31 research outputs found
Physics-based adaptivity of a spectral method for the Vlasov-Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space
We propose a spectral method for the 1D-1V Vlasov-Poisson system where the
discretization in velocity space is based on asymmetrically-weighted Hermite
functions, dynamically adapted via a scaling and shifting of the
velocity variable. Specifically, at each time instant an adaptivity criterion
selects new values of and based on the numerical solution of the
discrete Vlasov-Poisson system obtained at that time step. Once the new values
of the Hermite parameters and are fixed, the Hermite expansion is
updated and the discrete system is further evolved for the next time step. The
procedure is applied iteratively over the desired temporal interval. The key
aspects of the adaptive algorithm are: the map between approximation spaces
associated with different values of the Hermite parameters that preserves total
mass, momentum and energy; and the adaptivity criterion to update and
based on physics considerations relating the Hermite parameters to the
average velocity and temperature of each plasma species. For the discretization
of the spatial coordinate, we rely on Fourier functions and use the implicit
midpoint rule for time stepping. The resulting numerical method possesses
intrinsically the property of fluid-kinetic coupling, where the low-order terms
of the expansion are akin to the fluid moments of a macroscopic description of
the plasma, while kinetic physics is retained by adding more spectral terms.
Moreover, the scheme features conservation of total mass, momentum and energy
associated in the discrete, for periodic boundary conditions. A set of
numerical experiments confirms that the adaptive method outperforms the
non-adaptive one in terms of accuracy and stability of the numerical solution
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
Tethered Capacitor Charge Mitigation in Electron Beam Experiments
Energetic electron beams have been proposed for tracing magnetic field lines from the magnetosphere down to the ionosphere, in active experiments aimed at diagnosing mechanisms at play in the coupling between magnetosphere and ionosphere. It is recognized however that in the absence of an efficient mitigation technique, this approach would lead to unacceptably large spacecraft charging and positive potential buildup, which would result in environmental hazard for the spacecraft. This problem would be particularly acute in low density regions of the magnetosphere of interest in the study of magnetic field reconnection and substorm dynamics. A solution to this predicament could consist of creating a plasma contactor whereby a gas puff would be ionized, leading to the evacuation of positive charges and collection of cold electrons, thus compensating for the charges lost in the electron beam. A possible alternative is presented here, which consists of attaching a large passive conducting surface to the spacecraft, a “tethered capacitor”, from which negative charges would be drawn to compensate for those lost from the beam. This capacitor would then charge to a large positive potential, leaving the spacecraft and electron gun at a lower, acceptable positive potential. The tethered capacitor could have a relatively small mass; consisting only of a thin conducting surface that would be “inflated” as a result of repulsive electrostatic forces. This charge mitigation concept, as applied to active electron beam experiments, is explored using three dimensional particle-in-cell (PIC) simulations from which scaling laws can be inferred for the spacecraft and tethered capacitor potentials under proposed electron beam operations
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 .Comment: 8 pages, 3 figure
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 for electrons and 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 \% of all the current sheets identified.Comment: 9 pages, 6 figures. Submitted for publication to MNRA