Magnetic reconnection in high-temperature plasmas : excitation of the drift-tearing mode and the transport of electron thermal energy

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, February 2007.Includes bibliographical references (leaves 95-100).The problem of excitation of the drift-tearing mode (Coppi, 1964) in high-temperature plasmas is considered. Existing theories predict that under the conditions typical of modern toroidal experiments on nuclear fusion, the mode is linearly stable in both collisionless (Coppi et al., 1979), and in a weakly collisional (Antonsen and Drake, 1983) regimes. We propose that the presence of a spectrum of background microscopic modes leads to destabilization of the drift-tearing mode by significantly altering the electron thermal energy transport. Two phenomenological models that illustrate this possibility are considered. In particular, we demonstrate that a localized reduction in parallel electron thermal conductivity, or a localized depression in the electron temperature gradient cause a significant reduction of the mode excitation threshold, as measured by Acrit, the jump of the first derivative of the magnetic field across the reconnection layer. Both experimental observations and theoretical considerations indicate that in the regimes of interest the values of the perpendicular thermal diffusivity D are significantly higher than the corresponding collisional estimates. Therefore the influence of the perpendicular heat flux on the excitation properties of the drift-tearing mode must be analyzed.(cont.) The result is that for D above a certain critical value D, which depends on the parallel thermal diffusivity and parameter re = dlnTe/dlnx, the excitation threshold of the mode is significantly reduced, and can be negative. This indicates the presence of an additional drive for the mode, which has been identified as the perpendicular electron temperature gradient. When D > D, the growth rate of the mode is an increasing function of the parameter qe, which is in contrast to the regime of relatively small or zero perpendicular thermal diffusivity, D < D, where the mode becomes more stable as re is increased. In the collisionless regime the drift-tearing mode is stabilized by the effects of the electron Landau damping, which play a role similar to that of the parallel thermal conductivity in the weakly collisional regime. It is well known that Landau damping can be significantly affected by such effects as spatial and velocity-space diffusion. We consider the influence of the resonance broadening due to particle spatial diffusion on the excitation properties of the drift-tearing mode. Such resonance broadening is found to cause a reduction of the excitation threshold. However, the employed semi-analytical treatment of the problem allows only consideration of relatively small values of the corresponding diffusion coefficient. In this regime the reduction in the excitation threshold is rather small.by Vadim Roytershteyn.Ph.D

Spatial intermittency of particle distribution in relativistic plasma turbulence

Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form non-thermal power-law distribution functions in the momentum (or energy) space, $f(\gamma)d\gamma\propto \gamma^{-\alpha}d\gamma$, where $\gamma$ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has log-normal statistics, while the density of the accelerated particles, $n$, has a power-law distribution function, $P(n)dn\propto n^{-\beta}dn$. We argue that the scaling exponents are related as $\beta\approx \alpha+1$, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.Comment: 10 pages, 5 figures. Accepted for publication in Ap

Spectra of magnetic turbulence in a relativistic plasma

We present a phenomenological and numerical study of strong Alfv\'enic turbulence in a magnetically dominated collisionless relativistic plasma with a strong background magnetic field. In contrast with the non-relativistic case, the energy in such turbulence is contained in magnetic and electric fluctuations. We argue that such turbulence is analogous to turbulence in a strongly magnetized non-relativistic plasma in the regime of broken quasi-neutrality. Our 2D particle-in-cell numerical simulations of turbulence in a relativistic pair plasma find that the spectrum of the total energy has the scaling $k^{-3/2}$, while the difference between the magnetic and electric energies, the so-called residual energy, has the scaling $k^{-2.4}$. The electric and magnetic fluctuations at scale $\ell$ exhibit dynamic alignment with the alignment-angle scaling close to $\cos\phi_\ell\propto \ell^{1/4}$. At scales smaller than the (relativistic) plasma inertial scale, the energy spectrum of relativistic inertial Alfv\'en turbulence steepens to $k^{-3.5}$.Comment: 8 pages, 3 figures. Submitted to ApJ

Electron-only reconnection in kinetic Alfv\'en turbulence

We study numerically small-scale reconnection events in kinetic, low-frequency, quasi-2D turbulence (termed kinetic-Alfv\'en turbulence). Using 2D particle-in-cell simulations, we demonstrate that such turbulence generates reconnection structures where the electron dynamics do not couple to the ions, similarly to the electron-only reconnection events recently detected in the Earth's magnetosheath by Phan et al. (2018). Electron-only reconnection is thus an inherent property of kinetic-Alfv\'en turbulence, where the electron current sheets have limited anisotropy and, as a result, their sizes are smaller than the ion inertial scale. The reconnection rate of such electron-only events is found to be close to $0.1$.Comment: 8 pages, 3 figure

Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space

Spectral (transform) methods for solution of Vlasov-Maxwell system have shown significant promise as numerical methods capable of efficiently treating fluid-kinetic coupling in magnetized plasmas. We discuss SpectralPlasmaSolver (SPS), an implementation of three-dimensional, fully electromagnetic algorithm based on a decomposition of the plasma distribution function in Hermite modes in velocity space and Fourier modes in physical space. A fully-implicit time discretization is adopted for numerical stability and to ensure exact conservation laws for total mass, momentum and energy. The SPS code is parallelized using Message Passing Interface for distributed memory architectures. Application of the method to analysis of kinetic range of scales in plasma turbulence under conditions typical of the solar wind is demonstrated. With only 4 Hermite modes per velocity dimension, the algorithm yields damping rates of kinetic Alfvén waves with accuracy of 50% or better, which is sufficient to obtain a model of kinetic scales capable of reproducing many of the expected statistical properties of turbulent fluctuations. With increasing number of Hermite modes, progressively more accurate values for collisionless damping rates are obtained. Fully nonlinear simulations of decaying turbulence are presented and successfully compared with similar simulations performed using Particle-In-Cell method

Electron-Scale Current Sheets and Energy Dissipation in 3D Kinetic-Scale Plasma Turbulence with Low Electron Beta

3D kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is $\beta_e=0.1$ for electrons and $\beta_i=1$ for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth's magnetosheath, and other astrophysical systems. The simulations, performed using the fluid-kinetic spectral plasma solver (SPS) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electron-scale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length falls between the electron and ion inertial length. The pressure-strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20\% of the total volume. Some of the current sheets corresponding to the largest pressure-strain interaction are found to be associated with Alfv\'enic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about $1$\% of all the current sheets identified.Comment: 9 pages, 6 figures. Submitted for publication to MNRA

Wavelet Methods for Studying the Onset of Strong Plasma Turbulence

Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed turbulence from a laminar state. Originally applied to neutral fluid turbulence, an iterative wavelet technique decomposes the field into coherent and incoherent contributions. In contrast to Fourier power spectra, finite time Lyapunov exponents (FTLE), and simple measures of intermittency such as non-Gaussian statistics of field increments, the wavelet technique is found to provide a quantitative measure for the onset of turbulence and to track the transition to fully developed turbulence. The wavelet method makes no assumptions about the structure of the coherent current sheets or the underlying plasma model. Temporal evolution of the coherent and incoherent wavelet fluctuations is found to be highly correlated with the magnetic field energy and plasma thermal energy, respectively. The onset of turbulence is identified with the rapid growth of a background of incoherent fluctuations spreading across a range of scales and a corresponding drop in the coherent components. This is suggestive of the interpretation of the coherent and incoherent wavelet fluctuations as measures of coherent structures (e.g., current sheets) and dissipation, respectively. The ratio of the incoherent to coherent fluctuations $R_{ic}$ is found to be fairly uniform across different plasma models and provides an empirical threshold for turbulence onset. The technique is illustrated through examples. First, it is applied to the Kelvin--Helmholtz instability from different simulation models including fully kinetic, hybrid (kinetic ion/fluid electron), and Hall MHD simulations. Second, it is applied to the development of turbulence downstream of the bowshock in a magnetosphere simulation

The multi-dimensional Hermite-discontinuous Galerkin method for the Vlasov-Maxwell equations

We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov-Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions. The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge-Kutta integrators. The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability