Astrophysical Gyrokinetics: Basic Equations and Linear Theory

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 {\tt 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.Comment: emulateapj, 24 pages, 10 figures, revised submission to ApJ: references added, typos corrected, reorganized and streamline

Propagation of Electron Magnetohydrodynamic structures in a 2-D inhomogeneous plasma

The fully three dimensional governing equations in the electron magnetohydrodynamic (EMHD) regime for a plasma with inhomogeneous density is obtained. These equations in the two dimensional (2-D) limit can be cast in terms of the evolution of two coupled scalar fields. The nonlinear simulations for the two dimensional case are carried out to understand the propagation of EMHD magnetic structures in the presence of inhomogeneity. A novel effect related to trapping of dipolar magnetic structures in the high density plasma region in the EMHD regime is observed. The interpretation of this phenomena as well as its relevance to the problem of hot spot generation in the context of fast ignition is presented

Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits. We also propose a kinetic formulation for the Hall-MHD equations which contains as fluid closure different variants of the Hall-MHD model. Then, we prove the existence of global weak solutions for the incompressible viscous resistive Hall-MHD model. We use the particular structure of the Hall term which has zero contribution to the energy identity. Finally, we discuss particular solutions in the form of axisymmetric purely swirling magnetic fields and propose some regularization of the Hall equation

Spectral features of solar wind turbulent plasma

Spectral properties of a fully compressible solar wind Hall Magnetohydrodynamic plasma are investigated by means of time dependent three dimensional Hall MHD simulations. Our simulations, in agreement with spacecraft data, identify a spectral break in turbulence spectra at characteristic length-scales associated with electromagnetic fluctuations that are smaller than the ion gyroradius. In this regime, our 3D simulations show that turbulent spectral cascades in the presence of a mean magnetic field follow an omnidirectional anisotropic inertial range spectrum close to $k^{-7/3}$. The onset of the spectral break in our simulations can be ascribed to the presence of nonlinear Hall interactions that modify the spectral cascades. Our simulations further show that the underlying charachteristic turbulent fluctuations are spectrally anisotropic, the extent of which depends critically on the local wavenumber. The fluctuations associated with length scales smaller than the ion gyroradius are highly compressible and tend to exhibit a near equipartition in the velocity and magnetic fields. Finally, we find that the orientation of velocity and magnetic field fluctuations critically determine the character of nonlinear interactions that predominantly govern a Hall MHD plasma, like the solar wind.Comment: This paper is accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journa

Rapid dissipation of magnetic fields due to Hall current

We propose a mechanism for the fast dissipation of magnetic fields which is effective in a stratified medium where ion motions can be neglected. In such a medium, the field is frozen into the electrons and Hall currents prevail. Although Hall currents conserve magnetic energy, in the presence of density gradients, they are able to create current sheets which can be the sites for efficient dissipation of magnetic fields. We recover the frequency, $\omega_{MH}$, for Hall oscillations modified by the presence of density gradients. We show that these oscillations can lead to the exchange of energy between different components of the field. We calculate the time evolution and show that magnetic fields can dissipate on a timescale of order $1/\omega_{MH}$. This mechanism can play an important role for magnetic dissipation in systems with very steep density gradients where the ions are static such as those found in the solid crust of neutron stars.Comment: 9 pages, changed fig.

Gyrokinetic turbulence: a nonlinear route to dissipation through phase space

This paper describes a conceptual framework for understanding kinetic plasma turbulence as a generalized form of energy cascade in phase space. It is emphasized that conversion of turbulent energy into thermodynamic heat is only achievable in the presence of some (however small) degree of collisionality. The smallness of the collision rate is compensated by the emergence of small-scale structure in the velocity space. For gyrokinetic turbulence, a nonlinear perpendicular phase mixing mechanism is identified and described as a turbulent cascade of entropy fluctuations simultaneously occurring at spatial scales smaller than the ion gyroscale and in velocity space. Scaling relations for the resulting fluctuation spectra are derived. An estimate for the collisional cutoff is provided. The importance of adequately modeling and resolving collisions in gyrokinetic simulations is biefly discussed, as well as the relevance of these results to understanding the dissipation-range turbulence in the solar wind and the electrostatic microturbulence in fusion plasmas.Comment: iop revtex style, 14 pages, 1 figure; submitted to PPCF; invited talk for EPS Conference on Plasma Physics, Crete, June 2008; Replaced to match published versio

Relativistic Laser-Matter Interaction and Relativistic Laboratory Astrophysics

The paper is devoted to the prospects of using the laser radiation interaction with plasmas in the laboratory relativistic astrophysics context. We discuss the dimensionless parameters characterizing the processes in the laser and astrophysical plasmas and emphasize a similarity between the laser and astrophysical plasmas in the ultrarelativistic energy limit. In particular, we address basic mechanisms of the charged particle acceleration, the collisionless shock wave and magnetic reconnection and vortex dynamics properties relevant to the problem of ultrarelativistic particle acceleration.Comment: 58 pages, 19 figure

Recyclable transmission line (RTL) and linear transformer driver (LTD) development for Z-pinch inertial fusion energy (Z-IFE) and high yield.

Z-Pinch Inertial Fusion Energy (Z-IFE) complements and extends the single-shot z-pinch fusion program on Z to a repetitive, high-yield, power plant scenario that can be used for the production of electricity, transmutation of nuclear waste, and hydrogen production, all with no CO{sub 2} production and no long-lived radioactive nuclear waste. The Z-IFE concept uses a Linear Transformer Driver (LTD) accelerator, and a Recyclable Transmission Line (RTL) to connect the LTD driver to a high-yield fusion target inside a thick-liquid-wall power plant chamber. Results of RTL and LTD research are reported here, that include: (1) The key physics issues for RTLs involve the power flow at the high linear current densities that occur near the target (up to 5 MA/cm). These issues include surface heating, melting, ablation, plasma formation, electron flow, magnetic insulation, conductivity changes, magnetic field diffusion changes, possible ion flow, and RTL mass motion. These issues are studied theoretically, computationally (with the ALEGRA and LSP codes), and will work at 5 MA/cm or higher, with anode-cathode gaps as small as 2 mm. (2) An RTL misalignment sensitivity study has been performed using a 3D circuit model. Results show very small load current variations for significant RTL misalignments. (3) The key structural issues for RTLs involve optimizing the RTL strength (varying shape, ribs, etc.) while minimizing the RTL mass. Optimization studies show RTL mass reductions by factors of three or more. (4) Fabrication and pressure testing of Z-PoP (Proof-of-Principle) size RTLs are successfully reported here. (5) Modeling of the effect of initial RTL imperfections on the buckling pressure has been performed. Results show that the curved RTL offers a much greater buckling pressure as well as less sensitivity to imperfections than three other RTL designs. (6) Repetitive operation of a 0.5 MA, 100 kV, 100 ns, LTD cavity with gas purging between shots and automated operation is demonstrated at the SNL Z-IFE LTD laboratory with rep-rates up to 10.3 seconds between shots (this is essentially at the goal of 10 seconds for Z-IFE). (7) A single LTD switch at Tomsk was fired repetitively every 12 seconds for 36,000 shots with no failures. (8) Five 1.0 MA, 100 kV, 100 ns, LTD cavities have been combined into a voltage adder configuration with a test load to successfully study the system operation. (9) The combination of multiple LTD coaxial lines into a tri-plate transmission line is examined. The 3D Quicksilver code is used to study the electron flow losses produced near the magnetic nulls that occur where coax LTD lines are added together. (10) Circuit model codes are used to model the complete power flow circuit with an inductive isolator cavity. (11) LTD architectures are presented for drivers for Z-IFE and high yield. A 60 MA LTD driver and a 90 MA LTD driver are proposed. Present results from all of these power flow studies validate the whole LTD/RTL concept for single-shot ICF high yield, and for repetitive-shot IFE