predicts that the resulting phase and amplitude fluctuations of the fundamental mode are correlated for about 90 dynamo periods. Title: Book reviews Authors: Humphreys, R. M.; Kemp, S.; Savonije, G.; van der Hucht, K. A.; van der Kruit, P. C.; Miley, G.; Bumba, V.; van Nieuwkoop, J.; van Hoolst, T.; Cox, A.; Rutten, R. J.; Kleczek, J.; de Jager, Cornelis; Jerzykiewicz, M.; Zwaan, C.; Poedts, S.; Sakai, Jun-Ichi; Pecker, J. -C.; Heikkila, W.; de Jong, T.; Wilson, P. R.; Müller, E. A.; Hoyng, P.; Icke, V.; Shore, S. N.; Achterberg, A.; Lucchin, F.; Butcher, H.; Ne'Eman, Y.; Heidmann, J.; Belton, M. J. S.; de Graauw, Th.; Waters, L. B. F. M.; Pacini, F.; Hultqvist, B.; Akasofu, S. -I.; Vial, J. -C.; Schatzman, E.; van der Laan, H.; Cole, K. D.; Vanbeveren, D.; Southwood, D.; van der Klis, M.; Katgert, Peter Bibcode: 1996SSRv...76..339H Altcode: No abstract at ADS Title: STARS - Seismic Telescope for Astrophysical Research from Space. Report on the phase A study. Authors: Badiali, M.; Catala, C.; Favata, F.; Fridlund, M.; Frandsen, S.; Gough, D. O.; Hoyng, P.; Pace, O.; Roca-Cortés, T.; Roxburgh, I. W.; Sterken, C.; Volonté, S. Bibcode: 1996star.book.....B Altcode: STARS is an asteroseismology mission, which, through the acquisition of very accurate light curves, will detect oscillations in a wide variety of stars. This will allow, for the first time, the internal structure of stars of different age, composition and spectral type, to be studied directly, bringing the spectacular successes of helioseismology within reach for a large number of other stars spreading over most of the Hertzsprung-Russell diagram, including solar-type stars in open clusters. The results of the phase A study are presented in this report. Title: Solar and stellar dynamos Authors: Hoyng, P. Bibcode: 1996ASPC..109...59H Altcode: 1996csss....9...59H No abstract at ADS Title: STARS: Seismic Telescope for Astrophysical Research from Space Authors: Badiali, M.; Catala, C.; Favata, F.; Fridlund, M.; Frandsen, S.; Gough, D. O.; Hoyng, P.; Pace, O.; Roca-Cortes, T.; Roxburgh, I. W.; Sterken, C.; Volonte, A. Bibcode: 1996ESADS...4....1B Altcode: No abstract at ADS Title: Does the Sun Have a Memory? Authors: Ossendrijver, A. J. H.; Hoyng, P.; Schmitt, D. Bibcode: 1996sgmf.proc..247O Altcode: We study the effect of stochastic fluctuations in alpha using a simple axisymmetric mean feld dynamo model. There are two main features. Firstly, the excitation of higher eigenmodes of the dynamo equation, providing a possible explanation of asymmetries between the two hemispheres and, close to the equator, the formation of small regions of the 'wrong' polarity. Secondly, a correlation between fluctuations in phase and amplitude of the dipole field. Phase and amplitude are not locked onto one another, i.e. the dynamo has no 'memory'. We use the phase-amplitude correlation to compare the findings of our model with sunspot data, where a similar correlation is observed. This provides a rough estimate of the required strength of the alpha-fluctuations. It is found that alpha, defined as an azimuthal average, has fluctuations of the order delta alpha / alpha ~ 3 at mid latitudes. Title: Book Review: Lectures on solar and planetary dynamos [invited papers] / Cambridge U Press, 1995 Authors: Hoyng, P.; Somov, B. V.; Hoyng, P. Bibcode: 1995SoPh..160...61H Altcode: 1995SoPh..160...61P No abstract at ADS Title: Grail: a proposal for a gravitational Radiation Antenna in the Netherlands Authors: Frossati, G.; Steel, D.; de Zeeuw, T.; Gaemers, K.; Linde, F.; van den Heuvel, E.; van den Klis, M.; Sloot, P.; Hoekstra, A.; de Ronde, J.; van den Graaf, H.; Hartjes, F.; van Holten, J. W.; Nooren, G. J.; Oberski, J.; de Waele, A.; van den Heijden, R. W.; Rogalla, H.; Flokstra, J.; Ter Brake, H.; Veldhuis, D.; Fluitman, J. H.; Bereschot, J. W.; Eldersboek, M.; Lodder, J. C.; de Haab, P.; Hoyng, P.; Spallicci, A. Bibcode: 1995grai.rept....1F Altcode: No abstract at ADS Title: Dynamo spectroscopy. Authors: Hoyng, P.; Schutgens, N. A. J. Bibcode: 1995A&A...293..777H Altcode: We study the properties of the magnetic field {vec}(B) of a dynamo by expanding the field in a special set of base functions, namely the eigenfunctions of its dynamo equation [{vec}(B)={SIGMA}sigma_csigma^(t){vec}(b)sigma^({vec}(r))]. We prove that the time evolution of the mean <csigma^> and the frequency spectrum of csigma^(t) are completely determined by the eigenvalue λsigma_ of the dynamo equation. The spectrum is a Lorentzian with central frequency ωsigma_=Imλsigma_ and width γsigma_=-Reλsigma_. This property had been conjectured by Hoyng (1988), and is now shown to hold for arbitrary dynamos. The proof is relatively straightforward, and we point out the error in the analysis of Hoyng (1988). Finally, we illustrate how this property sheds light on the physical meaning of the dynamo equation, and we compare the predicted spectra qualitatively with recent studies of the global properties of the solar magnetic field. Title: The effect of random alpha-fluctuations and the global properties of the solar magnetic field. Authors: Hoyng, P.; Schmitt, D.; Teuben, L. J. W. Bibcode: 1994A&A...289..265H Altcode: We study the effect of rapid random fluctuations in the dynamo parameter α in a simple axisymmetric mean-field dynamo. The model is 1D; it is a shell with latitude-dependent fields. Radial turbulent diffusion is modeled by a prescribed factor exp(imagkr)/r in the field potentials. We consider mainly linear models. The fluctuations excite overtones of the fundamental mode which are otherwise damped. Butterfly diagrams and frequency spectra S_l_(ν) of the Legendre expansion coefficients c_l_(t) of the toroidal mean field [B(θ,t)={SIGMA}_l_c_l_(t)P_l_(cos θ)] are compared with observations of the solar magnetic field. The results are: (1). The model accounts for the observed relative phases of the coefficients c_l_(t) for odd l at the frequency 1/(22yr) of the fundamental mode, and potentially also for their relative amplitudes. (2). The spectra S_l_(ν) are broad and featureless for even l, while for odd l the frequency 1/(22yr) of the fundamental mode dominates. They agree qualitatively with the results of Gokhale and coworkers. It is unlikely that the modal structure in the surface field for even l found by Stenflo and colleagues can be produced by mean field models with random α-fluctuations. (3). Butterfly diagrams have a solar-type structure for 1<~kR<~5 (R = position of the bottom of the convection zone). The fluctuations generate many phenomena also seen in the solar cycle, such as slow activity modulations due to mode beating, accidental disappearances of the activity, transequatorial activity, and sometimes quite persistent North-South asymmetries in the butterfly diagram. The character of the latter depends sensitively on the value of kR. (4). The amplitudes of the eigenmodes are shown to behave as randomly excited coupled oscillators, which allows us to explain the excitation levels of the overtones, their frequency spectra and the structure of the North-South asymmetries. (5). In the latitude region where the dynamo operates the local fluctuations in ({vec}(u).∇ x {vec}(u))τ_c_ are ~60 to 70 times larger than the mean value of ({vec}(u).∇ x {vec}(u))τ_c_, and the fluctuations in α are 6 to 7 times larger than the mean value of α. Title: Distribution and flow of magnetic energy in an accretion disk Authors: Schramkowski, G. P.; van Niekerk, E. C. M.; Hoyng, P.; Achterberg, A. Bibcode: 1994SSRv...68..329S Altcode: No abstract at ADS Title: The solar dynamo Authors: Hoyng, P. Bibcode: 1994ASIC..433..387H Altcode: No abstract at ADS Title: Random forcing and the mode structure of the solar magnetic field Authors: Schmitt, D.; Hoyng, P.; Teuben, L. J. W. Bibcode: 1994smf..conf..110S Altcode: No abstract at ADS Title: Helicity fluctuations in mean field theory: an explanation for the variability of the solar cycle? Authors: Hoyng, P. Bibcode: 1993A&A...272..321H Altcode: We consider the effect of fluctuations δα(t) in the mean helicity α0 (both assumed independent of position) on a plane dynamo wave. The time scale τc of the fluctuations is much shorter than the diffusion time 1/β0κ20κ2τc ≪ 1; β0 = turbulent diffusion coefficient; κ = wave number). We distinguish weak and strong random forcing, according to whether (δαr.m.s.0)√β0κ2τc is small or large with respect to 1, and we present a detailed analysis of the weak forcing case.

Simple equations are derived for the phases and the logarithmic amplitudes of the poloidal and toroidal mean field, in which the forcing terms appear as additive noise. Phase difference and amplitude ratio of the poloidal and toroidal (mean) field are subject to small fluctuations of constant r.m.s. magnitude. Simple expressions are derived for the r.m.s. phase shift, amplitude drift and quality factor of the toroidal (mean) field. These depend on the fluctuations only through the quantity D = ¼( δαr.m.s.0)2β0κ2τc which plays the role of a diffusion coefficient. The results are: (1). Phase shift Δ and logarithmic amplitude Λ each perform a random walk; (2). In the α2-limit these random walks are uncorrelated; the phase is very stable but the amplitude is completely irregular; (3). In the αω-limit there exists a correlation: Λ + Δ ≃ 0, which persists for many dynamo periods. The quality factor is then given by Q = 1/D.

The model is then applied to the solar dynamo. The predicted correlation Λ + Δ ≃ 0 implies that weaker (stronger) cycles last longer (shorter) than average, which is a well-known observed feature of the solar cycle. We define Λ and Δ using the epochs of solar maxima and the sunspot numbers, and show that Λ + Δ ≃ 0 is obeyed rather well. This indicates that fluctuations in the mean helicity are an important mechanism causing the observed phase and amplitude variations of the solar cycle. Simulations show many features also seen in the solar cycle, such as quasi-periodicity, intermittency and long periods of low activity. Further inferences are: (1). The sunspot numbers appear to be proportional to the strength of the toroidal field; (2). The quality factor Q is about 10, which makes the solar dynamo a border-line case between weak and strong forcing; (3). The solar data indicate that it is necessary to allow for nonlinear effects; (4). The mean helicity fluctuations δα(t) are caused by very large spatial fluctuations in the local helicity. This could explain the discrepancy between theoretical estimates for α0 and values derived from mean field models. Title: Prisma - the First Space Mission to See Inside the Stars Authors: Appourchaux, T.; Gough, D. O.; Catala, C.; Frandsen, S.; Frohlich, C.; Hoyng, P.; Jones, A.; Lemaire, P.; Tondello, G.; Weiss, W. W. Bibcode: 1993ASPC...42..411A Altcode: 1993gong.conf..411A No abstract at ADS Title: Can Mean Helicity Fluctuations Explain the Variability of the Solar Cycle? Authors: Hoyng, P. Bibcode: 1993IAUS..157...71H Altcode: No abstract at ADS Title: Distribution of magnetic energy in -dynamos, I: The method Authors: van Geffen, J. H. G. M.; Hoyng, P. Bibcode: 1993GApFD..71..187V Altcode: In this paper a method for solving the equation for the mean magnetic energy <BB> of a solar type dynamo with an axisymmetric convection zone geometry is developed and the main features of the method are described. This method is referred to as the finite magnetic energy method since it is based on the idea that the real magnetic field B of the dynamo remains finite only if <BB> remains finite. Ensemble averaging is used, which implies that fields of all spatial scales are included, small-scale as well as large-scale fields. The method yields an energy balance for the mean energy density B2/8 of the dynamo, from which the relative energy production rates by the different dynamo processes can be inferred. An estimate for the r.m.s. field strength at the surface and at the base of the convection zone can be found by comparing the magnetic energy density and the outgoing flux at the surface with the observed values. We neglect resistive effects and present arguments indicating that this is a fair assumption for the solar convection zone. The model considerations and examples presented indicate that (1) the energy loss at the solar surface is almost instantaneous; (2) the convection in the convection zone takes place in the form of giant cells; (3) the r.m.s. field strength at the base of the solar convection zone is no more than a few hundred gauss; (4) the turbulent diffusion coefficient within the bulk of the convection zone is about 1014cm2s-1, which is an order of magnitude larger than usually adopted in solar mean field models. Title: PRISMA: Probing Stars from Core to Corona Authors: Appourchaux, T.; Catala, C.; Catalano, S.; Fransden, S.; Fröhlich, C.; Gough, D. O.; Hoyng, P.; Jones, A.; Lemaire, P.; Tondello, G.; Weiss, W. Bibcode: 1993ASSL..183..505A Altcode: 1993pssc.symp..505A No abstract at ADS Title: Stochastic excitation of global magnetic fields by fluctuations in the mean helicity Authors: Hoyng, P.; van Geffen, J. H. G. M. Bibcode: 1993GApFD..68..203H Altcode: The mean field B in the dynamo equation can be interpreted as a longitude-averaged field, and this implies that there are fluctuations in the mean parameters characterizing the turbulent flow. In this paper we study the effect of fluctuations in the mean helicity numerically and analytically in a very simple spherical 2-dynamo: there is no differential rotation and the non-fluctuating parts of and do not depend on position (we call this the 2-sphere dynamo). The dynamo equation then contains a term × (t)B, which describes the effect of the fluctuations in the mean helicity. We show that this type of random forcing implies that the dynamo has to operate (slightly) subcritically, and that in addition many eigenmodes are excited, rather than only the fundamental mode. The advantage of this simple α2-dynamo model is that we can support the numerical results with analytical estimates, for instance, for the value of the dynamo number at which the dynamo operates, the relative excitation levels of the modes, and their spectra. This is achieved with the help of an expansion technique: B is expanded in terms of a complete, orthogonal set of eigenfunctions. We have taken the mean helicity fluctuations to be position-independent for simplicity. This, however, renders the dynamo model so simple that only dipole fields are excited and magnetic field reversals are absent. We also briefly study the effect of non-linearities, in particular of α-effect quenching. Non-linearities provide a reference level to the fundamental mode, but do not affect the relative excitation levels of the modes. Title: Book review Authors: Hoyng, P. Bibcode: 1992SoPh..137..203H Altcode: No abstract at ADS Title: Book-Review - Helioseismology from Space Authors: Foing, B. H.; Hoyng, P. Bibcode: 1992SoPh..137..203F Altcode: No abstract at ADS Title: Mean Field Dynamo Theory Authors: Hoyng, P. Bibcode: 1992ASIC..373...99H Altcode: 1992sla..conf...99H No abstract at ADS Title: The velocity sensitivity of resonant scattering spectrometers employing a piezoelastic modulator Authors: Hoyng, P. Bibcode: 1991SoPh..133...43H Altcode: The resonant scattering spectrometers of the IRIS ground-based network for measuring whole-disc solar velocity oscillations make use of a piezoelastic modulator. The velocity noise generated by this optical component is analysed with particular emphasis on the required stability of the amplitude of oscillation, a. The product of the absolute stability ¦ a − am¦/amand the relative stability δar.m.s./am may not be larger than 10 −4 to 10 −5 (depending on specific wishes), where amis the optimum amplitude. The velocity noise due to photon statistics is slightly enhanced, but other instrumental sources of velocity noise remain unaffected. Title: Non-Steady Global Magnetic Fields in Kinematic Theory Authors: van Geffen, J. H. G. M.; Hoyng, P.; Zwaan, C. Bibcode: 1991LNP...380..129V Altcode: 1991IAUCo.130..129V; 1991sacs.coll..129V The dynamo equation for the mean field (B) contains a random forcing term of unknown magnitude, which is therefore always omitted. The influence of this term is potentially large. To evaluate its effect, we employ ensemble averaging. If an ensemble average is used, there is no random forcing term in the dynamo equation. The effect of fluctuations is that the ensemble members get out of phase, so that (B) 0. The damping time of (B) can be found by requiring that the mean energy (BB) remains finite. The eigenvalues of the dynamo equation then all have negative real parts. Im determines the period, and -Re/Im the relative period stability of the dynamo. We have developed a code to solve the equation for (BB) in a spherical shell (the convection zone), assuming axisymmetry. We report our first results, which do not yet include differential rotation. Using spherically symmetric boundary conditions, we reproduce the well known 2-dynamo, whose behaviour is known analytically. For instance, for an 2-dynamo located in a shell with inner boundary at R/2, we find that (BB) remains finite for R2/ = 1.48, where 3 represents turbulent diffusion and .y turbulent vorticity. Taking = 1/4(βy)1/2 — a factor of four below maximum helicity — implies that we have a dynamo number Ca ≡ Rα/β = 0.30. Using this value we find a damping time of 6 X 10-2 R 2/β for (B), which is a measure for the coherence time of B in a single ensemble member. This result implies that the large-scale field of this particular α2-dynamo reorganizes its structure completely on a time scale of only about one year (for solar values of R and β), and it shows the enormous influence of random forcing in general. Title: Book reviews Authors: Haubold, Hans Joachim; Snijders, M. A. J.; van Rensbergen, W.; de Jager, Cornelis; van de Weygaert, R.; Achterberg, A.; Linssen, P. F. J.; Hoyng, P.; Kleczek, J.; Bauer, Siegfried J.; Hayakawa, S. Bibcode: 1990SSRv...54..187H Altcode: No abstract at ADS Title: Mechanisms for Dynamo Mode Excitation Authors: Hoyng, P. Bibcode: 1990IAUS..142...45H Altcode: No abstract at ADS Title: Book Review: Instabilities in space and laboratory plasmas. / CUP, 1986. Authors: Hoyng, P. Bibcode: 1990SSRv...54..192H Altcode: 1990SSRv...54..192M No abstract at ADS Title: Excitation of Dynamo Modes Authors: Hoyng, P. Bibcode: 1990IAUS..138..359H Altcode: No abstract at ADS Title: Turbulent transport of magnetic fields. V. Distribution of magnetic energy in a simple 2-dynamo Authors: van Geffen, J. H. G. M.; Hoyng, P. Bibcode: 1990GApFD..53..109V Altcode: In this paper we analyse the stationary mean energy density tensor Tij = BiBj for the x2-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for Tij is found analytically. Only Trr, Tθθ and Tφ φ are unequal to zero, and we present their dependence on the radial distance r.

The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient β≈ < u2 > τ c/3 and the vorticity coefficient γ≈ <|dtri ×u|2>τc/3 where u(r, t) is the turbulent velocity and c its correlation time. But the solution is independent of the dynamo coefficient α≈-< u· dtri ×u> τc/3 although α does occur in the equation for Tij. This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which Tij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos. Title: On the Sensitivity of Resonant Scattering Spectrometers for Whole-Disk Solar Velocity Oscillation Measurements Authors: Hoyng, P. Bibcode: 1989ApJ...345.1088H Altcode: The sensitivity of resonant scattering spectrometers for measuring solar velocity oscillations in integrated light is analyzed. It is shown that, with the help of simple analytical tools and qualitative arguments, most of the contributions to the instrumental sensitivity can be estimated. Although the frequency dependence of the individual sources of instrument noise cannot always be predicted reliably in this way, it is possible to derive useful estimates of instrumental parameters via comparison with a desired noise level. Title: Turbulent transport of magnetic fields. IV - Damping of the mean field (B) in alpha-squared dynamos with alpha proportional to COS Theta Authors: van Geffen, J. H. G. M.; Hoyng, P. Bibcode: 1989A&A...213..429V Altcode: It is proven that the dynamo equation for the mean field (B) of the spherical alpha-squared dynamo with alpha proportional to cos Theta and constant beta have only exponentially damped solutions, if the mean energy density (B-squared) is nonzero and finite. The origin and interpretation of this phenomenon is reviewed. Title: Book Review: The internal solar angular velocity. / Reidel, 1987 Authors: Hoyng, P. Bibcode: 1989SSRv...49..438H Altcode: 1989SSRv...49..438D No abstract at ADS Title: Turbulent Transport of Magnetic Fields. III. Stochastic Excitation of Global Magnetic Modes Authors: Hoyng, P. Bibcode: 1988ApJ...332..857H Altcode: Studies outlining how the role of fluctuation in the turbulent convection can be analyzed with ensemble averages are reviewed and the relation between the observed magnetic field and the ensemble average magnetic field is solved by expanding the observed field in terms of eigenfunctions of the dynamo equation. The effect of the fluctuations is shown to take the form of stochastic excitation of all eigenmodes of the dynamo equation, rather than steady excitation of only the fundamental eigenmode, as in traditional dynamo models. The solar dynamo is considered and the occurrence of coronal holes and of field reversals in the earth's dynamo are discussed. A comparison is made between this problem and the problem of scalar transport. Title: Book review Authors: Hoyng, P. Bibcode: 1988SoPh..117..203H Altcode: No abstract at ADS Title: Book-Review - Advances in - and Asteroseismology Authors: Christensen-Dalsgaard, J.; Frandsen, S.; Hoyng, P. Bibcode: 1988SoPh..117..203C Altcode: No abstract at ADS Title: Turbulent transport of magnetic fields. I - A simple mechanical model. II - The role of fluctuations in kinematic theory Authors: Hoyng, P. Bibcode: 1987A&A...171..348H Altcode: In the present paper, a simple mechanical model is analysed that reproduces a few basic features of the average magnetic field in the Sun and the Earth. It provides an intuitive picture of how the α-effect operates in combination with differential rotation. The model serves three purposes: (1) it enhances an intuitive understanding of the behaviour of a magnetic field in turbulent fluids; (2) it shows that kinematic models (and ultimately, non-linear models also) must allow for fluctuations as one is essentially dealing with a stochastic process; (3) it serves as a starting point for a re-analysis of the kinematic dynamo problem. Title: Turbulent Transport of Magnetic Fields - Part Two - the Role of Fluctuations in Kinematic Theory Authors: Hoyng, P. Bibcode: 1987A&A...171..357H Altcode: It is argued that due to fluctuations in the turbulent convection, the ensemble averaged field < B > of a dynamo must damp out to zero if <BB>, in particular < B2 >, is to remain finite. This idea is supported by two case studies: a simple α2 dynamo and the αΩ dynamo in the local approximation. Apart from the well-known constants α and β, the equation for < BB > contains the parameter γ ≡ < ∣ V × u12 > τc/3, that also occurred in the model analysed the preceding paper. These results lead to a new statistical formulation of kinematic dynamo theory, which must eventually be extended to nonlinear theory. New aspects are: 1) Turbulent transport of B is a stochastic process and fluctuations have a large influence; 2) B in the dynamo fluctuates on all spatial scales and bears only a statistical relation to < B >; 3) The frequency stability δω/ω of αΩ dynamos and the average time between spontaneous reversals in α2 dynamos are determined by kinematic theory; for the solar dynamo δω/ω is estimated to be larger than observed, but nonlinear effects may cure this; 4) The average magnetic stress tensor (i. e. energy density, Lorentz force and field cross-correlation coefficients) as well as γ are determinable quantities (for the Sun γ ≍ 10-10 s-1); 5) In principle, helical turbulence (α ≠ 0) is not necessary for dynamo action; 6) The global resonances found by Stenflo and Vogel, and the appearance of coronal holes may correspond to stochastic excitations of overtones of the dynamo equation. The meaning of the ensemble average, the energy balance of the dynamo and the physics of turbulent mixing are discussed in detail. The limitations are: zero resistivity, and homogeneous, isotropic turbulence with a short correlation time. Title: Generalized Compton-Getting transformation for nonrelativistic particles. Authors: Stevens, G. A.; Hoyng, P. Bibcode: 1986A&A...168..354S Altcode: The problem of how to construct the particle distribution function in a frame of reference that moves with respect to the frame in which the observations were made is considered. The starting point of the analysis is to expand the velocity distribution functions in both frames of reference in spherical harmonics. A solution of this so-called transformation problem is given in integral form, together with a method that allows practical application. The (optimum) data acquisition and data reduction method is discussed in detail. Six examples are given that illustrate various aspects of the transformation problem. Finally, the transformation method is tested and conditions for a reliable construction of the three-dimensional distribution function in the moving frame are investigated. The statistical aspects of the problem are briefly discussed. Title: Book-Review - Localisation and Orientation in Biology and Engineering Authors: Ubbels, G. A.; Hovenier, J. W.; Russell, C. T.; Nieuwenhuijzen, H.; Heintze, J. R. W.; Linssen, P. F. J.; van der Kruit, P. C.; Thé, P. S.; Somogyi, Antal J.; Cuperman, S.; Rephaeli, Y.; Stirpe, G. M.; Kleczek, J.; Kresák, L.; de Kool, M.; Wapstra, A. H.; Swanenburg, B. N.; Hoyng, P.; Reijnen, G. C. M.; Somov, B. V.; van der Hucht, K. A.; Sehnal, L.; Namba, O.; Schwartz, A. W.; v. D. Stadt, H.; McNally, D.; de Hoop, D. Bibcode: 1986SSRv...44..393U Altcode: No abstract at ADS Title: Book-Review - Seismology of the Sun and the Distant Stars Authors: Gough, D. O.; Hoyng, P. Bibcode: 1986SSRv...44..401G Altcode: No abstract at ADS Title: Observations of Steady Anomalous Magnetic Heating in Thin Current Sheets Authors: Martens, P. C. H.; van den Oord, G. H. J.; Hoyng, P. Bibcode: 1985SoPh...96..253M Altcode: A faint steadily emitting loop-like structure has been observed by HXIS in its low energy channels (3.5-8.0 keV) on November 5/6, 1980. These HXIS observations have permitted us to follow the thermal evolution of this loop for a period of about 15 hr and from this study we conclude that only a fraction of 0.1% of the volume of the loop is steadily heated at the rather large rate of 0.6 erg cm-3 s-1. We interpret this heating as the dissipation of magnetic fields in thin current sheets and we find that the dissipation with classical resistivity is very unlikely, while ion-kinetic tearing, as proposed by Galeev et al. (1981), suits the observations very well. The enhancement of the resistivity over the classical resistivity then turns out to be a factor 4 × 104. Dissipation in extremely thin sheets via the ion-acoustic instability (Duijveman et al., 1981) cannot be completely excluded when the cross-field heat conductivity is anomalously enhanced by a factor 400. Title: Microwave and X-ray observations of delayed brightenings at sites remote from the primary flare locations Authors: Nakajima, H.; Dennis, B. R.; Hoyng, P.; Nelson, G.; Kosugi, T.; Kai, K. Bibcode: 1985ApJ...288..806N Altcode: Five examples of solar flares observed with the 17-GHz interferometer at Nobeyama in which a secondary microwave burst occurred at a distance of 100,000 km to 1,000,000 km from the primary flare site are presented. The secondary microwave burst in all five cases had a similar time profile to the primary burst with a delay of 2 to 25 s. The velocity of a triggering agent inferred from this delay and spatial separation is 10,000 km to 100,000 km/s. The intensity of the secondary burst was a factor of 3 to 25 smaller than that of the primary burst in all events except for one case in which it was a factor of 2 larger. The polarization degree of the secondary burst at 17 GHz was 35 percent, significantly higher than the average value for typical impulsive bursts. Two of the events were accompanied by meterwave type III/V bursts located high in the corona between the primary and secondary sites. For two of the other events, X-ray images of the secondary source were obtained with the hard-X-ray imaging spectrometer on the Solar Maximum Mission. These observations strongly suggest that the distant microwave bursts were produced by electrons with energies of 10 keV to 100 keV which were channeled along a huge loop from the main flare site to the remote location. Title: Kinematic dynamo theory for an arbitrary mean flow. Authors: Hoyng, P. Bibcode: 1984ESASP.220...97H Altcode: 1984ESPM....4...97H The problem of an arbitrary, incompressible mean flow v0 in kinematic dynamo theory is amenable to a systematic treatment leading to an intuitively simple result. The author's approach is based on the theory of stochastic differential equations. Title: Microwave and X-ray observations of delayed brightenings at sites remote from the primary flare locations Authors: Nakajima, H.; Dennis, B. R.; Hoyng, P.; Nelson, G.; Kosugi, T.; Kai, K. Bibcode: 1984STIN...8433326N Altcode: Five examples of solar flares observed with the 17-GHz interferometer at Nobeyama in which a secondary microwave burst occurred at a distance of 100,000 km to 1,000,000 km from the primary flare site are presented. The secondary microwave burst in all five cases had a similar time profile to the primary burst with a delay of 2 to 25 s. The velocity of a triggering agent inferred from this delay and spatial separation is 10,000 km to 100,000 km/s. The intensity of the secondary burst was a factor of 3 to 25 smaller than that of the primary burst in all events except for one case in which it was a factor of 2 larger. The polarization degree of the secondary burst at 17 GHz was 35%, significantly higher than the average value for typical impulsive bursts. Two of the events were accompanied by meterwave type III/V bursts located high in the corona between the primary and secondary sites. For two of the other events, X-ray images of he secondary source were obtained with the hard-X-ray imaging spectrometer on the Solar Maximum Mission. These observations strongly suggest that the distant microwave bursts were produced by electrons with energies of 10 keV to 100 keV which were channeled along a huge loop from the main flare site to the remote location. Title: Microwave and X-ray Observations of Delayed Brightenings at Sites Remote from the Primary Flare Locations Authors: Nakajima, H.; Dennis, B. R.; Hoyng, P.; Nelson, G.; Kosugi, T.; Kai, K. Bibcode: 1984BAAS...16..524N Altcode: No abstract at ADS Title: Report of ESA's topical team on solar and heliospheric physics. Authors: Christensen-Dalsgaard, J.; Delache, P.; Hoyng, P.; Priest, E. R.; Schwenn, R.; Stenflo, J. O. Bibcode: 1984ESASP1070...26C Altcode: No abstract at ADS Title: Hard X-Ray Studies of the Large Coronal Feature on June 29, 1980 Authors: Harrison, R. A.; Simnett, G. M.; Hoyng, P.; Lafleur, H.; van Beek, H. F. Bibcode: 1984sii..conf..287H Altcode: No abstract at ADS Title: Evidence for Extensive Magnetic Structures Between Two Active Regions from Studies of Flares on June 24, 1980 Authors: Simnett, G. M.; Harrison, R. A.; Hoyng, P.; van Beek, H. F. Bibcode: 1984sii..conf..273S Altcode: No abstract at ADS Title: Analysis of the 1980 November 18 limb flare observed by the hard X-ray imaging spectrometer (HXIS) Authors: Haug, E.; Elwert, G.; Hoyng, P. Bibcode: 1984AdSpR...4g.211H Altcode: 1984AdSpR...4..211H X-ray images of the 18 November 1980 limb flare taken by the HXIS instrument aboard SMM were analysed. The hard X-rays originated from three spots on the SW limb of the solar disk with different altitudes and time evolution. The locations of the brightest spots in hard and soft X-rays are compared with the predictions of flare models. The X-ray spctra from the pixels with highest count rates can be fitted by power laws. The spatial variation of the spectral index is in agreement with the existence of a non-thermal electron component. Title: Imaging of Impulsive Solar Flare Phenomena Authors: Duijveman, A.; Hoyng, P. Bibcode: 1983SoPh...86..279D Altcode: We review some recent advances in our understanding of impulsive solar flare phenomena obtained through new hard X-ray and radio imaging instruments (the Solar Maximum Mission and Hinotori satellites, the VLA and VLBI). Title: Microwave and hard X-ray imaging of a solar flare on 1980 November 5 Authors: Hoyng, P.; Marsh, K. A.; Zirin, H.; Dennis, B. R. Bibcode: 1983ApJ...268..865H Altcode: VLA and SMM hard X ray data on the solar flares of November 5, 1980 are analyzed and compared with data from other sources. The VLA provided measurements at 15 GHz at 10 sec intervals, using left and right circular polarizations with a 0.6 arcsec resolution. The hard X ray imaging spectrometer on the SMM obtained data in six bands from 3.5-30 keV, with 8 x 8 arcsec resolution and 1.5 sec separation. The data were examined for a possible nonthermal source for the microwave component of the emissions detected, the origin of 16-30 keV excess fluxes, the relation between the X ray and microwave sources, the magnetic connection between observed loops, and the physical characteristics of the radiating loop. The data were consistent with a model that assumes fast electrons are accelerated to a single power-law energy distribution and freely stream along the magnetic field. The data also agreed with a thick-target model for solar flare X ray emission. Title: The structure and evolution of a solar flare as observed in 3.5 30 keV X-rays Authors: Harrison, R. A.; Simnett, G. M.; Hoyng, P.; Lafleur, H.; van Beek, H. F. Bibcode: 1983SoPh...84..237H Altcode: On July 5, 1980 the Hard X-Ray Imaging Spectrometer on board the Solar Maximum Mission observed a complex flare event starting at 22 : 32 UT from AR 2559 (Hale 16955), then at N 28 W 29, which developed finally into a 2-ribbon flare. In this paper we compare the X-ray images with Hα photographs taken at the Big Bear Solar Observatory and identify the site of the most energetic flare phenomena. During the early phases of the event the hard X-rays (>16 keV) came from a compact source located near one of the two bright Hα kernels; we believe the latter are at the footpoints of a compact magnetic loop. The kernel identified with the X-ray source is immediately adjacent to one of the principal sunspots and in fact appears to `rotate' around the sunspot over 90° in the early phase of the flare. Two intense X-ray bursts occur at the site of the rotating kernel, and following each burst the loop fills with hot, X-ray emitting plasma. If the first burst is interpreted as bremsstrahlung from a beam of electrons impinging on a collisionally dominated medium, the energy in such electrons, >16 keV, is ∼ 5 × 1030 erg. The altitude of the looptop is 7-10 × 103 km. The temperature structure of the flare is extremely non-homogeneous, and the highest temperatures are found in the top of the loop. Title: X-Ray Imaging of Three Flares during the Impulsive Phase Authors: Duijveman, A.; Hoyng, P.; Machado, M. E. Bibcode: 1982SoPh...81..137D Altcode: The impulsive phases of three flares that occurred on April 10, May 21, and November 5, 1980 are discussed. Observations were obtained with the Hard X-ray Imaging Spectrometer (HXIS) and other instruments aboard SMM, and have been supplemented with Hα data and magnetograms. The flares show hard X-ray brightenings (16-30 keV) at widely separated locations that spatially coincide with bright Hα patches. The bulk of the soft X-ray emission (3.5-5.5 keV) originates from in between the hard X-ray brightenings. The latter are located at different sides of the neutral line and start to brighten simultaneously to within the time resolution of HXIS. Concluded is that: The bright hard X-ray patches coincide with the footpoints of loops. Title: Impulsive Acceleration and Heating in Flares Authors: Hoyng, P. Bibcode: 1982Obs...102..119H Altcode: No abstract at ADS Title: Observations of a POST Flare Radio Burst in X-Rays Authors: Svestka, Z.; Hoyng, P.; van Tend, W.; Boelee, A.; de Jager, C.; Stewart, R. T.; Acton, L. W.; Bruner, E. C.; Gabriel, A. H.; Rapley, C. G.; de Jager, C.; LaFleur, H.; Nelson, G.; Simnett, G. M.; van Beek, H. F.; Wagner, W. J. Bibcode: 1982SoPh...75..305S Altcode: More than six hours after the two-ribbon flare of 21 May 1980, the hard X-ray spectrometer aboard the SMM imaged an extensive arch above the flare region which proved to be the lowest part of a stationary post-flare noise storm recorded at the same time at Culgoora. The X-ray arch extended over 3 or more arc minutes to a projected distance of 95 000 km, and its real altitude was most probably between 110 000 and 180 000 km. The mean electron density in the cloud was close to 109 cm−3 and its temperature stayed for many hours at a fairly constant value of about 6.5 × 106 K. The bent crystal spectrometer aboard the SMM confirms that the arch emission was basically thermal. Variations in brightness and energy spectrum at one of the supposed footpoints of the arch seem to correlate in time with radio brightness suggesting that suprathermal particles from the radio noise regions dumped in variable quantities into the low corona and transition layer; these particles may have contributed to the population of the arch, after being trapped and thermalized. The arch extended along the H = 0 line thus apparently hindering any upward movement of the upper loops reconnected in the flare process. There is evidence from Culgoora that this obstacle may have been present above the flare since 15-30 min after its onset. Title: Origin and Location of the Hard X-Ray Emission in a Two-Ribbon Flare Authors: Hoyng, P.; Duijveman, A.; Machado, M. E.; Rust, D. M.; Svestka, Z.; Boelee, A.; de Jager, C.; Frost, K. T.; Lafleur, H.; Simnett, G. M.; van Beek, H. F.; Woodgate, B. E. Bibcode: 1981ApJ...246L.155H Altcode: No abstract at ADS Title: Fast plasma heating by anomalous and inertial resistivity effects in the solar atmosphere Authors: Duijveman, A.; Hoyng, P.; Ionson, J. A. Bibcode: 1981ApJ...245..721D Altcode: A simple model is presented to describe fast plasma heating by anomalous and inertial resistivity effects. It is noted that a small fraction of the plasma contains strong currents that run parallel to the magnetic field and are driven by an exponentiating electric field. The anomalous character of the current dissipation derives from the excitation of electrostatic ion-cyclotron and/or ion-acoustic waves. The possible role of resistivity deriving from geometrical effects ('inertial resistivity') is also considered. Using a marginal stability analysis, equations for the average electron and ion temperatures are derived and numerically solved. No loss mechanisms are taken into account. The evolution of the plasma is described as a path in the drift velocity diagram, where the drift velocity is plotted as a function of the electron to ion temperature ratio. Title: The Relationship Between the Microwave and Hard X-Ray Sources in a Solar Flare Authors: Marsh, K. A.; Zirin, H.; Hoyng, P.; Dennis, B. R. Bibcode: 1981BAAS...13..889M Altcode: No abstract at ADS Title: The limb flare of 1980 April 30 as seen by the hard X-ray imaging spectrometer Authors: van Beek, H. F.; de Jager, C.; Schadee, A.; Svestka, Z.; Boelee, A.; Duijveman, A.; Galama, M.; Hoekstra, R.; Hoyng, P.; Fryer, R.; Simnett, G. M.; Imhof, J. P.; LaFleur, H.; Maseland, H. V. A. M.; Mels, W. M.; Schrijver, J.; van der Laan, J. J. M.; van Rens, P.; van Tend, W.; Werkhoven, F.; Willmore, A. P.; Wilson, J. W. G.; Machado, M. E.; Zandee, W. Bibcode: 1981ApJ...244L.157V Altcode: X-ray imaging of the limb event of 1980 April 30 shows that the flaring involved two distinct components: a pointlike component, which was the source of the initial hard X-ray burst and an extensive tongue reaching some 30,000 km above the limb. The tongue had a higher temperature than the other parts of the structure and seemed to be enhanced by energetic electrons that derived their energy from the initial source. Title: Hard X-ray imaging of two flares in active region 2372 Authors: Hoyng, P.; Duijveman, A.; Boelee, A.; de Jager, C.; Galama, M.; Hoekstra, R.; Imhof, J.; Lafleur, H.; Machado, M. E.; Fryer, R. Bibcode: 1981ApJ...244L.153H Altcode: Hard X-ray images of two flares observed by the Hard X-ray Imaging Spectrometer (HXIS) aboard SMM on 1980 April 7 and 10 are discussed. A comparison with H-alpha images and the photospheric magnetic field maps shows that the emission originates in (arcades of) loops which differ greatly in the hardness of the X-ray spectra. On April 7 the hardest X-ray emission coincided with the brightest H-alpha patch. On April 10 the most intense X-ray emission appeared to be concentrated in a looplike structure with a softer spectrum at the top and a harder spectrum in the legs. Temperature estimates from flux ratios in different energy bands tend to confirm that small, hot components are embedded in more extensive, cooler flaring regions. Title: Structural development of the X-ray limb flare of 30 April 1980 Authors: de Jager, C.; Hoyng, P.; Lafleur, H.; Schadee, A.; Svestka, Z.; van Beek, H. F.; van Tend, W.; Fryer, R.; Simnett, G. M. Bibcode: 1981AdSpR...1m.251D Altcode: 1981AdSpR...1..251D We describe the development of the limb flare of 30 April 1980, 20:20 UT, as observed by the Hard X-ray Imaging Spectrometer (HXIS) aboard the Solar Maximum Mission (SMM). It consisted of a short-lived bright nucleus (FWHM < 10,000 km), just inside the Sun's limb; a longer lasting tongue, extending to a height of ~ 30,000 km, and a more complicated feature, approximately situated at the Sun's limb. The tongue was a pre-existing magnetic structure that started emitting X-rays only a few seconds after the bright nucleus, and which had a slightly higher temperature than the nucleus; its X-ray emission may be caused by electrons escaped from the nucleus. Title: Solar maximum mission experiment: Early results of the hard X-ray imaging experiment Authors: Boelee, A.; de Jager, C.; Duijveman, A.; Galama, M.; Hoekstra, R.; Hoyng, P.; Imhof, J. P.; Lafleur, H.; Maseland, H. V. A. M.; Mels, W. A.; Schadee, A.; Schrijver, J.; Svestka, Z.; van Beek, H. F.; van Rens, P.; van der Laan, J. J. M.; van Tend, W.; Werkhoven, F.; Wiersma, G.; Zandee, W.; Simnett, G. M.; Charlton, C. P.; Fryer, R.; Willmore, A. P.; Wilson, J. W. G.; Machado, M. E. Bibcode: 1981AdSpR...1m.255B Altcode: 1981AdSpR...1R.255B We have selected four widely different flares from the early period of operations of the Hard X-Ray Imaging Spectrometer (HXIS) on SMM to illustrate the characteristic imaging properties of this experiment. For the small flare of April 4, 1980, we demonstrate the instrument's capability for locating a compact source. In the weak, but extensive, flare of April 6 we show how well the instrument can display spatial structure, and also the low level of the instrument background. In the 1B flare of April 7 we are able to locate positions of the X-ray emission in the soft and hard channels, and estimate the positional variations of the emission patches. Finally, in the IN flare of April 10, which produced the strongest hard X-ray burst we have seen so far, we repeat some of the studies made for the April 7 event, and also demonstrate the capability of the HXIS instrument to study the development, with high time resolution, of individual 8'' × 8'' elements of the flare. Title: Solar Maximum Mission experiment - Early results of the hard X-ray imaging experiment Authors: Simnett, G. M.; Charlton, C. P.; Fryer, R.; Boelee, A.; de Jager, C.; Duijveman, A.; Galama, M.; Hoekstra, R.; Hoyng, P.; Imhof, J. P. Bibcode: 1981AdSpR...1m.255S Altcode: 1981AdSpR...1..255S Four widely different flares from the early period of operations of the Hard X-ray Imaging Spectrometer (HXIS) on SMM have been selected to illustrate the characteristic imaging properties of this experiment. For the small flare of April 4, 1980, the instrument's capability for locating a compact source is demonstrated. In the weak, but extensive, flare of April 6, the ability of the instrument to display spatial structure, and also the low level of the instrument background, are shown. In the 1B flare of April 7, positions of the X-ray emission in the soft and hard channels are capable of being located, and the positional variations of the emission patches can be estimated. Finally, in the 1N flare of April 10, which produced the strongest hard X-ray burst seen so far, some of the studies made for the April 7 event are repeated, and the capability of the HXIS instrument to study the development, with high time resolution, of individual 8 x 8 arcsec elements of the flare is also demonstrated. Title: Structural development of the X-ray limb flare of 30 April 1980. Authors: de Jager, C.; Fryer, R.; Hoyng, P.; Lafleur, H.; Schadee, A.; Simnett, G. M.; Svestka, Z.; van Beek, H. F.; van Tend, W. Bibcode: 1981hea..conf..251D Altcode: No abstract at ADS Title: Solar Maximum Mission experiment: early results of the hard X-ray imaging experiment. Authors: Simnett, G. M.; Boelee, A.; Charlton, C. P.; de Jager, C.; Duijveman, A.; Fryer, R.; Galama, M.; Hoekstra, R.; Hoyng, P.; Imhof, J. P.; Lafleur, H.; Machado, M. E.; Maseland, H. V. A. M.; Mels, W. A.; Schadee, A.; Schrijver, J.; Svestka, Z.; van Beek, H. F.; van Rens, P.; van der Laan, J. J. M.; van Tend, W.; Werkhoven, F.; Wiersma, G.; Willmore, A. P.; Wilson, J. W. G.; Zandee, W. Bibcode: 1981hea..conf..255S Altcode: No abstract at ADS Title: Strong Langmuir wave turbulence - Some results with selfconsistent Landau damping Authors: van Grunsven, T. F. J.; Hoyng, P.; Nicholson, D. R. Bibcode: 1980A&A....91....7V Altcode: An initial value problem of the high-frequency Langmuir wave electric field in two spatial dimensions expressed by the split-timestep Fourier method is solved for the case when two equally strong wave vector pumps are initialized in the k-space. One case corresponds to weak Langmuir turbulence indicating that time evolution agrees with weak turbulence concepts of Landau damping and three-wave decay interactions. In the case of strong Langmuir turbulence, the soliton collapse to the smallest length scales is prevented by Landau damping. It is concluded that the shape of electron velocity distribution is approximately constant up to a specific maximum velocity, but rapidly decreases at larger velocities. Title: Impulsive electron acceleration to energies of tens of kT/e/ by Langmuir wave turbulence Authors: Hoyng, P.; Duijveman, A.; van Grunsven, T. F. J.; Nicholson, D. R. Bibcode: 1980A&A....91...17H Altcode: An expression which describes the evolution of the tail of electron distribution determined by the spatial inhomogeneity of the Langmuir wave and escape of fast electrons from the acceleration region is applied to specific situations. One case analyzed a many-current-layer model with properties for accelerating electron streams which generate type III solar radio bursts; the model shows that it can emit an electron flux of 10 to the 32nd/s, with a switch-on time of 0.05 s, and a maximum acceleration energy of 50 keV. Another problem involves a single current layer (shock wave) accelerating electrons to energies of 10 kT(e); the electrons can be additionally accelerated by a second stage process. The first (fast stage) electron acceleration to 100 to 1000 kT(e) can only result from high frequency electrostatic wave turbulence if the shock has a complex structure. Title: Recent Results from the Solar Maximum Mission: Observational, Interpretational and Theoretical Aspects Authors: Hoyng, P. Bibcode: 1980BAAS...12..903H Altcode: No abstract at ADS Title: Multifarious Spatial Structure in a Compact Hard X-Ray Flare Authors: Harrison, R. A.; Vanbeek, H. F.; Hoyng, P.; Lafleur, H.; Simnett, G. M. Bibcode: 1980BAAS...12..911H Altcode: No abstract at ADS Title: A Study of the Impulsive Flares and Homologous Flares From AR2372 From April 6-13, Using Hard X-Ray Images Authors: Simnett, G. M.; Machado, M.; Harrison, R. A.; Hoyng, P.; Lafleur, H.; Svestka, Z.; Vanbeek, H. F. Bibcode: 1980BAAS...12S.899S Altcode: No abstract at ADS Title: Hard X-Ray Images of the Continuously Active Region 2478 from June 3-6, 1980 Authors: Fryer, R. J.; Hoyng, P.; Lafleur, H.; Simnett, G. M.; van Beek, H. V. Bibcode: 1980BAAS...12..892F Altcode: No abstract at ADS Title: Brief Report of Meeting - IAU / Solar Maximum Year Authors: Švestka, Zdenk; Van Hoven, Gerard; Hoyng, Peter; Kuperus, Max Bibcode: 1980SoPh...67..379S Altcode: No abstract at ADS Title: The hard X-ray imaging spectrometer (HXIS). Authors: van Beek, H. F.; Hoyng, P.; Lafleur, B.; Simnett, G. M. Bibcode: 1980SoPh...65...39V Altcode: The HXIS, a joint instrument of the Space Research Laboratory at Utrecht, The Netherlands, and the Department of Space Research of the University of Birmingham, U.K., images the Sun in hard X-rays: Six energy bands in energy range 3.5-30 keV, spatial resolution 8″ over Ø 2'40″ and 32″ over Ø 6'24″ field of view, and time resolution of 0.5-7 s depending on the mode of operation. By means of a `flare flag' it alerts all the other SMM instruments when a flare sets in and informs them about the location of the X-ray emission. The experiment should yield information about the position, extension and spectrum of the hard X-ray bursts in flares, their relation to the magnetic field structure and to the quasi-thermal soft X-rays, and about the characteristics and development of `type IV' electron clouds above flare regions. Title: A Model for Impulsive Electron Acceleration to Energies of Tens of Kt/e Authors: Hoyng, P.; Duijveman, A.; van Grunsven, T. F. J.; Nicholson, D. R. Bibcode: 1980IAUS...91..299H Altcode: No abstract at ADS Title: Energetic particles in solar flares Authors: Ramaty, R.; Paizis, C.; Colgate, S. A.; Dulk, G. A.; Hoyng, P.; Knight, J. W.; Lin, R. P.; Melrose, D. B.; Orrall, F.; Shapiro, P. R. Bibcode: 1980sfsl.work..117R Altcode: 1980sofl.symp..117R The various manifestations of energetic particles in solar flares are examined, and possible mechanisms for the acceleration of these particles are considered. Hard X-ray observations and possible mechanisms for the production of the dominant form of solar energetic particles, electrons with energies between 10 and 100 keV, are discussed, with consideration of thin-target models, thick-target models and thick-target models with reverse currents, and first-phase acceleration mechanisms for energetic electrons emitting impulsive microwave and fast-drift Type III radio bursts as well as impulsive hard X rays, which are detected themselves 20 min after the flare at 1 AU are considered. Radio evidence on the number, energy and pitch-angle distributions of energetic particles produced during solar flares is summarized, and observations at 1 AU of proton and electron energy spectra, the proton/electron ratio and energetic particle events rich in He-3 from solar flares are discussed. Finally, consideration is given to gamma-ray evidence of nuclear reactions in flares and white-light flares Title: Relaxation and bremsstrahlung of thick-target electron streams: a simple application of the Legendre expansion method. Authors: Hoyng, P.; Melrose, D. B.; Adams, J. C. Bibcode: 1979ApJ...230..950H Altcode: The Legendre series expansion of the three-dimensional equations for electron velocity and Langmuir wave distributions provides a numerical treatment for the relaxation of a stationary, axisymmetric electron stream in a homogeneous and fully ionized hydrogen plasma. Both quasilinear and Coulomb interactions figure in the treatment. The electrons are represented by a Fokker-Planck system of equations, which allows elimination of the distinction between background and stream electrons. A computation of the bremsstrahlung associated with the isotropic component of the electron distribution yields a simple model for radiation from thick-target electron streams, for example in impulsive hard X-ray emission from solar flares. Results of the study suggest power law-like bremsstrahlung spectra as they are often observed can be produced quite readily. Title: Practical use of the Legendre-expanded quasi-linear equations for anisotropic particles and Langmuir waves. Authors: Hoyng, P.; Stevens, G. A.; Melrose, D. B. Bibcode: 1979ApJ...230..961H Altcode: The Legendre expansion for the three-dimensional quasilinear equations for axisymmetric streams of particles and Langmuir waves is discussed. In particular, it is shown that a well-posed numerical problem based on the Legendre expansion can be defined for conditions equivalent to a decomposition into an arbitrary number of mutually coinciding one-dimensional streams of particles and waves. The difficulty of negative distribution functions occurring in the Legendre expansion has also proven tractable. The Legendre expansion method is applicable to the study of the suprathermal streams of electrons which occur frequently in astrophysical plasmas. Title: Energetic particles in solar flares. Chapter 4 in the proceedings of the 2nd SKYLAB Workshop on Solar Flares Authors: Ramaty, R.; Colgate, S. A.; Dulk, G. A.; Hoyng, P.; Knight, J. W., III; Lin, R. P.; Melrose, D. B.; Paizis, C.; Orrall, F.; Shapiro, P. R. Bibcode: 1978epsf.proc.....R Altcode: The recent direct observational evidence for the acceleration of particles in solar flares, i.e. radio emission, bremsstrahlung X-ray emission, gamma-ray line and continuum emission, as well as direct observations of energetic electrons and ions, are discussed and intercorrelated. At least two distinct phases of acceleration of solar particles exist that can be distinguished in terms of temporal behavior, type and energy of particles accelerated and the acceleration mechanism. Bulk energization seems the likely acceleration mechanism for the first phase while Fermi mechanism is a viable candidate for the second one. Title: Nonlinear Langmuir waves during type III solar radio bursts. Authors: Nicholson, D. R.; Goldman, M. V.; Hoyng, P.; Weatherall, J. C. Bibcode: 1978ApJ...223..605N Altcode: Type III solar radio bursts are thought to be associated with intense levels of electron-beam-excited Langmuir waves. The nonlinear evolution of these waves, in time and in two spatial dimensions, due to their coupling to other waves is studied numerically. For parameters appropriate to one-half the earth-sun distance, nonlinear effects are found to be important, as in previous one-dimensional work. However, a new and important phenomenon, two-dimensional soliton collapse, is found to occur. This collapse, induced directly by the wave-packet nature of the beam-excited waves, produces two-dimensional wave spectra extending over a much broader range of wave numbers than has been predicted by inhomogeneous quasi-linear theory. The results compare favorably with certain aspects of recent observations. The background magnetic field is neglected; while substantially justified for the present parameters, this neglect may require reexamination at locations closer to the sun. Title: Diagnostics of solar flare hard X-ray sources. Authors: Hoyng, P.; Knight, J. W.; Spicer, D. S. Bibcode: 1978SoPh...58..139H Altcode: The dynamics of hard X-ray producing electron beams in solar flares can be strongly affected by the occurrence of a reverse current. The parameter diagram for a beam can be divided into three regimes, one of which is the usual thick target case, the two others being due to two different possible consequences of the reverse current. The use of this parameter diagram as a possible diagnostic tool for solar flare hard X-ray sources is discussed, together with the necessary observations and their interpretation. Title: Legendre expansion of the quasi-linear equations for anisotropic particles and Langmuir waves. Authors: Hoyng, P.; Melrose, D. B. Bibcode: 1977ApJ...218..866H Altcode: The quasi-linear diffusion and friction coefficients for axisymmetric electron distributions interacting with Langmuir waves are evaluated explicitly by expanding the distribution of waves in Legendre polynomials. The quasi-linear equations are then reduced to a form in which both the distributions of waves and of particles are simultaneously expanded in Legendre polynomials, and all coefficients are evaluated explicitly. It is argued that such expansions are likely to be justified in practice and that the results obtained should prove useful in discussing quasi-linear relaxation under various conditions in three dimensions rather than one dimension. New results are anticipated for the problem of the propagation of electron streams causing type III solar radio bursts. The influence of the magnetic field on the Langmuir waves is neglected. Title: Book reviews Authors: Reijnen, G. C. M.; Ness, Norman F.; Kliore, Arvydas J.; Sonnenschein, F. J.; Hoogenboom, A. M.; Hack, Margherita; Johnson, F. S.; Reijnen, G. C. M.; Kleczek, J.; van Bueren, H. G.; de Graaff, W.; Hoyng, P.; Swider, W.; Grevesse, N. Bibcode: 1977SSRv...20..677R Altcode: No abstract at ADS Title: A two-component model of impulsive microwave burst emission consistent with soft and hard X rays. Authors: Boehme, A.; Fuerstenberg, F.; Hildebrandt, J.; Saal, O.; Krueger, A.; Hoyng, P.; Stevens, G. A. Bibcode: 1977SoPh...53..139B Altcode: A two-component (core-halo) emission model has been applied reconciling hard and soft X-ray burst emissions with the microwave burst radiation. The core region is represented by a nonthermal energy distribution (Maxwellian+power law tail) and assumed to be surrounded by a thermal halo. Parameters characterizing the energy distribution and emission measures have been derived numerically from soft and hard X-ray measurements. Using an artificial magnetic field model the microwave flux spectrum has been calculated on the basis of gyro-synchrotron emission and absorption by solving the equation of radiation transfer along the ray trajectories. Open parameters were used to adapt the spectrum to the radio measurements. Title: Radiation from a source in a cold magnetoactive plasma, re-examined. Application to cyclotron and multipole radiation Authors: Hoyng, P.; Stevens, G. A. Bibcode: 1977PhFl...20..520H Altcode: An analysis is presented of the radiation emitted by an arbitrary source embedded in a cold, magnetoactive plasma and physically distinct from the latter. The plasma is supposed to be infinite and homogeneous; its dielectric properties are described by a dielectric tensor ɛ. Expressions for the radiation fields are derived using the technique of Fourier decomposition. An expression for the vector potential is constructed and elaborated as far as possible for an arbitrary current source. The approach differs from that in previous work on technical points, the main one being the sequence in which the various integrations are carried out. The radiation flux is defined on the basis of Poynting's vector S; a distinction is made between current sources behaving as a given function of time and randomly fluctuating sources. In the latter case an ensemble average is preferred over a time average. A comparison is made with existing treatments in the literature, and a variety of defects is pointed out. The general result for the radiation flux is then specified for cyclotron radiation from a stationary ensemble of electrons and for multipole radiation. Throughout the paper a compact notation is used based on the work of Bremmer. Title: Book reviews Authors: Reijnen, G. C. M.; Kleczek, J.; Millman, Peter M.; Vesseur, H. J. A.; Bar-Nun, Akiva; de Jager, C.; van Albada, T. S.; Rawer, K.; Hinze, J. O.; Trümper, J.; de Jager, Cornelis; Müller, O.; Kovalevsky, J.; Hammerschlag, R. H.; Hoyng, Peter Bibcode: 1977SSRv...20..235R Altcode: No abstract at ADS Title: On the Nature of Impulsive Electron Acceleration in Solar Hard X-ray Flares. II. A Theory Authors: Hoyng, P. Bibcode: 1977A&A....55...31H Altcode: Summary. The suggestion is elaborated that shock wave generated Langmuir waves accelerate electrons in the adjoining plasma. Langmuir wave generation can be achieved in ion- acoustic unstable shocks by induced bremsstrahlung from electrons. A crude model analysis shows the Langmuir waves to have short wavelengths, k kD/4, while propagating almost parallel to the shock plane. It is possible that sufficient power in Langmuir waves is generated to explain the observed scale of electron acceleration. The evolution of the Langmuir wave distribution emerging from the shock is analyzed including the effects of spatial gradients. The initial stage is dominated by nonlinear Landau damping, which isotropizes the waves and increases their wavelengths, leading eventually to the onset of the modulational instability. Virtually all wave energy is now converted into fast electrons by Landau damping. Depending on parameters, these processes are completed within a distance of the order of 100 m from the shock. Next follows an extended nonthermal region in which fast electrons (+ selfconsistent level of Langmuir waves) slowly relax to thermal equilibrium. The length of this region is t0 -t0 km and depends among other factors, on the amount of fast electron scattering. The resulting fast electron velocity distribution is not discussed. However, there is hope for a universal distribution because strong wave-wave interactions take place before acceleration, while redistribution of energy between fast electrons occurs afterwards. Key words: solar flare hard X-rays shock wave stochastic acceleration parametric instability Title: On the nature of impulsive electron acceleration in solar hard X-ray flares. I. Inferences from observations. Authors: Hoyng, P. Bibcode: 1977A&A....55...23H Altcode: The nature of the impulsive electron acceleration regularly observed in solar flares is investigated on the basis of relevant observations, primarily in hard X-rays. Essential observational data are reviewed for flares that most clearly exhibit electron acceleration, the bremsstrahlung interpretation is adopted, and acceleration by a dc field or electron runaway is ruled out. Acceleration by collective wave-particle interactions is considered, with attention focused on Langmuir waves. It is proposed that Langmuir waves are most likely generated in the slow shock waves of Petschek's (1964) model of magnetic-field-line merging, after which they propagate outward and accelerate electrons in a relatively large volume. The generation mechanism of such waves in ion-acoustic turbulent shocks is then analyzed, and the question of electron acceleration is examined in some detail. The evolution of the Langmuir-wave distribution resulting in electron acceleration is computed along with the relaxation of the fast electrons back to thermal equilibrium. Title: High time resolution analysis of solar hard X-ray flares observed on board the ESRO TD-1A satellite. Authors: Hoyng, Peter; Brown, John C.; van Beek, H. Frank Bibcode: 1976SoPh...48..197H Altcode: The Utrecht solar hard X-ray spectrometer S-100 on board the ESRO TD-1A satellite covers the energy range above 25 keV with 12 logarithmically spaced channels. Continuous sun-pointing is combined with high time resolution: 1.2 s for the four low energy channels (25-90 keV) and 4.8 s for the others. It is emphasized that the instrument design and calibration yield data virtually free of pile-up and other instrumental defects. Title: An Error Analysis of Power Spectra Authors: Hoyng, P. Bibcode: 1976A&A....47..449H Altcode: Summary. An expression is derived for the uncertainty in the Fourier power spectrum due to noise present in the data. We consider both series with Poisson-distributed noise as well as with normal-distributed noise. The expressions for the errors involve only the power spectrum itself and they can be readily generalized to arbitrarily distributed noise. A working example is discussed. Key words: error analysis - power spectra - Fourier transform Title: Betatron acceleration in a large solar hard X-ray burst. Authors: Brown, J. C.; Hoyng, P. Bibcode: 1975ApJ...200..734B Altcode: The problem of diagnosing flare particle acceleration mechanisms from hard X-ray bursts is discussed, and it is argued that the electron trap model of bursts is more amenable to observational investigation at present than models of thick-target type. It is then shown that data for the large X-ray burst of 1972 August 4 are consistent with the source electrons being trapped in a very large vibrating coronal magnetic bottle. Furthermore, the observations show that the burst time profile is not dominated by collisional losses. It is proposed instead that the entire profile is essentially determined by betatron action of the varying trap field on the electrons. This betatron model is then analyzed in detail and shown to predict very well the observed correlation of electron flux and spectral index in this event when it is supposed that the electrons are initially produced by runaway in a direct electric field. Comparison of the model with observations permits inference of the approximate form of magnetic field evolution in the trap. Finally the physics behind this field evolution is briefly considered. Subject headings: flares, solar - X-rays, solar Title: Hard X-rays from the sun. Authors: van Beek, H. F.; Hoyng, P.; de Jager, C.; Stevens, G. A. Bibcode: 1975NTNA...41..101V Altcode: No abstract at ADS Title: High Time Resolution Analysis of Solar Flares Observed on the ESRO Td-Ia Satellite Authors: Hoyng, P.; Brown, J. C.; Stevens, G.; van Beek, H. F. Bibcode: 1975IAUS...68..233H Altcode: No abstract at ADS Title: Studies on hard X-ray emission from solar flares and on cyclotron radiation from a cold magnetoplasma Authors: Hoyng, P. Bibcode: 1975PhDT.........1H Altcode: This thesis proposes an interpretation of hard X-ray emission from solar flares and presents a theoretical study on the generation of cyclotron radiation by a source in a cold magnetically active plasma. Hard X-ray observations by the ESRO TD-1A satellite are analyzed, the solar flares of May 18 and August 4, 1972, are examined in detail, and a set of consistent parameters are derived for the flare of May 18 from observations of hard-X rays and simultaneously emitted centimeter radio waves. A model for the flare of August 4 is suggested in which a coronal magnetic trap is filled with fast electrons by some acceleration process, trap eigenmode oscillations are excited, and expansion occurs. It is proposed that electrons in ordinary solar flares are accelerated by resonant interactions with Langmuir waves generated in thin current sheets and propagating laterally from the sheets. In the cyclotron study, the radiation flux is defined on the basis of Poynting's vector, and an expression for the harmonic frequency is found which differs nontrivially from the one commonly used. Title: High time resolution analysis of solar flares observed on the ESRO TD-1A satellite. Authors: Hoyng, P.; Brown, J. C.; Stevens, G.; van Beek, H. F. Bibcode: 1975IAUS...68Q.233H Altcode: No abstract at ADS Title: High time resolution analysis of solar flares observed on the ESRO TD-1A satellite. Authors: Hoyng, P.; Brown, J. C.; Stevens, G.; van Beek, H. F. Bibcode: 1975IAUS...68R.233H Altcode: No abstract at ADS Title: Studies on hard X-ray emission from solar flares and on cyclotron radiation from a cold magnetoplasma. Authors: Hoyng, P. Bibcode: 1975UtrOv.311.....H Altcode: No abstract at ADS Title: On the Determination of the Photospheric Velocity Distribution from Profiles of Weak Fraunhofer Lines Authors: Rutten, R. J.; Hoyng, P.; de Jager, C. Bibcode: 1974SoPh...38..321R Altcode: We derive the conditions under which the profile of a weak Fraunhofer line can be described as the convolution of the separate profiles of damping, thermal and non-thermal motions at the average depth of formation of the line. The average velocity distribution along the line of sight, rather than its customary chosen macro- and micro-turbulent components, is then found from the deconvolution of the observed profile with the known other contributions. Reversely, the observed profiles can be compared to predicted profiles on the basis of De Jager's (1974) theoretical turbulence broadening curves. Title: On the Formation and Unfolding of Pulse Height Distributions Authors: Hoyng, P.; Stevens, G. A. Bibcode: 1974Ap&SS..27..307H Altcode: Spacecraft measurements of X-ray or particle pulse height distributions have become increasingly accurate during the last fifteen years, and they will continue to do so. The present paper deals with the question how one can reconstruct original photon or particle spectra from measured pulse height distributions. The statistical aspects of the formation of pulse height distributions are investigated. A method is presented that allows for a reliable reconstruction of the original spectrum. Its essentials are the formulation and subsequent solution of a matrix equation connecting pulse height distribution with photon/particle spectrum; an error analysis of the reconstructed spectrum is given. The present method has two advantages over the usualχ 2-minimum method: It is able to recover more spectral detail and it requires less computing time. Finally, a numerical example is given. Title: Interpretation of a Hard Solar X-Ray Burst Authors: Hoyng, P.; Stevens, G. A. Bibcode: 1973sari.conf...97H Altcode: No abstract at ADS