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Seminars (MSI)

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Event When Speaker Title Presentation Material
MSIW01 6th September 2004
11:30 to 12:35
R Rosner Stellar magnetic activity (overview)
MSIW01 6th September 2004
15:30 to 16:40
Introduction to MHD and dynamo theory I

Magnetic fields in astrophysics are generated by the inductive action of turbulence in the conducting fluid medium. This turbulence is usually generated by buoyancy forces and strongly influenced by coriolis effects, and in consequence 'lacks reflexional symmetry'; in particular, the mean helicity is nonzero, i.e. there is a correlation between velocity and vorticity fields. This property in general leads to an 'alpha-effect' in the fluid, whereby magnetic field grows on length-scales large compared with the dominant energy-containing scale of the turbulence. At the same time, the turbulent diffusivity controls the growth of the field. The primary problem of mean-field dynamo theory is to obtain reliable expressions for alpha and for the turbulent diffusivity in terms of the statistical properties and the magnetic Reynolds number of the turbulence. The first lecture will be concerned with this problem.

The second lecture will focus on dynamic back-reaction effects: as the magnetic field grows by turbulent dynamo action, the Lorentz force ultimately modifies the turbulence tending to reduce both alpha and turbulent diffusivity, until some kind of equilibrium is established, this equilibrium depending on the mechanism by which energy is supplied to the turbulence. Some aspects of this problem, which is the subject of much current debate, will be considered.

MSIW01 6th September 2004
16:40 to 17:05
Universal mechanism of dynamo saturation:dynamics of magnetic helicity

The nonlinear saturation mechanism based on the magnetic helicity evolution is discussed. It is shown that this universal mechanism is nearly independent of the form of the flux of magnetic helicity, and it requires only a nonzero flux of magnetic helicity. Different forms of the flux of magnetic helicity are discussed. We also studied a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We found a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic alpha-quenching. We compared the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstrate behaviour comparable with the observed phenomenology, provided that a suitable set of governing dynamo parameters is chosen. On the other hand, the observational data are shown to be rich enough to reject some other sets of governing parameters. We conclude that, in spite of the very preliminary state of the observations and the crude nature of the model, the idea of using observational data to constrain our ideas concerning magnetic field generation in the framework of the solar dynamo appears promising.

MSIW01 6th September 2004
17:05 to 17:30
Finite amplitude convection in rotating spherical fluid shells and its Prandtl number dependence
MSIW01 7th September 2004
09:00 to 10:10
Introduction to MHD and dynamo theory II

Magnetic fields in astrophysics are generated by the inductive action of turbulence in the conducting fluid medium. This turbulence is usually generated by buoyancy forces and strongly influenced by coriolis effects, and in consequence 'lacks reflexional symmetry'; in particular, the mean helicity is nonzero, i.e. there is a correlation between velocity and vorticity fields. This property in general leads to an 'alpha-effect' in the fluid, whereby magnetic field grows on length-scales large compared with the dominant energy-containing scale of the turbulence. At the same time, the turbulent diffusivity controls the growth of the field. The primary problem of mean-field dynamo theory is to obtain reliable expressions for alpha and for the turbulent diffusivity in terms of the statistical properties and the magnetic Reynolds number of the turbulence. The first lecture will be concerned with this problem.

The second lecture will focus on dynamic back-reaction effects: as the magnetic field grows by turbulent dynamo action, the Lorentz force ultimately modifies the turbulence tending to reduce both alpha and turbulent diffusivity, until some kind of equilibrium is established, this equilibrium depending on the mechanism by which energy is supplied to the turbulence. Some aspects of this problem, which is the subject of much current debate, will be considered.

MSIW01 7th September 2004
10:10 to 10:35
I Rogachevskii Effect of differential rotation on nonlinear mean electromotive force and stellar dynamos

An effect of the mean differential rotation on the nonlinear electromotive force is found. It includes a nonhelical $\alpha$ effect which is caused by a differential rotation, and it is independent of a hydrodynamic helicity. There is no quenching of this effect contrary to the quenching of the usual $\alpha$ effect caused by a hydrodynamic helicity. The nonhelical $\alpha$ effect vanishes when the rotation is constant on the cylinders which are parallel to the rotation axis. The mean differential rotation causes the "shear-current" effect. The ''shear-current" effect is associated with the $\bar{\bf W} {\bf \times} \bar{\bf J}$-term in the mean electromotive force and results in the generation of the mean magnetic field even in a nonhelical homogeneous turbulence (where $\bar{\bf W}$ is the mean vorticity caused by the differential rotation and $\bar{\bf J}$ is the mean electric current). The ''shear-current" effect changes its sign with the nonlinear growth of the mean magnetic field at some value $\bar{\bf B}_\ast$. The magnitude $\bar{\bf B}_\ast$ determines the level of the saturated mean magnetic field which is less than the equipartition field. However, there is no quenching of this effect. It is shown that the background magnetic fluctuations due to the small-scale dynamo enhance the "shear-current" effect, and reduce the magnitude $\bar{\bf B}_\ast$. When the level of the background magnetic fluctuations is larger than $1/3$ of the kinetic energy of the turbulence, the mean magnetic field can be generated due to the "shear-current" effect for an arbitrary exponent of the energy spectrum of the velocity fluctuations. These phenomena determine the nonlinear evolution of the stellar and solar large-scale magnetic fields. An effect of a uniform rotation on the nonlinear electromotive force is also studied. A nonlinear theory of the ${\bf \Omega} {\bf \times} \bar{\bf J}$ effect is developed, and the quenching of the hydrodynamic part of the $\alpha$ effect which is caused by a uniform rotation and inhomogeneity of turbulence, is found. Other contributions of a uniform rotation to the nonlinear electromotive force are also determined. All these effects are studied using the $\tau$-approximation (the Orszag third-order closure procedure). An axisymmetric mean-field dynamo is considered. Applications of these effects to the stellar and solar large-scale magnetic fields are discussed.

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MSIW01 7th September 2004
10:35 to 11:00
Magneto-rotational instability in the solar core and Ap star envelopes

The radiative core of the Sun rotates uniformly as suggested by helioseismological observations. It also rotates as slow as the average surface rotation. The pre-main squence Sun probably rotated much faster. If surface breaking has slowed down the Sun, a fast angular-momentum transport would be necessary to reduce the rotation rate of the core, too. Pure microscopic viscosiy is not sufficient. The problem of slow-down and equalizing of the core rotation is attributed to the magneto-rotational instability. Time-scales of 10-100 mill yr are found. A similar scenario may be possible in the radiative envelopes of Ap stars. Given their shorter life-times, the redistribution of angular momentum must be an ongoing process.

MSIW01 7th September 2004
11:25 to 12:30
What we know about stellar interiors (overview)
MSIW01 7th September 2004
15:30 to 16:40
AM Title Observations of magnetic fields on the Sun I

New and old techniques allow us to observe sunspots in a range of wavelengths, to determine the associated flow systems at a range of heights, to detect oscillations and waves and to determine the strength and angular distributions of their magnetic fields. This lecture will provide a selection of examples of processes associated with the sunspot phenomena. But rather that providing a comprehensive review, the goal of the talk is to raise questions

MSIW01 7th September 2004
16:40 to 17:05
A Voegler Decay of a simulated bipolar magnetic field in the solar surface layers

Using MURaM - a MHD code designed for applications in the solar photosphere and convection zone, we have studied the evolution of a mixed-polarity magnetic field in the surface layers of the Sun. The simulations, which have a horizontal extent of 6 Mm x 6 Mm and contain the visible surface around optical depth unity, include a detailed treatment of non-local radiative transfer effects in the photosphere in order to allow a direct comparison with observations. We discuss the time-evolution of magnetic structures and their statistical properties, present details of the flux-cancellation process and comment on its signatures in simulated observations of our numerical model. We show that the rate at which the field decays is consitent with the expected turbulent decay time scale and discuss the dependence of the decay rate on the initial conditions.

MSIW01 7th September 2004
17:05 to 17:30
YV Dumin Heating the stellar plasma in the transitional region from the inductive to drift freezing of magnetic field

Because of a dramatic variation in the plasma density along the radius of a star, the process of magnetic field freezing occurs there in two substantially different regimes: in the lower (collisional) layers it is caused by generation of circular currents , compensating variations of the magnetic field in the co-moving (with plasma) flux tubes; whereas in the upper (collisionless) layers the magnetic field freezing is maintained by synchronism of the plasma drift, due to a divergence-free character of the magnetic field and an electric equipotentiality of the magnetic field lines [e.g. Yu.V. Dumin, Solar Sys. Res., v.32, p.323 (1998)]. Transitional region between the two regimes of freezing is a natural place for reconstruction of the current systems and, therefore, the energy release. In the particular case of the Sun (where all parameters are known with a reasonable accuracy), predicted position of the transitional region corresponds very well to the zone of sharp temperature increase in the base of the solar corona [Yu.V. Dumin, Adv. Space Res., v.30, p.565 (2002)].

MSIW01 8th September 2004
09:00 to 10:10
Magnetic activity in rapidly rotating stars I
MSIW01 8th September 2004
10:10 to 10:35
Influence of external flows on the stability of magnetic flux tubes in a stellar convection zone

A fundamental question in connection with the dynamo mechanism is how to retain the magnetic flux in the convection zone (or below) for a time sufficiently long to be amplified by differential rotation. Magnetic buoyancy poses a serious problem, for it might lead to a rapid loss of magnetic flux from the convection zone and thus prevent the operation of the dynamo.

Apart from observations of the solar surface, there are indirect hints for the existence of a strong toroidal system of magnetic flux at the bottom of the solar convection zone. The concentration of magnetic flux into flux tubes has important consequences for its storage. In this context, the stability of toroidal flux tubes has been subject of research since the 1980's, starting with Spruit and van Ballegooijen (1982).

In this talk I will report on an ongoing investigation which extends previous research on the stability properties of a thin toroidal flux tube. A new feature is the inclusion of external velocity fields other than rotation; this is motivated by the necessity of including the effects of a meridional flow into the stability analysis.

MSIW01 8th September 2004
10:35 to 11:00
Connecting solar irradiance variability to the solar dynamo using the virial theorem

The variability of solar radiance over a solar cycle is thought the result of a delicate balance between the blocking effect of sunspots and the positive contribution of bright plage and network faculae. Although the net effect is small, it must imply structural changes of the Sun or partial layers of it as an unavoidable consequence of the virial theorem. Using a general form of the virial theorem for continua including the magnetic field it is shown, how solar radiance variability might be connected to a deeply seated flux-tube dynamo and how this connection is established on a hydrodynamical time-scale.

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MSIW01 8th September 2004
11:25 to 12:35
AM Title Observations of magnetic fields on the Sun II

New and old techniques allow us to observe sunspots in a range of wavelengths, to determine the associated flow systems at a range of heights, to detect oscillations and waves and to determine the strength and angular distributions of their magnetic fields. This lecture will provide a selection of examples of processes associated with the sunspot phenomena. But rather that providing a comprehensive review, the goal of the talk is to raise questions

MSIW01 9th September 2004
09:00 to 10:10
Magnetic activity in rapidly rotating stars II
MSIW01 9th September 2004
10:10 to 10:35
R Tavakol Dynamo models and differential rotation in sun and stars
MSIW01 9th September 2004
10:35 to 11:00
Different limiting mechanisms for nonlinear dynamos

Theoreticians often study nonlinear dynamos by postulating a specific force field designed to produce a flow which is known to give rise to an effective kinematic dynamo. The subsequent evolution is then followed numerically to determine how the dynamo equilibrates. The most studied example is the (1,1,1) ABC flow, with the supplied forcing proportional to the inverse kinetic Reynolds number. In this case, scaling arguments can be adduced which give very pessimistic estimates for the high Reynolds number performance of the dynamo. Recently Archontis (PhD thesis, 2000) found an interesting example of a dynamo where the performance is far superior, with approximately equal scaled magnetic and velocity fields which are very close to (sin z,sin x,sin y) when the kinetic and magnetic Reynolds numbers are large. Numerical results will be described which attempt to show how and why this and some similar dynamos work so well, and whether such behaviour can be expected in real astrophysical objects.

MSIW01 9th September 2004
11:25 to 12:35
Magnetoconvection I

In these lectures I give a description, starting from basic concepts, of the effects of magnetic fields on convection and of convection on the fields. The principal motivation for studying such interaction is given by observations of photospheric magnetic fields, which are manifested on a wide range of scales from the largest sunspots down to small network bright points.

In the first lecture I shall discuss the fundamental kinematics and dynamics of the interaction, with emphasis on simplified models to illustrate the main ideas, including flux concentration, horizontal scale selection, the occurrence of oscillations, and local evacuation. In the second lecture I shall focus on numerical models of various types, which aim to simulate observed behaviour in the Sun.

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MSIW01 9th September 2004
15:30 to 16:40
Young stars I

Young solar-type stars exhibit strongly enhanced levels of magnetic activity. In addition, a complex set of behaviors arise from the presence of circumstellar accretion disks with their own magnetic fields, along with the interaction between the stellar magnetic field and the disk. I will review the observational evidence for the star-disk-magnetosphere paradigm, discuss angular momentum regulation, and point out current theoretical challenges.

MSIW01 9th September 2004
16:40 to 17:05
Localised states in magnetoconvection

Convection in an imposed vertical magnetic field can lead to localised states in domains of large horizontal extent. This phenomenon can be seen as an instability of convection rolls that arises naturally from the fact that the magnetic flux through the layer is conserved. Nonlinear states in two dimensions can be found involving only a single convection cell (known as a "convecton") surrounded by almost stationary fluid, or, conversely, a single column of concentrated magnetic flux surrounded by convection cells. Similar localised solutions can be found when convection is oscillatory. In three dimensions, these states are unstable and the behaviour is usually time-dependent, but localisation can still occur.

MSIW01 9th September 2004
17:05 to 17:30
Large scale simulations of compressible convection

We present the results of three-dimensional direct numerical simulations of fully compressible polytropic turbulent convection in a very large aspect ratio ($\lambda=42.6$) cartesian box with $1024\times 1024\times 82$ mesh points. We investigate the general properties of this flow and discuss the similarities and differences between such an idealized experiment and the known properties of photospheric convection. We particularly focus on the emergence of large-scale coherent structures in the simulation and consider the potential implications of these results for the problem of the origin of mesogranular and supergranular flows and the large scale distribution of magnetic fields at the solar surface.

MSIW01 10th September 2004
09:00 to 10:10
Magnetoconvection II

In these lectures I give a description, starting from basic concepts, of the effects of magnetic fields on convection and of convection on the fields. The principal motivation for studying such interaction is given by observations of photospheric magnetic fields, which are manifested on a wide range of scales from the largest sunspots down to small network bright points.

In the first lecture I shall discuss the fundamental kinematics and dynamics of the interaction, with emphasis on simplified models to illustrate the main ideas, including flux concentration, horizontal scale selection, the occurrence of oscillations, and local evacuation. In the second lecture I shall focus on numerical models of various types, which aim to simulate observed behaviour in the Sun.

Related Links

MSIW01 10th September 2004
10:00 to 10:35
Modelling photospheric magnetoconvection in the weak field regime

High resolution observations can now provide detailed information regarding the complex interactions between convective motions and magnetic fields in the solar photosphere. This problem is investigated theoretically through numerical simulation of three dimensional compressible magnetoconvection in a large aspect ratio box. Attention is focused on the regime in which the imposed vertical magnetic field is relatively weak. Turbulent convection patterns and intermittent field structures are found. For a moderately weak imposed field, large elongated magnetic structures are found, similar to those found in plage regions on the solar surface. Decreasing the total magnetic flux further causes the magnetic structures to become almost point-like, similar to those seen in the quiet Sun. Calculation of the fractal dimension allows quantitative analysis of the surface distribution of the magnetic field. Although coming from idealised simulations, these results can be closely related to solar observations.

MSIW01 10th September 2004
10:35 to 11:00
Current status of facular region and sunspot models
MSIW01 10th September 2004
11:25 to 12:35
Young stars II

Young solar-type stars exhibit strongly enhanced levels of magnetic activity. In addition, a complex set of behaviors arise from the presence of circumstellar accretion disks with their own magnetic fields, along with the interaction between the stellar magnetic field and the disk. I will review the observational evidence for the star-disk-magnetosphere paradigm, discuss angular momentum regulation, and point out current theoretical challenges.

MSIW01 10th September 2004
15:30 to 16:40
Sunspots I

Sunspots provide the best test of magnetohydrodynamic theory under astrophysical conditions. Nowhere else in astrophysics is the theory confronted with such a wealth of detailed observations. Recent, remarkable advances in high-resolution observations provide us with key information that allows us to begin to assemble a coherent picture of the formation of a sunspot, its complicated magnetic and thermal structure, and associated flows and oscillations. Numerical simulations of nonlinear magnetoconvection are beginning to reproduce some of the fine structure observed in a sunspot, including umbral dots, penumbral grains, and light bridges. A new picture of penumbral structure has emerged from the observations, involving two components, with different magnetic field inclination, that remain essentially distinct over the lifetime of the spot. The darker component, in which the magnetic field is more nearly horizontal, includes "returning" magnetic flux tubes that dive back down below the solar surface near the outer edge of the penumbra. These arched flux tubes carry most of the photospheric Evershed flow, which can be attributed to siphon flows driven by pressure drops along thin flux tubes. The returning flux tubes and the curious "interlocking-comb" structure of the penumbral magnetic field can be understood to be a consequence of downward pumping of magnetic flux by the turbulent granular convection in the moat surrounding a sunspot. This robust flux-pumping mechanism, which has been demonstrated in three-dimensional numerical simulations of fully compressible convection, is an important key to understanding the formation and maintenance of the penumbra and the behavior of moving magnetic features in the moat.

Another key to understanding the structure of a sunspot is the array of characteristic oscillations observed in the umbra and penumbra, which serve as a probe of sunspot structure. The techniques of helioseismology have shown that sunspots absorb a significant fraction of the power in incident p-modes. This absorption seems to be due to a conversion of acoustic waves to slow magneto-acoustic waves that leak downward out of the p-mode cavity. Time-distance helioseismology has been used to detect flow patterns in the convection zone beneath a sunspot. A better understanding of the interaction between acoustic and magnetic-acoustic waves in realistic sunspot models is needed in order for the techniques of sunspot seismology to reach their full potential.

MSIW01 10th September 2004
16:40 to 17:05
AC Birch Forward modeling for local helioseismology

In order to interpret measurements made with local helioseismology it is crucial to understand the sensitivity of these measurements to different types of perturbations to a solar model. Local helioseismic measurements are sensitive not only to subsurface mass flows, sound-speed variations, and magnetic field, but also to local changes in the wave damping and excitation rates. I will show example calculations of the sensitivity of travel-times measured by time-distance helioseismology and phase shifts measured by acoustic holography to flows, sound speed perturbations, and local changes in the wave excitation and damping rates.

MSIW01 13th September 2004
09:00 to 10:10
Fine structure of solar magnetic fields
MSIW01 13th September 2004
10:10 to 10:35
Emergence of magnetic flux into the solar atmosphere: three dimensional experiments
MSIW01 13th September 2004
10:35 to 11:00
NH Brummell What is a magnetic flux tube?

Using 3D nonlinear MHD simulations, we examine the interaction of localised velocity shear and magnetic fields. We find that buoyant magnetic structures resembling flux tubes are generated by the interaction of induced magnetic buoyancy and the shear. Depending on the parameters, the generation process can result in steady (equilibrated) structures, or cyclic and chaotic emerging structures. By integrating along magnetic field lines and constructing return maps, we examine the relationship of these spontaneously-produced structures to the preconceived concept of a flux tube. We discuss how these results impact our simple ideas of a flux tube as an object with an inside and an outside whose dynamics are constrained by this assertion.

MSIW01 13th September 2004
11:25 to 12:35
Sunspots II

Sunspots provide the best test of magnetohydrodynamic theory under astrophysical conditions. Nowhere else in astrophysics is the theory confronted with such a wealth of detailed observations. Recent, remarkable advances in high-resolution observations provide us with key information that allows us to begin to assemble a coherent picture of the formation of a sunspot, its complicated magnetic and thermal structure, and associated flows and oscillations. Numerical simulations of nonlinear magnetoconvection are beginning to reproduce some of the fine structure observed in a sunspot, including umbral dots, penumbral grains, and light bridges. A new picture of penumbral structure has emerged from the observations, involving two components, with different magnetic field inclination, that remain essentially distinct over the lifetime of the spot. The darker component, in which the magnetic field is more nearly horizontal, includes "returning" magnetic flux tubes that dive back down below the solar surface near the outer edge of the penumbra. These arched flux tubes carry most of the photospheric Evershed flow, which can be attributed to siphon flows driven by pressure drops along thin flux tubes. The returning flux tubes and the curious "interlocking-comb" structure of the penumbral magnetic field can be understood to be a consequence of downward pumping of magnetic flux by the turbulent granular convection in the moat surrounding a sunspot. This robust flux-pumping mechanism, which has been demonstrated in three-dimensional numerical simulations of fully compressible convection, is an important key to understanding the formation and maintenance of the penumbra and the behavior of moving magnetic features in the moat.

Another key to understanding the structure of a sunspot is the array of characteristic oscillations observed in the umbra and penumbra, which serve as a probe of sunspot structure. The techniques of helioseismology have shown that sunspots absorb a significant fraction of the power in incident p-modes. This absorption seems to be due to a conversion of acoustic waves to slow magneto-acoustic waves that leak downward out of the p-mode cavity. Time-distance helioseismology has been used to detect flow patterns in the convection zone beneath a sunspot. A better understanding of the interaction between acoustic and magnetic-acoustic waves in realistic sunspot models is needed in order for the techniques of sunspot seismology to reach their full potential.

MSIW01 13th September 2004
15:30 to 16:40
Small-scale dynamos I

Small-scale dynamo action describes the generation of magnetic fields on scales comparable with, or smaller than the characteristic scale of the velocity. It is believed to occur quite naturally in turbulent fluids when the magnetic Reynolds number --- a dimensionless measure of the electrical conductivity --- is sufficiently high. In general terms dynamo action succeeds if, on average, field amplification exceeds field destruction. In a turbulent system, field generation is due to the stretching of field lines by the flow, while field destruction is due to enhanced diffusivity. In these lectures I will review some of the efforts to provide a quantitative description of these two processes. I will introduce ideas like the Lyapunov exponents and the topological entropy to measure the stretching rate, and the cancellation exponent to measure the rate of enhanced diffusion. I will also distinguish between dynamos driven by smooth velocities and dynamos driven by rough velocities, i.e. velocities that are strongly fluctuating on the scale at which magnetic reconnection occurs. Physically these two cases correspond to fluids whose magnetic Prandtl number---the ratio of the viscosity to the magnetic diffusivity---is larger (smooth case), or smaller (rough case) than unity.

MSIW01 13th September 2004
16:40 to 17:05
AG Kosovichev Helioseismic observations of magnetohydrodynamics of the solar interior

Observations of the Sun's interior with the MDI instrument on board the SOHO spacecraft has provided tremendous amount of new information about basic physical MHD processes inside the Sun, formation of magnetic structures in the solar plasma and mechanisms of solar and stellar activity. In particular, the new results have revealed the deep structure of sunspots and associated complicated patterns of plasma flows, the dynamics of the emerging magnetic flux and formation of active regions, the supergranular structure and dynamics of the upper convection zone, as well as the global structures and circulation patterns in the deep interior, evolving with the activity cycle. In addition, first attempts are made to find the links between the internal dynamics and processes of magnetic energy release in the solar corona. Understanding of these results, often puzzling and counter-intuitive, represents a major challenge for MHD theories of astrophysical plasma.

MSIW01 14th September 2004
09:00 to 10:10
Magnetohydrodynamics of stably stratified stars

Magnetic fields can be created in stably stratified (non-convective) layers in a differentially rotating star. A magnetic instability in the toroidal field (wound up by differential rotation) replaces the role of convection in closing the field amplification loop.Tayler instability is likely to be the most relevant magnetic instability. A dynamo model is developed from these ingredients, and applied to the problem of angular momentum transport in stellar interiors. It produces a predominantly horizontal field. This dynamo process is found to be more effective in transporting angular momentum than the known hydrodynamic mechanisms. It may account for the observed pattern of rotation in the solar core.

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MSIW01 14th September 2004
10:10 to 10:35
Photospheric MHD simulations of solar pores

We have performed simulations of solar pores using the MURaM -- Max-Planck Institute for Aeronomy, University of Chicago, RAdiative Magnetohydrodynamics -- code. The code is a MHD code and includes both radiative transfer and the effects of partial ionization, both of which are necessary for a realistic treatment of the photosphere. The simulations allow a direct comparison with observations to be made. We shall present such a comparison of the temperature structure, the magnetic and velocity fields, and the centre to limb variation of the intensity. Part of the value of this type of simulation is that the knowledge of the full state of the system allows the physics to be understood, and so we shall relate our comparison between the simulation and observation to the underlying physics.

MSIW01 14th September 2004
10:35 to 11:00
A Brandenburg Catastrophic alpha quenching alleviated by helicity flux and shear

A new simulation set-up is proposed for studying mean field dynamo action. The model combines the computational advantages of local cartesian geometry with the ability to include a shear profile that resembles the sun's differential rotation at low latitudes. It is shown that in a two-dimensional mean field model this geometry produces cyclic solutions with dynamo waves traveling away from the equator -- as expected for a positive alpha effect in the northern hemisphere. In three dimensions with turbulence driven by a helical forcing function, an alpha effect is self-consistently generated in the presence of a finite imposed toroidal magnetic field. The results suggest that, due to a finite flux of current helicity out of the domain, alpha quenching appears to be non-catastrophic -- at least for intermediate values of the magnetic Reynolds number. For larger values of the magnetic Reynolds number, however, there is evidence for a reversal of the trend and that $\alpha$ may decrease with increasing magnetic Reynolds number. Control experiments with closed boundaries confirm that in the absence of a current helicity flux, but with shear as before, alpha quenching is always catastrophic and alpha decreases inversely proportional to the magnetic Reynolds number. For solar parameters, our results suggest a current helicity flux of about 0.001 G^2/s. This corresponds to a magnetic helicity flux, integrated over the northern hemisphere and over the 11 year solar cycle, of about 10^{46}Mx^2.

Related Links

MSIW01 14th September 2004
11:25 to 12:35
Small-scale dynamos II

Small-scale dynamo action describes the generation of magnetic fields on scales comparable with, or smaller than the characteristic scale of the velocity. It is believed to occur quite naturally in turbulent fluids when the magnetic Reynolds number --- a dimensionless measure of the electrical conductivity --- is sufficiently high. In general terms dynamo action succeeds if, on average, field amplification exceeds field destruction. In a turbulent system, field generation is due to the stretching of field lines by the flow, while field destruction is due to enhanced diffusivity. In these lectures I will review some of the efforts to provide a quantitative description of these two processes. I will introduce ideas like the Lyapunov exponents and the topological entropy to measure the stretching rate, and the cancellation exponent to measure the rate of enhanced diffusion. I will also distinguish between dynamos driven by smooth velocities and dynamos driven by rough velocities, i.e. velocities that are strongly fluctuating on the scale at which magnetic reconnection occurs. Physically these two cases correspond to fluids whose magnetic Prandtl number---the ratio of the viscosity to the magnetic diffusivity---is larger (smooth case), or smaller (rough case) than unity.

MSIW01 14th September 2004
15:30 to 16:40
Internal rotation of the Sun I: Results from helioseismology

In this first of two lectures on the Sun's internal rotation and seismic probing of solar and stellar interiors, I shall review the results obtained with helioseismology regarding the internal rotation of the Sun, and compare those inferences with the results coming out of numerical simulations.

MSIW01 14th September 2004
16:40 to 17:05
Numerical simulations of small scale dynamo activity; spectra and critical magnetic Reynolds numbers

There is as yet no consensus on the appearance of the large Reynolds number energy spectrum of non-helical MHD turbulence without background field. We use direct numerical simulations with up to 1024^3 meshpoints, together with simulations with hyperdiffusion, in an attempt to see this large Reynolds number limit. We show that the energy spectra consist of a sub-inertial range, around the forcing wavenumber, where the magnetic energy is in sub-equipartition. At larger wavenumbers there is first a range where the magnetic energy is in super-equipartition, followed by a possible equipartition range with a k^(-5/3) slope, before we see a small bottleneck and the diffusive range at the smallest scales. We also investigate the critical magnetic Reynolds number (Rmc) for dynamo action. We find Rmc to be at a minimum for magnetic Prandtl numbers slightly above unity. For magnetic Prandtl numbers smaller than unity we find Rmc=Re^alpha, where alpha is 1/3 for magnetic Prandtl numbers larger than 1/8, and possibly 1 for smaller magnetic Prandtl numbers.

MSIW01 15th September 2004
09:00 to 10:10
Internal rotation of the Sun II

In the first lecture I considered the results from helioseismic probing of the Sun's internal rotation. In this lecture I focus on the theoretic and analytical methods used for making inferences about the rotation of the interior of the Sun and stars from seismological observations.

MSIW01 15th September 2004
10:10 to 10:35
Magnetic-field generation in low-magnetic-Prandtl-number plasmas

Magnetic Prandtl number Pm is a key parameter for astrophysical MHD fluids. The Pm>>1 regime is realised in high-temperature low-density plasmas of galaxies and clusters. It has been firmly established both theoretically and numerically that large-Pm turbulent plasmas can generate equipartition-level magnetic fluctuation energy via the small-scale dynamo. In numerical simulations, this regime qualitatively persists down to values of Pm~1 [astro-ph/0312046]. The plasmas in stellar (solar) convective zones and protostellar discsare denser and have low Pm. There is ample observational evidence that the solar photosphere contains large amounts of small-scale magnetic field. This field may be generated by small-scale dynamo or induced via shredding by turbulence of the large-scale ("mean") solar field --- or both. We have recently shown numerically that small-scale dynamo in the low-Pm is problematic: it either does not exist at all (i.e., there is a critical Pm_c) or requires extremely large magnetic Reynolds numbers (i.e., there is a critical Rm_c) numerically inaccessible at current resolutions [PRL 92, 054502 (2004)]. I will discuss these numerical results as well as report some new ones that improve on them. I will also discuss theoretical arguments in favour of and against the dynamo. I emphasise that there is no numerical or laboratory evidence available at present that would show that low-Pm turbulence is a dynamo, nor is there a physical scenario that would explain how such a dynamo is possible. In this context, small-scale magnetic fluctuations induced by a mean field acquire renewed relevance. While it is not possible to perform adequately resolved simulations that incorporate both the self-consistent generation of the large-scale fields and the small-scale turbulence, it is certainly possible to study the effect of an imposed mean field on the latter. I will report an extensive numerical study of the properties of induced small-scale fields (in nonhelical turbulence). Their possible role in explaining the photospeheric fields and in quenching the mean-field dynamo mechanisms will be discussed. Furthermore, these results are subject to direct comparison with experimental liquid-metal results of laboratory dynamo experiments in unconstrained geometries (e.g., Lyon, Maryland, and Wisconsin). Finally, I will present some analytical considerations on the interaction between large- and small-scale dynamo-generated magnetic fields in the case of large scale seprations between the system size, the turbulence scale, and the magnetic dissipation scale.

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MSIW01 15th September 2004
10:35 to 11:00
AS Brun Dynamo action in turbulent convective shells with or without rotation
MSIW01 15th September 2004
11:25 to 12:35
Solar and stellar dynamos I

These lectures will provide an introduction to the mathematics and physics underpinning research into solar and stellar dynamos. Here I will focus on the large scale fields generated in these stars.

In the first lecture I shall review the observations of large-scale magnetic activity in the Sun and other stars, including historical and proxy data. I shall then review the current paradigms for solar dynamo action discussing the physics behind both interface and flux transport dynamos

In the second lecture I shall review in detail the attempts to model solar and stellar dynamos, discussing large-scale computations, mean-field electrodynamics and illustrative low-order models. I shall discuss the limitations of each approach, and conclude by speculating on possible future avenues of research.

MSIW01 16th September 2004
09:00 to 10:10
Solar and stellar dynamos II

These lectures will provide an introduction to the mathematics and physics underpinning research into solar and stellar dynamos. Here I will focus on the large scale fields generated in these stars.

In the first lecture I shall review the observations of large-scale magnetic activity in the Sun and other stars, including historical and proxy data. I shall then review the current paradigms for solar dynamo action discussing the physics behind both interface and flux transport dynamos

In the second lecture I shall review in detail the attempts to model solar and stellar dynamos, discussing large-scale computations, mean-field electrodynamics and illustrative low-order models. I shall discuss the limitations of each approach, and conclude by speculating on possible future avenues of research.

MSIW01 16th September 2004
10:10 to 10:35
AA Ruzmaikin Non-axisymmetric solar magnetic fields

Solar magnetic activity tends to cluster at ``preferred" longitudes, which indicates the involvement of non-axisymmetric large-scale (mean) magnetic fields in the process of the activity formation. We investigate the generation of non-axisymmetric modes of the mean solar magnetic field and their coupling to the axisymmetric mode.

Our dynamo model incorporates the solar rotation reconstructed by inversion of helioseismic data in the convection zone and simulated distributions of the turbulent resistivity and the mean kinetic helicity. We demonstrate first that the dynamo breaks the axial symmetry by exciting non-axisymmetric modes even when all sources of generation are axisymmetric. Then we couple axisymmetric and non-axisymmetric modes using a non-axisymmetric addition to the mean helicity. Mathematically, it is done in the kinematic approximation without the use of a non-linear quenching.

We find that this coupling of non-axisymmetric and axisymmetric modes (1) reproduces the phase relation between these modes observed in the solar cycle; (2) the non-axisymmetric modes are localized near the base of the convection zone (thus influencing the formation of active regions) and appear near 30 degrees latitude.

MSIW01 16th September 2004
10:35 to 11:00
Non-axisymmetric solar interface dynamos
MSIW01 16th September 2004
11:25 to 12:35
Dynamo experiments I

The generation of a magnetic field by a flow of liquid sodium has been observed in recent experiments (Karlsruhe, Riga). We emphasize two very interesting features displayed by these experiments. - The observed dynamo threshold is in good agreement with the one computed from the mean flow alone, i. e. neglecting turbulent fluctuations although the kinematic Reynolds number is of order 105 to 106. - On the contrary, the mean magnetic field measured above dynamo threshold is 1000 times larger than the one predicted from a laminar weakly nonlinear calculation. We first understand these two observations and give the expected scaling law for the magnetic energy above dynamo threshold.

We then consider magnetic fluctuations above dynamo threshold or in MHD turbulence and report a Kolmogorov type spectrum in the inertial range and 1/f noise at low frequency.

Finally, we discuss the effect of turbulence and rotation on dynamo onset and saturation in flows without strong geometrical constraints.

MSIW01 16th September 2004
15:30 to 16:40
Direct simulation of planetary and stellar dynamos I: methods and results

The first computer simulations of convection and magnetic field generation in a 3D spherical fluid shell were made two decades ago in an attempt to understand the solar dynamo. Early on the Boussinesq equations were replaced with the anelastic equations to more realistically represent the density-stratified solar interior. Many more global models were developed during the past decade to simulate the geodynamo; however, most have employed the Boussinesq equations because of the relatively small density stratification of the Earth's fluid core. These simulations have demonstrated that thermal convection in a rotating electrically-conducting fluid shell can maintain a global magnetic field. Geodynamo simulations have produced fields that have intensity, structure and time dependence at the surface that are surprisingly similar to those of the geomagnetic field. However, one must question how realistic the dynamo mechanism is well below the surface in these simulations. The early solar convection simulations produced a surface equatorial acceleration similar to the sun's; but the internal differential rotation in those simulations was later shown not to agree with that inferred from helioseismology.

In this first talk I will briefly review some of the numerical models that have been employed in these 3D global simulations. Some example dynamo simulations for the sun, Jupiter and the Earth will be presented. However, because of insufficient computing resources, none of these simulations are strongly turbulent. The challenges for future generation models to overcome this limitation and others will be discussed in the second talk.

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MSIW01 16th September 2004
16:40 to 17:05
Nonlinear dynamo action in rotating convection and shear

(joint work with Pu Zhang, Andrew Soward, Keke Zhang).

Magnetic field amplification is studied in a rotating plane layer system. A shearing fluid flow is driven by motion of the bottom boundary and takes the form of an Ekman boundary layer. Above this layer, convection is driven. The combination of shear and convection amplifies magnetic field by means of an alpha-omega dynamo mechanism, and the saturation of magnetic fields is discussed by means of numerical simulations.

MSIW01 16th September 2004
17:05 to 18:15
Dynamo experiments II
MSIW01 17th September 2004
09:00 to 10:10
Direct simulation of planetary and stellar dynamos II: future challenges

The past two decades of 3D global simulations of convective dynamos have improved our understanding of how stars and planets generate their magnetic fields. However, no global dynamo simulation has yet been able to afford the spatial resolution required to simulate the turbulent convection which exists in the low-viscosity fluid interiors of these bodies. They have all employed greatly enhanced "eddy" diffusivities to crudely account for the transport and mixing by the small unresolved (subgrid scale) turbulence and to numerically stabilize the low resolution numerical solutions. Consequently convection in most numerical simulations has been laminar with spatial scales comparable to the size of the convection zone instead of being a broad spectrum of anisotropic heterogeneous turbulence. Many dynamo simulations have also ignored density stratification, which is a major source of vorticity in rotating turbulent convection. So, how robust are the results of the current models? We will not know until next-generation dynamo models are run at much higher spatial resolution and much lower viscosity, which will require more computational resources and improved numerical methods. In the mean time we can get some insight by testing 2D models, which, although lack the correct geometry, can simulate strong turbulence within a large density stratification. Current 2D tests reveal important issues regarding convective penetration, gravity waves, Alfven waves and the maintenance of differential rotation.

MSIW01 17th September 2004
10:10 to 10:35
Numerical simulations of the solar tachocline
MSIW01 17th September 2004
10:35 to 11:00
Comparison of three-dimensional geodynamo calculations with mean-field models

Mean-field theory has been proven to be a useful description of stellar dynamos. It provides a conceptual understanding of the induction mechanisms that lead to the generation of large-scale magnetic field in stellar interiors. Our aim is to test the validity and reliability of mean-field theory by a comparison of three-dimensional geodynamo calculations with corresponding mean-field models. Therefore, we calculated the full \(\alpha\) and \(\beta\) tensors with the help of three-dimensional MHD-simulations. The resulting mean-field coefficients are confirmed by an independent analytical calculation that is applicable under the first-order-smoothing approximation. In a second step, we used these coefficients in a mean-field model and compared the results with three-dimensional calculations. Basic characteristics of the geodynamo benchmark-model,"case1", were reproduced by our mean-field model. Applied to this example, mean-field theory is a valid approximation. The investigation to which extent the mean-field approach is correct for more complicated dynamos and which of the mean-field coefficients are most important is work in progress.

MSI 21st September 2004
10:00 to 11:30
Parameter dependence of convection in spherical shells and its dynamo action
MSI 23rd September 2004
10:00 to 11:30
Planetary dynamos
MSI 28th September 2004
10:00 to 11:30
K Shibata Modelling magnetic activity in the sun, stars and accretion discs
MSI 30th September 2004
10:00 to 11:30
D Galloway Different limiting mechanisms for nonlinear dynamos: a more detailed account.
MSI 5th October 2004
10:00 to 11:30
R Rosner Validating astrophysical simulations
MSI 7th October 2004
14:30 to 16:00
N Hurlburt Modeling Magnetoconvection in active regions
MSIW02 11th October 2004
11:25 to 12:35
Computational MHD: A model problem for widely separated time and space scales (Chair: R Rosner)

The numerical simulaton of the dynamics of magnetized plasmas is among the most challenging problems in computational physics. Strongly magnetized plasmas are characterized widely separated space and time scales, and by extreme anisoptopy. All of these issues affect the design of algorithms. The fundamental mathematical description requires the simultaneous solution of the 6-dimensional kinetic equation along with Maxwell's equations. This is impossible in all but the very simplest cases, so reduced fluid models can be derived by taking velocity moments of the kinetic equation and assuming a closure condition. Different closure assumptions result in different fluid models. MHD is the simplest of these, although by no means universally applicable. MHD appears to be an excellent model for the dynamics of stellar interiors, where the problem reduces to computing large Reynolds' number turbulence. Memory and speed limitations of even the most powerful computer then dictate a further reduction by means of averaging and statistical closures to capture the effect of the sub-grid scale dynamics on the long wave length motions. There is no concensus on the form of these closures. For the case of low density, high temperature, strongly magnetized plasmas, as occur in laboratory fusion experiments, MHD is clearly not a good model on the smallest scales, and the closure problem becomes one of characterizing non-local kinetic effects in a local transport formalism. This is also an unsolved problem, so in both cases it can be said that there is no agreement on what equations to solve. Because of the differing plasma parameters in these 2 cases, different algorithms must be applied. The audience is already familiar with techniques for computing MHD turbulence. Here we will primarily be concerned with methods developed to simulate ther long time scale dynamics of highly magnetized plasmas, as occur in fusion plasmas and the solar corona. Methods of spatial and temporal differencing will be discussed, and examples of the computed dynamics of laboratory and coronal plasmas will be given. Limitations on the scope of simulations for the foreseeable future will be given. Perhaps some of the issues discussed here will also prove to be useful for stellar interiors.

MSIW02 11th October 2004
15:30 to 16:40
Planetary convection and dynamos (Chair: N Weiss)

The past decade has seen enormous progress in numerical modelling of planetary dynamos. In this talk I will review some of this work, the numerical techniques that are used, and some of the physics that makes this problem so difficult. I will also compare and contrast the situation in planets versus other astrophysical objects, and try to explain why quite different numerical techniques are often used in the planetary context.

MSIW02 11th October 2004
16:40 to 17:05
DNS of anisotropic MHD flows (Chair: N Weiss)

We will present preliminary results of the direct numerical simulation of the incompressible MHD problem. The system is forced at large-scale and an external magnetic field $B_0 \hat{z}$ is applied. Anisotropy is studied in terms of the decomposition group for rotation in $3D$, the so-called $SO(3)$ group. Similarities and differences with the anisotropic pure hydrodynamical case will be discussed.

MSIW02 11th October 2004
17:05 to 17:30
Convective instabilities in pre-runaway white dwarfs (Chair: N Weiss)

Studying the evolution of the convective burning process before and during the thermonuclear runaway in a white dwarf is crucial in order to measure the enrichment of the hydrogen envelope by convective overshoot. Recent numerical simulations, that start when the temperature at the base of the envelope is close to 10^8 K, show that in a few hundreds seconds the temperature grows up to 2 10^8 K. At this time the runaway takes place. Our simulations, performed by running a high order of accuracy code, with low numerical viscosity, show that care must be taken in the choice of the initial and boundary conditions. We have observed, in fact, the onset of fast convective instabilities that are driven by boundary effects and affect the dynamics of the pre-runaway phase. We plan, as a next step, to take the initial equilibrium with a peak of temperature close to 10^7 K, that corresponds to earlier and less unstable phase of the white dwarf evolution.

MSIW02 12th October 2004
09:00 to 10:10
Staggered mesh approaches to MHD- and charged-particle simulations of astrophysical turbulence (Chair: DJ Galloway)

I will discuss the computational techniques behind recent modeling of MHD-turbulence in several astrophysical context; e.g. supersonic and super-Alfvenic turbulence in the interstellar medium and molecular clouds, subsonic MHD-turbulent in strongly stratified stellar surface layers, magnetic dissipation in the solar corona, and relativistic turbulence in collisionless shocks.

The computational techniques we have applied in all of these circumstances are related to the more conventional (Godunov-inspired) techniques in much the same way that RISC-technology relates to CISC-technology in the context of CPU-design; we attempt to minimize the number of floating point operations per meshpoint update, and hence to maximize the number of meshpoint updates per CPU per second, while still retaining a high spatial and temporal order of the updates, and the ability to capture and resolve shocks and current sheets.

I will also briefly describe the extension of these techniques to the modeling of relativistic charged particles with a particle-in-mesh (PIC) code, with which it is possible to obtain a grid resolution comparable to reasonably serious MHD-simulations; publications have already appeared based on runs with of the order of 30 million mesh points and a billion particles.

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MSIW02 12th October 2004
10:10 to 10:35
NH Brummell Magnetic field transport in turbulent compressible convection (Chair: DJ Galloway)

Magnetic field transport is essential to certain elements of the solar dynamo scenario. It is crucial (a) to move poloidal field from the convection zone to the tachocline relatively quickly, and (b) to transport the magnetic structures created in the tachocline through the convection zone towards the solar surface, for the current dynamo paradigm to work. Here, we examine the competition between magnetic buoyancy and magnetic pumping mechanisms in such situations via high resolution numerical simulations of turbulent compressible penetrative magnetoconvection.

MSIW02 12th October 2004
10:35 to 11:00
PLUTO: a modular code for computational astrophysics (Chair: DJ Galloway)

PLUTO is a modular, Godunov-type code intended mainly for astrophysical applications. Written in C, it currently supports classical, relativistic and magneto fluid dynamics modules in curvilinear coordinates in 1, 2 and 3 dimensions. Implementation of the relativistic MHD equations has been recently added. The code is particularly suitable for treating hypersonic flows with strong discontinuities, and several numerical algorithms (TVD, PPM) are available for testing. Source terms include gravity, rotations and optically thin radiative losses. PLUTO works on non-uniform grids and runs either on a single processor or on parallel architectures (using MPI libraries), and has been extensively used on Beowulf clusters (16 and 32 nodes) for 3D relativistic jet applications, accretion on compact objects and accretion disks problems.

MSIW02 12th October 2004
11:25 to 12:35
Astrophysical dynamos (Chair: DJ Galloway)
MSIW02 12th October 2004
15:30 to 16:40
Global modelling of solar convection, differential rotation and magnetism (Chair: MRE Proctor)
MSIW02 12th October 2004
16:40 to 17:05
M Browning Simulations of core convection and resulting dynamo action rotating A-type stars (Chair: MRE Proctor)

We present the results of 3--D nonlinear simulations of magnetic dynamo action by core convection within A-type stars of 2 solar masses, at a range of rotation rates. We consider the inner 30% by radius of such stars, with the spherical domain thereby encompassing the convective core and a portion of the surrounding radiative envelope. The compressible Navier-Stokes equations, subject to the anelastic approximation, are solved to examine highly nonlinear flows that span multiple scale heights, exhibit intricate time dependence, and admit magnetic dynamo action. Small initial seed magnetic fields are found to be amplified greatly by the convective and zonal flows, ultimately yielding fields that possess structure on many scales, are strong enough to modify the flows themselves, and persist for as long as we have continued our calculations. The central columns of strikingly slow rotation found in some of our progenitor hydrodynamic simulations continue to be realized in some simulations to a lesser degree, with such differential rotation arising from the redistribution of angular momentum by the nonlinear convection and magnetic fields. We assess the properties of the magnetic fields thus generated, the extent of convective penetration, and the excitation of gravity waves within the radiative envelope, as a number of simulation parameters are varied.

MSIW02 12th October 2004
17:05 to 17:30
Mach number dependence of the onset of dynamo action (Chair: MRE Proctor)

The effect of compressibility on the onset of nonhelical turbulent dynamo action is investigated using both direct simulations as well as simulations with shock-capturing viscosities, keeping however the regular magnetic diffusivity. It is found that the critical magnetic Reynolds number for the onset of dynamo activity increases from about 35 in the subsonic regime to about 70 in the supersonic regime. Although the shock structures are sharper in the high resolution direct simulations compared to the low resolution shock-capturing simulations, the magnetic field looks roughly similar in both cases and does not show shock structures. Similarly, the onset of dynamo action is not significantly affected by the shock-capturing viscosity.

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MSIW02 13th October 2004
09:00 to 10:10
R Klein Verification and validation of astrophysical radiation-hydrodynamics (Chair: JM Stone)

The development of sophisticated multi-dimensional self-gravitational radiation hydrodynamic codes in astrophysics has brought important focus onto the verification and the validation of the physical models within the codes as well the integrated codes themselves. In this lecture I shall discuss new methodologies we have developed embodying high order accurate techniques to solve the three-dimensional equations of self-gravitational radiation hydrodynamics using adaptive mesh refinement. I will discuss the astrophysics of strongly coupled radiation hydrodynamic flows in two problems of great current interest; the development of photon bubble instabilities in neutron star atmospheres and accretion disks and the problem of high mass star formation. I will then discuss various approaches to the verification of the equations and the algorithms including the testing of hydrodynamics, radiation transport and coupled radiation hydrodynamics. I shall then describe laboratory experiments we have conducted to validate the component physics of both the radiation and the hydrodynamics in the code and novel work I am engaged in to design an experiment on ultraintense petawatt lasers to simulate for the first time, photon bubbles in the laboratory.

MSIW02 13th October 2004
10:10 to 10:35
Modelling of relativistic magnetically dominated plasmas (Chair: JM Stone)

Many phenomena of relativistic astrophysics involve flows of magnetically dominated plasma which are somewhat difficult for analytical and numerical modelling. In this talk we describe three closly related mathematical frameworks used in recent studies of black hole magnetospheres, namely resistive electrodynamics, magnetodynamics, and magnetohydrodynamics, focusing on their advantages and limitations. Particular attention is paid to numerical aspects revealed in recent simulations.

MSIW02 13th October 2004
10:35 to 11:00
AA Schekochihin Turbulence in magnetized plasma: do we understand and can we simulate Braginskii viscosity? (Chair: JM Stone)

In low-density high-temperature astrophysical plasmas, e.g., intracluster gas, protogalaxies, the ion Larmor radius is much smaller than the mean free path already for very weak magnetic fields. In this regime, while the magnetic field may not yet be dynamically important, plasma is magnetised and the adiabatic invariant is approximately coserved. This leads to the anisotropisation of the pressure (viscous stress) tensor, so the the viscous dissipation along and across the field is different. When pressure is anisotropic, there appear very fast plasma instabilities. Their growth rates are proportional to the parallel wavenumber of the perturbation, so small-scale fluctuations grow at very small scales and with growth rates that far exceed the rate of strain of the turbulent eddies. The instabilities are not fully suppressed by either Braginskii viscosity or, in the collisionless regime, by the magnetic Landau damping. The stabilisation only occurs at scales somewhat above the ion cyclotron radius, where plasma is no longer perfectly magnetised. I will present a theoretical description of these instabilities both for collisional MHD with Braginskii viscosity and in the collisionless regime. Estimates are made for the effective magnetic cutoff scale. I will also discuss the feasibility of numerical simulations of MHD with Braginskii viscosity and report on some preliminary numerical studies.

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MSIW02 13th October 2004
11:25 to 12:35
E Mueller Supernovae and numerical (R)MHD: challenges and developments (Chair: JM Stone)

After reviewing the current paradigm of core collapse supernova physics, the delayed neutrino driven explosion mechanism, possible effects of magnetic fields on the dynamics of core collapse supernovae are discussed. In order to simulate such effects robust and accurate MHD or RMHD schemes for multi-dimensional supersonic flow are required. To this end some interesting developments in numerical (R)MHD will be addressed. Finally, recent results from magneto-rotational core collapse simulations are presented, and future developments in the field are pointed out.

MSIW02 14th October 2004
09:00 to 10:10
Kinetic modeling of magnetic reconnection in space and astrophysical systems (Chair: PH Diamond)

The large scale dynamics of magnetized plasma systems are typically modeled with the MHD equations. However, the MHD description typically breaks down at spatial scales where dissipation is required to either break magnetic field lines, allowing reconnection to occur, or to locally dissipate energy. In the case of magnetic reconnection, the Hall MHD model has been found to accurately reproduce the rates of reconnection determined by kinetic modeling, a consequence of the role of dispersive waves in reconnection. However, critical issues in space and astrophysics remain that require a kinetic description and at the same time have significant consequences for the description of the large-scale dynamics of plasma systems. After reviewing the recent kinetic model of fast reconnection, I will focus on two generic topics, electron heating and kinetic scale turbulence and its role in driving reconnection. Nearly half of the magnetic energy released in solar flares is channeled into energetic electrons and recent observations in the magnetosphere confirm that reconnection can directly drive electrons to near relativistic energies. Simulations reveal that reconnection leads to the formation of extended density cavities that map the magnetic separatrices and support a finite parallel electric field. These cavities act as electron accelerators and as a result of multiple passses through these acceleration cavities electrons quickly reach relativistic energies. In boundary layers of the magnetosphere, where large-scale parallel electric fields are expected from modeling, parallel electric fields take the form of intense, spatially-localized, bipolar structures (electron holes) and double-layers. These are manifestly kinetic nonlinear structures where electrons and ions can directly exchange energy with large scale fields. Simulations of reconnection reveal the self-consistent development of these structures, facilitating the exploration of their role in providing the dissipation required to drive reconnection.

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MSIW02 14th October 2004
10:10 to 10:35
3D simulation of emerging flux and magnetic reconnection using the Earth Simulator (Chair: PH Diamond)

The Earth Simulator is a parallel vector supercomputer system of the distributed-memory type, installed at the Earth Simulator Centre, in Yokohama, Japan. It has been at the position of the world's fastest supercomputer since 2002. After some introduction of the Earth Simulator, we present the results of three dimensional MHD simulation of solar emerging flux and magnetic reconnection carried out on the Earth Simulator. In the case of emregence of magnetic sheet, we found that filamentary structure arised due to Rayleigh-Taylor instability. Then many filamentary current sheets were formed in the emerging flux, supporting the iear that the corona are heated by dissipation of small scale current sheets. We also found that magnetic reconnection between the emerging flux and the coronal field occurs in spatially intermittent way. We also present some preliminary result of the case of emerging twisted flux tube and its reconnection with ambient field.

MSIW02 14th October 2004
10:35 to 11:00
R Keppens Grid-adaptive simulations of magnetized jet flows (Chair: PH Diamond)

We present high resolution numerical simulations of magnetized plasma jets,modeled by means of the compressible magnetohydrodynamic equations. The computations employ Adaptive Mesh Refinement, which makes it possible to investigate long-term jet dynamics where both large-scale and small-scale effects are at play. We first discuss recent findings for periodic single shear flow layers at moderate Mach numbers (around unity) and large plasma beta values. In such cases, a trend to large scales occurs by continuous pairing/merging between adjacent vortices, simultaneously with the introduction of small-scale features by magnetic reconnection events. The vortices form as a result of Kelvin-Helmholtz unstable shear flow layers, and their coalescence arises from the growth of subharmonic modes at multiple wavelengths of the fastest growing Kelvin-Helmholtz instability. Extensions to 2D jets investigate how varying jet width alters the coalescence process occuring at both edges, e.g. by introducing bachelor coupling between vortices formed at opposing weakly magnetized, close shear layers. Finally, periodic segments of supersonic magnetized jets are simulated in two and three dimensional cases, which are characterized by violent shock-dominated transients.

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MSIW02 14th October 2004
11:25 to 12:35
Large scale simulations of astrophysical turbulence (Chair: PH Diamond)

In hydrodynamic and hydromagnetic turbulence simulations, high spatial and temporal accuracy is of the essence. This is why pseudo-spectral methods are to be preferred. However, because of their intrinsic nonlocality, such methods are not well suited for massively parallel machines. In this talk the Pencil Code will be discussed, which uses sixth order finite differences for various types of turbulence simulations at resolutions up to 1024 cubed meshpoints on up to 256 processors: forced turbulence, shear flow turbulence due to the magneto-rotational instability, and convection. For simulations in spheres the physically interesting domain is embedded in a box. Some important results will be discussed and also the issue of code maintenance, development by many people and code validation will be addressed.

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MSIW02 14th October 2004
15:30 to 16:40
Non-ideal MHD and beyond (Chair: NE Hurlburt)
MSIW02 14th October 2004
16:40 to 17:05
A numerical scheme for multi-fluid MHD (Chair: NE Hurlburt)

In this talk I shall describe a numerical scheme for multi-fluid hydrodynamics in the limit of small mass densities of the charged particles. The inertia of the charged particles can then be neglected, which makes it possible to write an evolution equation for the magnetic field that can be solved using an implicit scheme. This avoids the severe restriction on the stable timestep that would otherwise arise at high resolution, or when the Hall effect is large. Numerical tests show that the scheme can accurately model steady multi-fluid shock structures both with and without sub-shocks. Although the emphasis is on shocks in molecular clouds, a multi-dimensional version of this code could be applied to any Astrophysical flow in which ambi-polar diffusion or the Hall effect, or both play a significant role.

MSIW02 14th October 2004
17:05 to 17:30
A new CT-Godunov MHD algorithm with application to the MRI (Chair: NE Hurlburt)

In recent years there has been an increased emphasis on applying high order Godunov-type algorithms to the system of ideal MHD. This is motivated by their strong shock capturing and their conservation properties which make them ideally suited for use in combination with adaptive mesh refinement. Such efforts, however, have traditionally met with difficulty owing to the divergence free constraint on the magnetic field. We describe a new, unsplit MHD Godunov-type integration algorithm which uses the Constrained Transport approach to ensure the divergence free character of the magnetic field. The algorithm includes two novel features, 1) the incorporation of MHD source terms in the PPM-type reconstruction procedure and 2) an upwind CT-algorithm for combining the Godunov fluxes to calculate the electric fields needed for CT. We present test calculations comparing this algorithm against previously published results. Finally, we apply this algorithm to the study of the MRI including radiative cooling.

MSIW02 14th October 2004
17:30 to 17:55
DS Balsara Amplification of interstellar magnetic fields by supernova-driven turbulence (Chair: NE Hurlburt)

Several lines of evidence suggest that magnetic fields grow rapidly in protogalactic and galactic environments. However, mean field dynamo theory has always suggested that the magnetic fields grow rather slowly, taking of order a Hubble time to reach observed values. The theoretical difficulties only become worse when the system has a high magnetic Reynold’s number, as is the case for galactic and protogalactic environments. The discrepancy can be reconciled if fast processes for amplifying magnetic field could operate. Following Balsara, Benjamin & Cox (2001), we show that an interstellar medium that is dominated by realistic energy input from supernova explosions will naturally become a strongly turbulent medium with large positive and negative values of the kinetic helicity. Even though the medium is driven by compressible motions, the kinetic energy in this high Mach number flow is mainly concentrated in solenoidal rather than compressible motions. These results stem from the interaction of strong shocks with each other and with the interstellar turbulence they self-consistently generate in our model. Moreover, this interaction also generates large kinetic helicities of either sign. The turbulent flow that we model has two other characteristics of a fast dynamo: magnetic energy growth independent of scale, and with a growth time that is comparable to the eddy turn-over time. This linear phase of growth permits the field to grow rapidly until the magnetic energy reaches about 1% of the kinetic energy. At that stage, other astrophysical processes for producing magnetic fields can take over. Energetics, power spectra, statistics and structures of the turbulent flow are studied here. Shock-turbulence interaction is shown to be a very general mechanism for helicity generation and magnetic field amplification with applicability to damped Ly-a systems, protogalaxies, the Galaxy, starburst galaxies, the inter-cluster medium and molecular clouds.

MSIW02 15th October 2004
09:00 to 10:10
Simulations of astrophysical jets (Chair: A Ruzmaikin)

Collimated supersonic flows are present in many different astrophysical contexts ranging from Young Stellar Objects to Active Galactic Nuclei. Simulations of these flows have to take into account several different physical effects like, for example, radiative losses in jets from Young Stellar Objects or relativistic effects in jets from Active Galactic Nuclei. These simulations have to address the issues of the jet formation, collimation and propagation and I will give an overview of their main problems and results.

MSIW02 15th October 2004
10:10 to 10:35
Short and long term simulations of relativistic magnetized jets (Chair: A Ruzmaikin)

We will present a series of numerical simulations addressed to understand the morphology and dynamics of relativistic, magnetized, axisymmetric jets. Some of the simulations have been specifically set up to follow the long term evolution of extragalactic jets under idealized conditions. The simulations have been done with an extension of the GENESIS code (Aloy et al 1999a} suitable for relativistic magnetohydrodynamcs applications. The code is based on a Godunov-type scheme whose building block is a method of lines. The numerical algorithm can provide up to third order of accuracy and makes use of a constrained transport method in order to keep the divergence--free condition of the magnetic field.

MSIW02 15th October 2004
10:35 to 11:00
A Ferrari AMR simulations of supersonic magnetized jet acceleration from accretion discs (Chair: A Ruzmaikin)

We present a 2.5D magnetohydrodynamic (MHD) simulation of the acceleration of a collimated jet from a magnetized accretion disk employing a MHD code with Adaptive Mesh Refinement (FLASH code -- University of Chicago). Thanks to this tool we can follow the evolution of the system for many dynamical timescales with a high spatial resolution. Assuming an initial condition in which an equilibrium Keplerian disk is threaded by a uniform azimuthal magnetic field, we show how both the accretion inflow and the acceleration of the outflow occur and we present in great detail which are the forces responsible for the launch and the collimation of the jet. Our simulation also shows how the collimating forces due to the self-generated toroidal magnetic field can produce some peculiar knotty features.

MSIW02 15th October 2004
11:25 to 12:35
J Hawley The magneto-rotational instability (Chair: A Ruzmaikin)

Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in differentially rotating systems. The key conceptual point is that the combination of a subthermal magnetic field and outwardly decreasing differential rotation rapidly generates magnetohydrodynamical (MHD) turbulence via the magnetorotational instability. With the aid of supercomputers, it is now possible to study accretion disk turbulence at a level comparable to that of stellar convection. This talk will present a review of this instability and the MHD turbulence it generates, and some recent results from fully three-dimensional global disk simulations.

MSI 19th October 2004
10:00 to 11:30
Dynamical tides and wave attractors in rotating fluid bodies
MSI 21st October 2004
10:00 to 11:30
Dynamics associated with the inner core tangent cylinder
MSI 26th October 2004
10:00 to 11:30
Long dynamo waves
MSI 28th October 2004
10:00 to 11:30
Helicity and helicity fluxes in turbulent dynamos
MSI 2nd November 2004
10:00 to 11:30
Towards two-dimensional stellar models: a non-perturbative approach to rapidly rotating stars
MSI 4th November 2004
10:00 to 11:30
Passive scalar decay in simple mappings
MSIW03 8th November 2004
10:00 to 11:00
DO Gough Review of observational results
MSIW03 8th November 2004
11:25 to 12:45
Panel discussion of the observations led by J Christensen-Dalsgaard (Aarhus)
MSIW03 8th November 2004
15:30 to 16:30
Theoretical issues raised by the tachocline
MSIW03 8th November 2004
16:30 to 17:30
Discussion led by MJ Thompson (Sheffield) Interactions between theory and observations
MSIW03 9th November 2004
09:00 to 10:00
Magnetic confinement of the tachocline
MSIW03 9th November 2004
10:00 to 11:00
Solar tachocline dynamics
MSIW03 9th November 2004
11:30 to 12:00
Dynamics of the fast solar tachocline
MSIW03 9th November 2004
12:00 to 12:45
Discussion led by NO Weiss (DAMTP, Cambridge)
MSIW03 9th November 2004
15:30 to 16:00
Shellular turbulence in the Earth's atmosphere
MSIW03 9th November 2004
16:00 to 17:00
Turbulence in the tachocline
MSIW03 9th November 2004
17:00 to 17:45
Discussion led by HC Spruit (MPA, Garching)
MSIW03 10th November 2004
09:00 to 10:00
PA Gilman Hydrodynamic and magnetohydrodynamic instabilities in the tachocline
MSIW03 10th November 2004
10:00 to 11:00
Magnetic buoyancy instabilities and shear in the tachocline
MSIW03 10th November 2004
11:30 to 12:45
Discussion led by PS Cally (Monash, Melbourne)
MSIW03 11th November 2004
09:00 to 10:00
Angular momentum transport by magnetohydrodynamic turbulence
MSIW03 11th November 2004
10:00 to 11:00
Discussion led by PH Diamond (UCSD) Transport and transport barriers in the tachocline
MSIW03 11th November 2004
11:30 to 12:30
The solar dynamo and the tachocline
MSIW03 11th November 2004
15:30 to 17:30
Discussion led by SM Tobias (Leeds)
MSIW03 12th November 2004
09:00 to 10:00
R Rosner What have we learnt? Where do we go from here?
MSI 16th November 2004
10:00 to 11:30
The solar dynamo as a model of the solar cycle
MSI 18th November 2004
10:00 to 11:30
Acoustics of surface magnetic fields
MSI 23rd November 2004
10:00 to 11:00
Aspects of mean field dynamo theory
MSI 23rd November 2004
16:30 to 17:30
The role of mathematics in Newton's natural philosophy
MSI 25th November 2004
10:00 to 11:00
P Diamond Transport barriers
MSI 30th November 2004
10:00 to 11:30
A Ferriz Mas Some comments on the use of Chandrasekhar's adiabatic exponents in compressible hydrodynamics
MSI 2nd December 2004
10:00 to 11:15
J Beer Long-term solar variability derived from cosmogenic radionuclides
MSI 2nd December 2004
11:30 to 12:45
Modulation of cyclic activity in the Sun
MSIW05 6th December 2004
11:00 to 11:45
Plasmas in the laboratory and in astrophysics
MSIW05 6th December 2004
12:00 to 12:45
Helioseismology and the rotation of the sun
MSIW05 6th December 2004
14:30 to 15:15
The strange properties of sunspots
MSIW05 6th December 2004
15:30 to 16:15
Magneto-shear instabilities in stars
MSIW05 6th December 2004
16:45 to 17:30
Magnetic fields in galaxies
MSI 7th December 2004
10:00 to 10:40
Shear barriers
MSI 7th December 2004
10:40 to 10:55
Near-wall structures
MSI 7th December 2004
10:55 to 11:10
B Kerr Non-linear models
MSI 7th December 2004
11:25 to 11:40
N Kevlahan RDT of near-wall turbulence
MSI 7th December 2004
12:00 to 12:40
Mean-field MHD
MSI 7th December 2004
12:40 to 13:00
Passive scalar diffusion
MSI 7th December 2004
14:00 to 14:20
Scaling in MHD turbulence
MSI 7th December 2004
14:40 to 15:20
C Vassilicos Two-particle diffusion
MSI 7th December 2004
15:40 to 15:55
Passive scalars and coherent structures
MSI 7th December 2004
15:55 to 16:10
Diffusion of inertial particles
MSI 7th December 2004
16:10 to 16:25
Scalar dissipation rates
MSI 9th December 2004
10:30 to 11:30
The structure of small-scale magnetic flux tubes
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons