Showing papers by "Steven Cowley published in 2006"

Astrophysical Gyrokinetics: Basic Equations and Linear Theory

Abstract: Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of astrophysical plasmas, including accretion disks, the solar wind, and the interstellar and intracluster medium. On small scales, this turbulence is often expected to consist of highly anisotropic fluctuations with frequencies small compared to the ion cyclotron frequency. For a number of applications, the small scales are also collisionless, so a kinetic treatment of the turbulence is necessary. We show that this anisotropic turbulence is well described by a low-frequency expansion of the kinetic theory called gyrokinetics. This paper is the first in a series to examine turbulent astrophysical plasmas in the gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations and explore the linear properties of gyrokinetics as a prelude to nonlinear simulations. The linear dispersion relation for gyrokinetics is obtained, and its solutions are compared to those of hot-plasma kinetic theory. These results are used to validate the performance of the gyrokinetic simulation code GS2 in the parameter regimes relevant for astrophysical plasmas. New results on global energy conservation in gyrokinetics are also derived. We briefly outline several of the problems to be addressed by future nonlinear simulations, including particle heating by turbulence in hot accretion flows and in the solar wind, the magnetic and electric field power spectra in the solar wind, and the origin of small-scale density fluctuations in the interstellar medium.

Turbulence, magnetic fields, and plasma physics in clusters of galaxies

Abstract: Observations of galaxy clusters show that the intracluster medium (ICM) is likely to be turbulent and is certainly magnetized. The properties of this magnetized turbulence are determined both by fundamental nonlinear magnetohydrodynamic interactions and by the plasma physics of the ICM, which has very low collisionality. Cluster plasma threaded by weak magnetic fields is subject to firehose and mirror instabilities. These saturate and produce fluctuations at the ion gyroscale, which can scatter particles, increasing the effective collision rate and, therefore, the effective Reynolds number of the ICM. A simple way to model this effect is proposed. The model yields a self-accelerating fluctuation dynamo whereby the field grows explosively fast, reaching the observed, dynamically important, field strength in a fraction of the cluster lifetime independent of the exact strength of the seed field. It is suggested that the saturated state of the cluster turbulence is a combination of the conventional isotropic magnetohydrodynamic turbulence, characterized by folded, direction-reversing magnetic fields and an Alfven-wave cascade at collisionless scales. An argument is proposed to constrain the reversal scale of the folded field. The picture that emerges appears to be in qualitative agreement with observations of magnetic fields in clusters.

Magneto-hydrodynamic stability of the H-mode transport barrier as a model for edge localized modes: an overview*

Abstract: The progress that has been made in understanding the processes responsible for edge localized modes is reviewed. Attention is restricted to the role of ideal magneto-hydrodynamics and extensions of this model. As well as reviewing the current understanding, future research needs are discussed and speculative ideas for further development are proposed.

Characterizing Electron Temperature Gradient Turbulence Via Numerical Simulation

Abstract: Numerical simulations of electron temperature gradient (ETG) turbulence are presented that characterize the ETG fluctuation spectrum, establish limits to the validity of the adiabatic ion model often employed in studying ETG turbulence, and support the tentative conclusion that plasma-operating regimes exist in which ETG turbulence produces sufficient electron heat transport to be experimentally relevant. We resolve prior controversies regarding simulation techniques and convergence by benchmarking simulations of ETG turbulence from four microturbulence codes, demonstrating agreement on the electron heat flux, correlation functions, fluctuation intensity, and rms flow shear at fixed simulation cross section and resolution in the plane perpendicular to the magnetic field. Excellent convergence of both continuum and particle-in-cell codes with time step and velocity-space resolution is demonstrated, while numerical issues relating to perpendicular (to the magnetic field) simulation dimensions and resolution are discussed. A parameter scan in the magnetic shear, s, demonstrates that the adiabatic ion model is valid at small values of s (s < 0.4 for the parameters used in this scan) but breaks down at higher magnetic shear. A proper treatment employing gyrokinetic ions reveals a steady increase in the electron heat transport with increasing magnetic shear, reaching electron heat transport rates consistent with analyses of experimental tokamak discharges. (c) 2006 American Institute of Physics.

Interplanetary and interstellar plasma turbulence

Abstract: Theoretical approaches to low-frequency magnetized turbulence in collisionless and weakly collisional astrophysical plasmas are reviewed. The proper starting point for an analytical description of these plasmas is kinetic theory, not fluid equations. The anisotropy of the turbulence is used to systematically derive a series of reduced analytical models. Above the ion gyroscale, it is shown rigourously that the Alfven waves decouple from the electron-density and magnetic-field-strength fluctuations and satisfy the Reduced MHD equations. The density and field-strength fluctuations (slow waves and the entropy mode in the fluid limit), determined kinetically, are passively mixed by the Alfven waves. The resulting hybrid fluid-kinetic description of the low-frequency turbulence is valid independently of collisionality. Below the ion gyroscale, the turbulent cascade is partially converted into a cascade of kinetic Alfven waves, damped at the electron gyroscale. This cascade is described by a pair of fluid-like equations, which are a reduced version of the Electron MHD. The development of these theoretical models is motivated by observations of the turbulence in the solar wind and interstellar medium. In the latter case, the turbulence is spatially inhomogeneous and the anisotropic Alfvenic turbulence in the presence of a strong mean field may coexist with isotropic MHD turbulence that has no mean field.

Electron temperature gradient driven transport in a MAST H-mode plasma

Abstract: Gyrokinetic simulation of a MAST-like equilibrium is used to establish the turbulent transport resulting from the electron temperature gradient driven mode for core and edge parameters. The thermal diffusion coefficients calculated in these simulations are found to be experimentally significant for core parameters but underestimate the observed transport on outer flux-surfaces.

Fast growth of magnetic fields in galaxy clusters: A self-accelerating dynamo

Abstract: We propose a model of magnetic-field growth in galaxy clusters whereby the field is ampli.fied by a factor of about 108 over a cosmologically short time of ∼ 108 yr. Our model is based on the idea that the viscosity of the intracluster medium during the field-amplification epoch is determined not by particle collisions but by plasma microinstabilities: these give rise to small-scale .uctuations, which scatter particles, increasing their effective collision rate and, therefore, the effective Reynolds number. This gives rise to a bootstrap effect as the growth of the field triggers the instabilities which increase the Reynolds number which, in turn, accelerates the growth of the field. The growth is explosive and the result is that the observed field strength is reached over a fraction of the cluster lifetime independent of the exact strength of the seed field (which only needs to be above ∼ 10–15 G to trigger the explosive growth). (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Turbulence, magnetic fields and plasma physics in clusters of galaxies

Abstract: Observations of galaxy clusters show that the intracluster medium (ICM) is likely to be turbulent and is certainly magnetized. The properties of this magnetized turbulence are determined both by fundamental nonlinear magnetohydrodynamic interactions and by the plasma physics of the ICM, which has very low collisionality. Cluster plasma threaded by weak magnetic fields is subject to firehose and mirror instabilities. These saturate and produce fluctuations at the ion gyroscale, which can scatter particles, increasing the effective collision rate and, therefore, the effective Reynolds number of the ICM. A simple way to model this effect is proposed. The model yields a self-accelerating fluctuation dynamo whereby the field grows explosively fast, reaching the observed, dynamically important, field strength in a fraction of the cluster lifetime independent of the exact strength of the seed field. It is suggested that the saturated state of the cluster turbulence is a combination of the conventional isotropic magnetohydrodynamic turbulence, characterized by folded, direction-reversing magnetic fields and an Alfv\'en-wave cascade at collisionless scales. An argument is proposed to constrain the reversal scale of the folded field. The picture that emerges appears to be in qualitative agreement with observations of magnetic fields in clusters.

Stability of highly shifted equilibria in a large-aspect-ratio tokamak.

Abstract: High beta poloidal tokamaks can confine plasma pressures an order of magnitude higher than their low beta poloidal counterparts. The theoretical stability of these high beta poloidal magnetohydrodynamics equilibria was left unresolved for many years. Using modern computational tools, such configurations are now found stable to Mercier, resistive and high-n (ideal and resistive) ballooning criteria as well as fixed and free-boundary modes for a wide range of current density profiles in the framework of a low field large-aspect-ratio machine.

FLR effects in nonlinear tearing mode reconnection

Abstract: Introduction Magnetic reconnection is a plasma physics phenomenon whereupon magnetic field lines which are being convected with the flows in the plasma suddenly break and reconnect in a different configuration. Magnetic energy is released in this process, giving rise to high velocity plasma flows, energetic particles and plasma heating. Reconnection is widely believed to be the cause of solar flares; it is also manifest in the interaction between the solar wind and the Earth’s magnetic field in the magnetopause and magnetotail. In fusion devices it plays a crucial role in the development of the sawtooth instability, which has potentially disastrous consequences to the plasma confinement. In many plasmas of interest it has long been suspected that an MHD description is too simple to fully explain the complexity of the observations. The discrepancy is obvious in the observed and calculated reconnection rates which, in the MHD framework, differ by several orders of magnitude. Interest has diverged to non-MHD effects which might cause a speed-up of this process. The potential candidates differ depending on the specific geometry and plasma parameters. For example, in most present fusion plasmas, the ion Larmor radius should exceed, or at least be comparable to, the width of the dissipation region. Thus, ion finite Larmor radius (FLR) effects cannot be neglected and are, in fact, known to produce a speed up of the reconnection rate [1]. From the numerical point of view, the FLR terms bring about one further complication: they introduce the Kinetic Alfven wave (KAW) into the system, which has a dispersive character, i.e., ω ∼ k ⊥ (the counterpart to this in the absence of a strong magnetic field is the Hall term in Ohm’s law, which also introduces a dispersive wave, the whistler). Explicit numerical integration schemes show great difficulties in coping with this wave, the time step being thus set to an impractically low value. Building on previous work [2, 3] we present a new semi-implicit method that stabilizes the KAW and the Alfven wave (AW), while remaining accurate in the linear and nonlinear regimes. Timestep enhancements over the CFL condition of ∼ 100 are obtained. Comparison with a fully explicit calculation is presented and preliminary linear and nonlinear results are briefly discussed.

Plasma physics: Thermonuclear ringtones

Abstract: The ability to confine alpha particles within a burning deuterium–tritium plasma is likely to be crucial to the future of fusion power generation. Resonant interactions between alpha particles and magnetohydrodynamic vibrations could threaten their confinement.

FLR effects in nonlinear tearing mode reconnection

Abstract: Introduction Magnetic reconnection is a plasma physics phenomenon whereupon magnetic field lines which are being convected with the flows in the plasma suddenly break and reconnect in a different configuration. Magnetic energy is released in this process, giving rise to high velocity plasma flows, energetic particles and plasma heating. Reconnection is widely believed to be the cause of solar flares; it is also manifest in the interaction between the solar wind and the Earth’s magnetic field in the magnetopause and magnetotail. In fusion devices it plays a crucial role in the development of the sawtooth instability, which has potentially disastrous consequences to the plasma confinement. In many plasmas of interest it has long been suspected that an MHD description is too simple to fully explain the complexity of the observations. The discrepancy is obvious in the observed and calculated reconnection rates which, in the MHD framework, differ by several orders of magnitude. Interest has diverged to non-MHD effects which might cause a speed-up of this process. The potential candidates differ depending on the specific geometry and plasma parameters. For example, in most present fusion plasmas, the ion Larmor radius should exceed, or at least be comparable to, the width of the dissipation region. Thus, ion finite Larmor radius (FLR) effects cannot be neglected and are, in fact, known to produce a speed up of the reconnection rate [1]. From the numerical point of view, the FLR terms bring about one further complication: they introduce the Kinetic Alfven wave (KAW) into the system, which has a dispersive character, i.e., ω ∼ k ⊥ (the counterpart to this in the absence of a strong magnetic field is the Hall term in Ohm’s law, which also introduces a dispersive wave, the whistler). Explicit numerical integration schemes show great difficulties in coping with this wave, the time step being thus set to an impractically low value. Building on previous work [2, 3] we present a new semi-implicit method that stabilizes the KAW and the Alfven wave (AW), while remaining accurate in the linear and nonlinear regimes. Timestep enhancements over the CFL condition of ∼ 100 are obtained. Comparison with a fully explicit calculation is presented and preliminary linear and nonlinear results are briefly discussed.