Wave dispersion in the hybrid-Vlasov model: Verification of Vlasiator (original) (raw)
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Journal of Computational Physics, 2007
We present a numerical scheme for the integration of the Vlasov-Maxwell system of equations for a non-relativistic plasma, in the hybrid approximation, where the Vlasov equation is solved for the ion distribution function and the electrons are treated as a fluid. In the Ohm equation for the electric field, effects of electron inertia have been retained, in order to include the small scale dynamics up to characteristic lengths of the order of the electron skin depth. The low frequency approximation is used by neglecting the time derivative of the electric field, i.e. the displacement current in the Ampere equation.
Vlasov simulation is a method to solve time evolution of a plasma by directly time advancing the distribution function in the position-velocity phase space. Vlasov simulation is free from thermal (numerical) noise and thus is advantageous in analyzing ne details of nonlinear plasma phenomena. With this background in mind, we have developed a new Vlasov simulation code (1-d in the real space, 3-d in the velocity space), in order to study basic properties of nonlinear evolution of large amplitude magnetohydrodynamic (MHD) waves in the solar wind. In contrast to traditional Vlasov simulations in which electron waves are of major concern, our simulation code focuses on solving plasma behavior around the ion scales, assuming a massless electron uid. Since we mainly deal with low frequency MHD waves propagating quasi-parallel to the background magnetic eld, cyclotron coupling can be assumed to be weak for parameters typical to the solar wind. Thus, in our code, the Vlasov equation is solved only along the longitudinal direction, whereas the Hall-MHD equations are solved for the transverse directions. Propagation properties of Alfv en and ion acoustic waves in the simulation agree with analytically obtained dispersion relations. Some results on the parametric decay instability of Alfv en waves are also reported.
Vlasov Equation for Magnetized Plasma Particles in the Arbitrary Magnetic Field
The linearized Vlasov equation is rewritten for charged particles in the two-dimensional axisymmetric plasma models using the cylindrical coordinates. There is described a method of its solution by the Fourier expansions of the perturbed distribution functions over the gyrophase angle in velocity space, conservation integrals of particle motion in the curvilinear magnetic field and smallness of the magnetization parameters. Such an approach allows us to evaluate the main contributions of untrapped and trapped particles to the transverse and longitudinal dielectric tensor components for electromagnetic waves in tokamaks, straight mirror-traps, laboratoty dipole magnetospheric plasmas and inner part of the Earth's magnetosphere. KEY WORDS: Vlasov equation, kinetic wave theory, tokamaks, mirror traps, magnitospheric plasmas. ... ... , 4,
VLASOV SIMULATIONS OF MULTI-ION PLASMA TURBULENCE IN THE SOLAR WIND
The Astrophysical Journal, 2013
Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles, and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the reference frame given by the local magnetic field. Anisotropy is found to be higher in regions of high magnetic stress. Both ion species manifest a preferentially perpendicular heating, although the anisotropy is more pronounced for the alpha particles, according to solar wind observations. The anisotropy of the alpha particle, moreover, is correlated to the proton anisotropy and also depends on the local differential flow between the two species. Evident distortions of the particle distribution functions are present, with the production of bumps along the direction of the local magnetic field. The physical phenomenology recovered in these numerical simulations reproduces very common measurements in the turbulent solar wind, suggesting that the multi-ion Vlasov model constitutes a valid approach to understanding the nature of complex kinetic effects in astrophysical plasmas.
Particle in Cell Simulations of Electrostatic Waves in Saturn's Magnetosphere
2012
The characteristics of electrostatic waves are investigated using PIC simulations of a four component plasma: cool and hot electrons, cool ions and an electron beam. The velocities are defined by Maxwellian distributions. The system is one dimensional and simulates a collisionless, unmagnetized plasma. Langmuir waves, electron acoustic waves, beam-driven waves and ion acoustic waves are excited in the simulations. The results are analysed using the dispersion relation and compared with previous investigations and analytical results.
Vlasov simulations of Kinetic Alfv\'en Waves at proton kinetic scales
Physics of Plasmas
Kinetic Alfv\'en waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton inertial length dpd_pdp and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfv\'en waves at proton kinetic scales, in typical conditions of the solar wind environment. In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to...
Vlasov simulations of parallel potential drops
Annales Geophysicae, 2013
An auroral flux tube is modelled from the magnetospheric equator to the ionosphere using Vlasov simulations. Starting from an initial state, the evolution of the plasma on the flux tube is followed in time. It is found that when applying a voltage between the ends of the flux tube, about two thirds of the potential drop is concentrated in a thin double layer at approximately one Earth radius altitude. The remaining part is situated in an extended region 1-2 Earth radii above the double layer. Waves on the ion timescale develop above the double layer, and they move toward higher altitude at approximately the ion acoustic speed. These waves are seen both in the electric field and as perturbations of the ion and electron distributions, indicative of an instability. Electrons of magnetospheric origin become trapped between the magnetic mirror and the double layer during its formation. At low altitude, waves on electron timescales appear and are seen to be non-uniformly distributed in space. The temporal evolution of the potential profile and the total voltage affect the double layer altitude, which decreases with an increasing field aligned potential drop. A current-voltage relationship is found by running several simulations with different voltages over the system, and it agrees with the Knight relation reasonably well.
Enabling technology for global 3D + 3V hybrid-Vlasov simulations of near-Earth space
Physics of Plasmas
We present methods and algorithms that allow the Vlasiator code to run global, three-dimensional hybrid-Vlasov simulations of Earth's entire magnetosphere. The key ingredients that make Vlasov simulations at magnetospheric scales possible are the sparse velocity space implementation and spatial adaptive mesh refinement. We outline the algorithmic improvement of the semi-Lagrangian solver for six-dimensional phase space quantities, discuss the coupling of Vlasov and Maxwell equations' solvers in a refined mesh, and provide performance figures from simulation test runs that demonstrate the scalability of this simulation system to full magnetospheric runs.
2022
Ultra-low frequency (ULF) waves are routinely observed in Earth's dayside magnetosphere. Here we investigate the influence of externally-driven density variations in the near-Earth space in the ULF regime using global 2D simulations performed with the hybrid-Vlasov model Vlasiator. With the new time-varying boundary setup, we introduce a monochromatic Pc5 range periodic density variation in the solar wind. A breathing motion of the magnetopause and changes in the bow shock standoff position are caused by the density variation, the time lag between which is found to be consistent with propagation at fast magnetohydrodynamic speed. The oscillations also create large-scale stripes of variations in the magnetosheath and modulate the mirror and electromagnetic ion cyclotron modes. We characterize the spatialtemporal properties of ULF waves at different phases of the variation. Less prominent EMIC and mirror mode wave activities near the center of magnetosheath are observed with decreasing upstream Mach number. The EMIC wave occurrence is strongly related to pressure anisotropy and β , both vary as a function of the upstream conditions, whereas the mirror mode occurrence is highly influenced by fast waves generated from upstream density variations.