Author name code: ossendrijver ADS astronomy entries on 2022-09-14 author:"Ossendrijver, Mathieu" year:1990-2010 ------------------------------------------------------------------------ Title: Magnetoconvection and dynamo coefficients. III. α-effect and magnetic pumping in the rapid rotation regime Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Stix, M. Bibcode: 2006A&A...455..401K Altcode: 2006astro.ph..2111K Aims.The α- and γ-effects, which are responsible for the generation and turbulent pumping of large scale magnetic fields, respectively, due to passive advection by convection are determined in the rapid rotation regime corresponding to the deep layers of the solar convection zone.
Methods.A 3D rectangular local model is used for solving the full set of MHD equations in order to compute the electromotive force (emf), E = overline {u × b}, generated by the interaction of imposed weak gradient-free magnetic fields and turbulent convection with varying rotational influence and latitude. By expanding the emf in terms of the mean magnetic field, Ei = aij overline B_j, all nine components of aij are computed. The diagonal elements of aij describe the α-effect, whereas the off-diagonals represent magnetic pumping. The latter is essentially the advection of magnetic fields by means other than the underlying large-scale velocity field. Comparisons are made to analytical expressions of the coefficients derived under the first-order smoothing approximation (FOSA).
Results.In the rapid rotation regime the latitudinal dependence of the α-components responsible for the generation of the azimuthal and radial fields does not exhibit a peak at the poles, as is the case for slow rotation, but at a latitude of about 30°. The magnetic pumping is predominantly radially down- and latitudinally equatorward as in earlier studies. The numerical results compare surprisingly well with analytical expressions derived under first-order smoothing, although the present calculations are expected to lie near the limits of the validity range of FOSA.
Title: Alpha-Effect and Turbulent Pumping In The Rapid Rotation Regime - Implications For Solar Dynamo Models Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Stix, M.; Tuominen, I. Bibcode: 2006IAUJD...8E..46K Altcode: We use local 3D convection calculations to compute the alpha-effect and turbulent pumping of mean magnetic fields in the rapid rotation regime corresponding to the deep layers of the solar convection zone. We find that in this regime the alpha-effect responsible for generating the poloidal field out of the toroidal one peaks at around latitude 30 degrees, in contrast to the slow rotation case and the often adopted prescription in mean-field models of the solar dynamo, where the maximum values are found at the poles. Furthermore, the turbulent pumping of mean fields is predominantly down- and equatorward. We find that the downward pumping is decreased near the equator for rapid rotation and can be upward for the toroidal field component. In order to investigate the implications of the obtained local results for the problems in mean-field dynamo theory arising from the helioseismically determined solar rotation profile, namely the poleward migration of activity belts at low latitudes and the activity being concentrated at too high latitudes, we introduce the alpha-effect and turbulent pumping as they were found in the local calculations into a kinematic mean-field model of the solar dynamo. We also investigate the effect of a one-cell counter-clockwise meridional flow pattern on the dynamo solutions. We find that using the alpha-effect and turbulent pumping adapted from the results of the local calculations, the migration of the activity belts is equatorward also at low latitudes. When the meridional flow is added, the activity belts are shifted further closer to the equator, and a poleward migration belt appears at high latitudes. With all the effects included, the activity still appears at too high latitudes (5...60 degrees). Other remaining problems include the somewhat too short cycle periods for the solar-like dipole solutions. Title: Local models of stellar convection. III. The Strouhal number Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Tuominen, I. Bibcode: 2006A&A...448..433K Altcode: 2004astro.ph.10586K Aims.The Strouhal number (St), which is a nondimensional measure of the correlation time, is determined from numerical models of convection. The Strouhal number arises in the mean-field theories of angular momentum transport and magnetic field generation, where its value determines the validity of certain widely used approximations, such as the first order smoothing (hereafter FOSA). More specifically, the relevant transport coefficients can be calculated by means of a cumulative series expansion if St < Stcrit ≈ 1.Methods.We define the Strouhal number as the ratio of the correlation and turnover times, which we determine separately, the former from the autocorrelation of velocity, and the latter by following test particles embedded in the flow.Results.We find that the Strouhal numbers are, generally, of the order of 0.1 to 0.4 which is close to the critical value above which deviations from FOSA become significant. Increasing the rotational influence tends to shorten both timescales in such a manner that St decreases. However, we do not find a clear trend as a function of the Rayleigh number for the parameter range explored in the present study. Title: Transport coefficients for solar and stellar dynamos Authors: Ossendrijver, M.; Käpylä, P. J. Bibcode: 2006IAUS..233....3O Altcode: The large-scale magnetic field of the Sun and solar-type stars is probably generated near the interface of the radiative core and the convection zone. One of the well-known difficulties of interface-type and other dynamo models is to explain the latitudinal distribution of magnetic fields as observed on the Sun. In this contribution new results of numerical MHD simulations of transport coefficients of magnetic fields in the rapid rotation regime, relevant for the base of the solar convection zone, are presented that may contribute to explaining the latitudinal distribution of magnetic fields observed on the Sun. A brief outlook on further numerical simulations of transport coefficients and their relevance for mean-field dynamo theory is given. Title: Approaching the solar dynamo Authors: Ossendrijver, Mathieu Bibcode: 2006AdSpR..38..832O Altcode: The origin of the solar magnetic field remains a stubborn challenge of astrophysics. At the solar surface the magnetic field assumes a complex, hierarchical structure in space and time. Systematic features such as the solar cycle and the butterfly diagram point to the existence of a deep-rooted large-scale predominantly toroidal magnetic field. In this review of solar dynamo theory new developments in our understanding of processes relevant for the solar dynamo are discussed. In recent years there has been significant progress with regard to tachocline physics, magnetic helicity conservation, the α effect, magnetic pumping, and the storage and amplification of the magnetic field. Remaining uncertainties about the nature of the deep-seated magnetic field and the α effect have thus far prevented the formulation of a coherent model for the solar dynamo. It is proposed that further progress is best achieved through a combination of approaches including high-resolution numerical simulations and global mean-field modeling. Along these lines some recent numerical simulations of magnetic pumping and flux expulsion in a magnetic layer are presented. The computations were performed with a new anelastic Cartesian finite-difference MHD code, which is the appropriate tool for studying processes near the base of stellar convection zones with a high spatial resolution. Possible implications for the solar dynamo are discussed. Title: Estimates of the Strouhal number from numerical models of convection Authors: Käpylä, P. J.; Korpi, M. J.; Ossendrijver, M.; Tuominen, I. Bibcode: 2005AN....326..186K Altcode: 2004astro.ph.10587K We determine the Strouhal number (hereafter St), which is essentially a nondimensional measure of the correlation time, from numerical calculations of convection. We use two independent methods to estimate St. Firstly, we apply the minimal tau-approximation (MTA) on the equation of the time derivative of the Reynolds stress. A relaxation time is obtained from which St can be estimated by normalising with a typical turnover time. Secondly, we calculate the correlation and turnover times separately, the former from the autocorrelation of velocity and the latter by following test particles embedded in the flow. We find that the Strouhal number is in general of the order of 0.1 to 1, i.e. rather large in comparison to the typical assumption in the mean-field theories that St ≪ 1. However, there is a clear decreasing trend as function of the Rayleigh number and increasing rotation. Furthermore, for the present range of parameters the decrease of St does not show signs of saturation, indicating that in stellar convection zones, where the Rayleigh numbers are much larger, the Strouhal number may indeed be significantly smaller. Title: The dynamo layer in solar-type stars Authors: Ossendrijver, M. Bibcode: 2005AN....326..166O Altcode: The role of the dynamo layer for dynamo action in solar-type stars is discussed. As a result of instabilities, magnetic flux is expelled from the dynamo layer into the convection zone above it. The resulting partial evacuation of the dynamo layer and amplification of the deep-seated toroidal magnetic field is investigated in an illustrative 3D numerical simulation. The simulation is performed with a finite-difference code that solves the anelastic MHD equations for a Cartesian geometry. It is found that the field strength in the dynamo layer is amplified by a factor of up to about 7. Title: Understanding the solar dynamo Authors: Ossendrijver, M. Bibcode: 2004cosp...35.3775O Altcode: 2004cosp.meet.3775O The solar magnetic field continues to be an outstanding challenge of astrophysics. At the solar surface the magnetic field assumes a complex, hierarchical structure consisting of widely different spatial and temporal scales. Systematic features such as the solar cycle and the butterfly diagram point to the existence of a deep-rooted large-scale magnetic field, subject to variability on widely different timescales. At the other end of the spatial scale are magnetic elements and mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the α effect, field amplification by differential rotation and other mechanisms, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated magnetic field and the α effect have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of current dynamo models favors a buoyancy-driven or distributed scenario. It is proposed that progress in understanding the solar dynamo is best achieved through a combination of approaches including high-resolution numerical simulations and global mean-field modeling. Title: Book Review: ADVANCES IN NONLINEAR DYNAMOS / Taylor and Francis, 2003 Authors: Ossendrijver, Mathieu Bibcode: 2003SoPh..218..359O Altcode: No abstract at ADS Title: What can we learn from Local Convection Simulations in the Context of mean Field Models of Stellar Rotation and Magnetism? Authors: Käpylä, Petri J.; Korpi, Maarit J.; Ossendrijver, Mathieu; Stix, Michael Bibcode: 2003ANS...324...63K Altcode: 2003ANS...324..I02K No abstract at ADS Title: Do spherical α2-dynamos oscillate? Authors: Rüdiger, G.; Elstner, D.; Ossendrijver, M. Bibcode: 2003A&A...406...15R Altcode: 2002astro.ph.12203R The question of whether kinematic alpha 2-shell-dynamos are able to produce a cyclic activity is addressed. The alpha -effect is allowed to be latitudinally inhomogeneous and anisotropic but it is assumed as radially uniform in the turbulent shell. For a symmetric alpha -tensor we only find oscillatory solutions if i) the alpha -tensor component alpha zz vanishes or is of the opposite sign as alpha phi phi , ii) the alpha -effect is strongly concentrated in the equatorial region and iii) the alpha -effect is concentrated in a rather thin outer shell. In the other cases almost always the nonaxisymmetric field mode S1 (which slowly drifts along the azimuthal direction) possesses the lowest critical dynamo number. The uniform but anisotropic alpha -effect (e.g. alpha zz = 0) leads to nonaxisymmetric solutions as is experimentally confirmed by the Karlsruhe dynamo installation. One of the antisymmetric parts of the alpha -tensor, however, plays the role of differential rotation in the induction equation. Using the results of a numerical simulation for the alpha -tensor of the solar convection zone for the radial profile of this effect, one finds the possibility of oscillating alpha 2-dynamos even without the existence of a real nonuniform rotation law. Compared with the results of numerical simulations of the full alpha -tensor, the amplitude of the antisymmetric part of the tensor must be artifically increased by only a factor of three in order to find oscillating solutions. Title: Anelastic Simulations of Convection and Magnetic Fields in Cartesian Geometry Authors: Ossendrijver, Mathieu Bibcode: 2003ANS...324...64O Altcode: 2003ANS...324..I03O No abstract at ADS Title: Crisis-induced intermittency due to attractor-widening in a buoyancy-driven solar dynamo Authors: Ossendrijver, M.; Covas, E. Bibcode: 2003IJBC....8.2327O Altcode: In a recent paper [M. A. J. H. Ossendrijver, A&A, 359, 364 (2000)] numerical simulations of a 2D mean-field model where shown to produce grand minima, typical of the long-term behavior of solar magnetic activity. The model consisted of dynamo that features an alpha effect based on the buoyancy instability of magnetic fluxtubes, which gives rise to the switching back and forth from grand minima to ``regular'' solar behavior. In this Letter, we report evidence from a time-series analysis of the model for the presence of crisis induced intermittency due to attractor-widening. We support this finding by showing that the average duration of the minima, , follows the theoretically predicted scaling ~ (C-C*)^(gamma), where C is the bifurcation parameter of interest, together with other statistical evidence. As far as we are aware, this is the first time concrete and detailed evidence has been produced for the occurrence of this type of crisisinduced intermittency -- due to attractor widening - for such dynamo models. Title: The Solar Dynamo: A Challenge for Theory and Observations (Invited review) Authors: Ossendrijver, M. Bibcode: 2003ASPC..286...97O Altcode: 2003ctmf.conf...97O No abstract at ADS Title: The solar dynamo Authors: Ossendrijver, Mathieu Bibcode: 2003A&ARv..11..287O Altcode: The solar dynamo continues to pose a challenge to observers and theoreticians. Observations of the solar surface reveal a magnetic field with a complex, hierarchical structure consisting of widely different scales. Systematic features such as the solar cycle, the butterfly diagram, and Hale's polarity laws point to the existence of a deep-rooted large-scale magnetic field. At the other end of the scale are magnetic elements and small-scale mixed-polarity magnetic fields. In order to explain these phenomena, dynamo theory provides all the necessary ingredients including the α effect, magnetic field amplification by differential rotation, magnetic pumping, turbulent diffusion, magnetic buoyancy, flux storage, stochastic variations and nonlinear dynamics. Due to advances in helioseismology, observations of stellar magnetic fields and computer capabilities, significant progress has been made in our understanding of these and other aspects such as the role of the tachocline, convective plumes and magnetic helicity conservation. However, remaining uncertainties about the nature of the deep-seated toroidal magnetic field and the α effect, and the forbidding range of length scales of the magnetic field and the flow have thus far prevented the formulation of a coherent model for the solar dynamo. A preliminary evaluation of the various dynamo models that have been proposed seems to favor a buoyancy-driven or distributed scenario. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches including local numerical experiments and global mean-field modeling. Title: The solar dynamo: a challenge for theory and observation Authors: Ossendrijver, Mathieu Bibcode: 2002ESASP.506..797O Altcode: 2002svco.conf..797O; 2002ESPM...10..797O The theory of the solar dynamo is reviewed with an emphasis on recent advances of numerical simulations, and the possible consequences for various dynamo scenarios. The solar dynamo poses a challenge to both theoreticians and observers. Theoreticians are plagued by the forbidding range of length scales in the solar convection zone, which has thus far prevented succesful global MHD dynamo calculations in spherical geometry. Observers have access only to the surface magnetic field, which has been studied in great detail. While some observations (solar cycle, butterfly diagram, Hale's polarity laws) provide clues about the deep-rooted large-scale magnetic field, the diagnostic value of other surface observations for the solar dynamo is less easily established. With the increased of computer capabilities, significant advances have been made through local simulations in our understanding of various aspects of the solar dynamo. From box simulations of magnetoconvection, transport coefficients for the large-scale mean field have been estimated, and these can serve as input information for global models. Several alternative dynamo scenarios for the generation of the large-scale magnetic field coexist. They differ mainly with regard to the nature of the α-effect. The viewpoint proposed here is that progress in understanding the solar dynamo and explaining the observations can be achieved only through a combination of approaches which include local numerical experiments as well as global mean-field modeling. Title: Magnetoconvection and dynamo coefficients. II. Field-direction dependent pumping of magnetic field Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A.; Rüdiger, G. Bibcode: 2002A&A...394..735O Altcode: 2002astro.ph..2299O We study the pumping of magnetic flux in three-dimensional compressible magnetoconvection in the context of stellar dynamos. The simulation domain represents a rectangular section from the lower part of a stellar convection zone plus the underlying stably stratified layer, with a total depth of up to five pressure scale heights. Once convection has attained a statistically stationary state, a magnetic field is introduced. The magnetic field is subsequently modified by the convective motions, and the resulting pumping effects are isolated by calculating various coefficients of the expansion of the electromotive force, /line{u}x{b}, in terms of components of the mean magnetic field. The dependence of the pumping effects on rotation, latitude and other parameters is studied. First numerical evidence is found for the existence of pumping effects in the horizontal directions. Evidence is found that the pumping effects act differently on different components of the mean magnetic field. Latitudinal pumping is mainly equatorward for a toroidal field, and can be poleward for a poloidal field. Longitudinal pumping is mainly retrograde for the radial field but prograde for the latitudinal field. The pumping effect in the vertical direction is found to be dominated by the diamagnetic effect, equivalent to a predominating downward advection with a maximum speed in the turbulent case of about 10% of the rms convective velocity. Where possible, an attempt is made to identify the physical origin of the effect. Finally, some consequences of the results for stellar dynamos are discussed. 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: Magnetoconvection and dynamo coefficients:. Dependence of the alpha effect on rotation and magnetic field Authors: Ossendrijver, M.; Stix, M.; Brandenburg, A. Bibcode: 2001A&A...376..713O Altcode: 2001astro.ph..8274O We present numerical simulations of three-dimensional compressible magnetoconvection in a rotating rectangular box that represents a section of the solar convection zone. The box contains a convectively unstable layer, surrounded by stably stratified layers with overshooting convection. The magnetic Reynolds number, Rm, is chosen subcritical, thus excluding spontaneous growth of the magnetic field through dynamo action, and the magnetic energy is maintained by introducing a constant magnetic field into the box, once convection has attained a statistically stationary state. Under the influence of the Coriolis force, the advection of the magnetic field results in a non-vanishing contribution to the mean electric field, given by <vec{u}xvec{b}>. From this electric field, we calculate the alpha -effect, separately for the stably and the unstably stratified layers, by averaging over time and over suitably defined volumes. From the variation of alpha we derive an error estimate, and the dependence of alpha on rotation and magnetic field strength is studied. Evidence is found for rotational quenching of the vertical alpha effect, and for a monotonic increase of the horizontal alpha effect with increasing rotation. For Rm~ 30, our results for both vertical and horizontal alpha effect are consistent with magnetic quenching by a factor [1+Rm (B0/Beq)2]-1. The signs of the small-scale current helicity and of the vertical component of alpha are found to be opposite to those for isotropic turbulence. Title: Crisis-induced intermittency due to attractor-widening in a buoyancy-driven solar dynamo Authors: Covas, Eurico; Ossendrijver, Mathieu Bibcode: 2001nlin......7007C Altcode: In a recent paper [M. A. J. H. Ossendrijver, A&A {\bf 359}, 364 (2000)] numerical simulations of a 2D mean--field model where shown to produce grand minima, typical of the long-term behavior of solar magnetic activity. The model consisted of dynamo that features an $\alpha$ effect based on the buoyancy instability of magnetic fluxtubes, which gives rise to the switching back and forth from grand minima to ``regular'' solar behavior. In this Letter, we report evidence from a time-series analysis of the model for the presence of crisis--induced intermittency due to attractor--widening. We support this finding by showing that the average duration of the minima, $<\tau>$, follows the theoretically predicted scaling $<\tau> \sim (C_{\delta\alpha}-C_{\delta\alpha}^*)^{-\gamma}$, where $C_{\delta\alpha}$ is the bifurcation parameter of interest, together with other statistical evidence. As far as we are aware, this is the first time concrete and detailed evidence has been produced for the occurrence of this type of crisis--induced intermittency -- due to attractor widening -- for such dynamo models. 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: Grand minima in a buoyancy-driven solar dynamo Authors: Ossendrijver, M. A. J. H. Bibcode: 2000A&A...359..364O Altcode: Numerical simulations of a 2D mean-field model are presented which show that grand minima, typical for the long-term behaviour of solar magnetic activity, can be produced by a dynamo that features an alpha effect based on the buoyancy instability of magnetic fluxtubes. The buoyancy-driven alpha effect functions only if the magnetic field strength exceeds a minimal value necessary for instability. It opens the possibility of dynamo action within the solar overshoot layer, where a strong magnetic field, B~ 105 G, is thought to be stored. The existence of a magnetic threshold for dynamo action can lead to interruptions of the magnetic cycle, similar to the grand minima of solar activity. Transitions across the instability threshold are triggered by magnetic-flux injections from the convection zone. This is modelled by allowing for a small-scale kinematic alpha effect in the convection zone, and convective downdrafts that penetrate the overshoot layer. Title: The dynamo effect of magnetic flux tubes Authors: Ossendrijver, M. A. J. H. Bibcode: 2000A&A...359.1205O Altcode: It is shown that toroidal magnetic flux tubes in a rotating star do not provide a net dynamo effect, even if they are subject to random forcing, unless the tubes are unstable to small displacements. The dynamo effect is produced by transverse helical waves that propagate along the flux tube, resulting in an electric current (anti-) parallel to the unperturbed magnetic field, equivalent to an alpha effect. For unstable flux tubes, the alpha effect is enabled by a systematic phase difference between the velocity and magnetic field perturbations. For stable flux tubes subject to random forcing, phase differences do occur, but they vanish in the mean. The requirement for instability is met if the magnetic field strength exceeds a threshold value. Therefore a stellar dynamo based on flux tubes is not self-excited, but needs triggering until the magnetic threshold is surpassed. Title: The α-Effect of Toroidal Fluxtubes and its Application in a Mean-Field Solar Dynamo Authors: Ossendrijver, M. Bibcode: 1999ASPC..178..127O Altcode: 1999sdnc.conf..127O 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: Book Review: The cosmic dynamo / Kluwer, 1993 Authors: Ossendrijver, M.; Ossendrijver, M. Bibcode: 1994SoPh..155..207O Altcode: 1994SoPh..155..207K No abstract at ADS