Abstract:The existence and properties of low Mach-number (M 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. Using this semi-analytical model, we study the effect of electron-to-ion temperature ratio and presence of impurities… Show more
“…1, and so our model is valid, the shock properties do not change qualitatively, so the effect of collisions on φ max is rather weak. The reflected ion fraction where F " 2φ max {M 2 and it takes values close to 1 for most cases of interest, as discussed in (Pusztai et al 2018). We find that α increases strongly with M -as seen in figure 9a -since φ max increases stronger than M 2 , corresponding to higher values of F .…”
Section: Appendix C Parameter Region For Relevance and Reflected Ionsupporting
confidence: 58%
“…For , this result reduces to where and it takes values close to 1 for most cases of interest, as discussed by Pusztai et al. (2018). Figure 9.( a ) Reflected ion fraction plotted as , as a function of and .…”
Section: Figurementioning
confidence: 59%
“…The one-dimensional (1-D) collisionless shock problem has a steady state solution, which has been considered by Pusztai et al. (2018); its solution, in the frame of the shock, is derived from the time-independent Vlasov–Poisson system, where . To keep the following discussion focused on collisional effects and avoid issues with inter-species collisions, the model considered in this paper only concerns single ion species distributions, , and the electrons are assumed to be Maxwell–Boltzmann distributed, which results in , where is the electron density which balances both the incoming and reflected ions.…”
In strictly collisionless electrostatic shocks, the ion distribution function can develop discontinuities along phase-space separatrices, due to partial reflection of the ion population. In this paper, we depart from the strictly collisionless regime and present a semi-analytical model for weakly collisional kinetic shocks. The model is used to study the effect of small but finite collisionalities on electrostatic shocks, and they are found to smooth out these discontinuities into growing boundary layers. More importantly, ions diffuse into and accumulate in the previously empty regions of phase space, and, by upsetting the charge balance, lead to growing downstream oscillations of the electrostatic potential. We find that the collisional age of the shock is the more relevant measure of the collisional effects than the collisionality, where the former can become significant during the lifetime of the shock, even for weak collisionalities.: Email address for correspondence: andsunds@chalmers.se
“…1, and so our model is valid, the shock properties do not change qualitatively, so the effect of collisions on φ max is rather weak. The reflected ion fraction where F " 2φ max {M 2 and it takes values close to 1 for most cases of interest, as discussed in (Pusztai et al 2018). We find that α increases strongly with M -as seen in figure 9a -since φ max increases stronger than M 2 , corresponding to higher values of F .…”
Section: Appendix C Parameter Region For Relevance and Reflected Ionsupporting
confidence: 58%
“…For , this result reduces to where and it takes values close to 1 for most cases of interest, as discussed by Pusztai et al. (2018). Figure 9.( a ) Reflected ion fraction plotted as , as a function of and .…”
Section: Figurementioning
confidence: 59%
“…The one-dimensional (1-D) collisionless shock problem has a steady state solution, which has been considered by Pusztai et al. (2018); its solution, in the frame of the shock, is derived from the time-independent Vlasov–Poisson system, where . To keep the following discussion focused on collisional effects and avoid issues with inter-species collisions, the model considered in this paper only concerns single ion species distributions, , and the electrons are assumed to be Maxwell–Boltzmann distributed, which results in , where is the electron density which balances both the incoming and reflected ions.…”
In strictly collisionless electrostatic shocks, the ion distribution function can develop discontinuities along phase-space separatrices, due to partial reflection of the ion population. In this paper, we depart from the strictly collisionless regime and present a semi-analytical model for weakly collisional kinetic shocks. The model is used to study the effect of small but finite collisionalities on electrostatic shocks, and they are found to smooth out these discontinuities into growing boundary layers. More importantly, ions diffuse into and accumulate in the previously empty regions of phase space, and, by upsetting the charge balance, lead to growing downstream oscillations of the electrostatic potential. We find that the collisional age of the shock is the more relevant measure of the collisional effects than the collisionality, where the former can become significant during the lifetime of the shock, even for weak collisionalities.: Email address for correspondence: andsunds@chalmers.se
“…In this regard, the continuum method employed here should be viewed as a complementary approach to the general task of modelling kinetic plasmas because of the high resolution the method provides in phase space at an acceptable computational cost – the linear spline simulation has roughly the same cost as the , piecewise quadratic Serendipity element simulation. We believe the power of this complementary continuum kinetic approach is made manifest by the results of this study, in addition to previous studies of similar phenomena in the unmagnetized regime, such as collisionless shocks (Pusztai et al 2018; Sundström et al 2019), the one-dimensional Weibel instability (Cagas et al 2017), and the plasma dynamo (Pusztai et al 2020).…”
Monte Carlo methods are often employed to numerically integrate kinetic equations, such as the particle-in-cell method for the plasma kinetic equation, but these methods suffer from the introduction of counting noise to the solution. We report on a cautionary tale of counting noise modifying the nonlinear saturation of kinetic instabilities driven by unstable beams of plasma. We find a saturated magnetic field in under-resolved particle-in-cell simulations due to the sampling error in the current density. The noise-induced magnetic field is anomalous, as the magnetic field damps away in continuum kinetic and increased particle count particle-in-cell simulations. This modification of the saturated state has implications for a broad array of astrophysical phenomena beyond the simple plasma system considered here, and it stresses the care that must be taken when using particle methods for kinetic equations.
“…(2018) and Pusztai et al. (2018)). However, the use of non-periodic, open-boundary conditions with the filtered, Fourier–Fourier transformed Vlasov–Poisson simulation algorithm, the only algorithm with the filamentation and recurrence problems solved, has remained questionable.…”
Simulations of one-dimensional Vlasov–Maxwell solutions with non-periodic boundary conditions are discussed. Results obtained using a recently developed filtered flux-balance simulation system are compared to those obtained using a filtered, Fourier–Fourier transformed system. Excellent agreement is confirmed except for the appearance of the Gibbs phenomenon on the discontinuous simulated solutions of the transformed system. Recovery of the flux-balance results from the Fourier transformed results using the inverse polynomial reconstruction method is demonstrated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
