ترغب بنشر مسار تعليمي؟ اضغط هنا

Fourier-Hermite spectral representation for the Vlasov-Poisson system in the weakly collisional limit

130   0   0.0 ( 0 )
 نشر من قبل Joseph Parker
 تاريخ النشر 2014
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We study Landau damping in the 1+1D Vlasov-Poisson system using a Fourier-Hermite spectral representation. We describe the propagation of free energy in phase space using forwards and backwards propagating Hermite modes recently developed for gyrokinetics [Schekochihin et al. (2014)]. The change in the electric field corresponds to the net Hermite flux via a free energy evolution equation. In linear Landau damping, decay in the electric field corresponds to forward propagating Hermite modes; in nonlinear damping, the initial decay is followed by a growth phase characterised by the generation of backwards propagating Hermite modes by the nonlinear term. The free energy content of the backwards propagating modes increases exponentially until balancing that of the forward propagating modes. Thereafter there is no systematic net Hermite flux, so the electric field cannot decay and the nonlinearity effectively suppresses Landau damping. These simulations are performed using the fully-spectral 5D gyrokinetics code SpectroGK [Parker et al. 2014], modified to solve the 1+1D Vlasov-Poisson system. This captures Landau damping via an iterated Lenard-Bernstein collision operator or via Hou-Li filtering in velocity space. Therefore the code is applicable even in regimes where phase-mixing and filamentation are dominant.



قيم البحث

اقرأ أيضاً

Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {it in-situ} spacecraft observations and numerical simulations suggest a novel scenario for turbulen ce, characterized by a so-called phase space cascade -- the formation of fine structures, both in physical and velocity space. This new concept is here extended by directly taking into account the role of inter-particle collisions, modeled through the nonlinear Landau operator or the simplified Dougherty operator. The characteristic times, associated with inter-particle correlations, are derived in the above cases. The implications of introducing collisions on the phase space cascade are finally discussed.
We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, $N$. When the advection term in Vlasov equation i s dominant, the convergence with $N$ of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced in [J. D. Crawford and P. D. Hislop, Ann. Phys. 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase space vortices, compare our results with numerical simulations of the Vlasov-Poisson system and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed.
110 - O. Pezzi , Y. Yang , F. Valentini 2019
Kinetic simulations based on the Eulerian Hybrid Vlasov-Maxwell (HVM) formalism permit the examination of plasma turbulence with useful resolution of the proton velocity distribution function (VDF). The HVM model is employed here to study the balance of energy, focusing on channels of conversion that lead to proton kinetic effects, including growth of internal energy and temperature anisotropies. We show that this Eulerian simulation approach, which is almost noise-free, is able to provide an accurate energy balance for protons. The results demonstrate explicitly that the recovered temperature growth is directly related to the role of the pressure-strain interaction. Furthermore, analysis of local spatial correlations indicates that the pressure-strain interaction is qualitatively associated with strong-current, high-vorticity structures, although other local terms -- such as the heat flux -- weaken the correlation. These numerical capabilities based on the Eulerian approach will enable deeper study of transfer and conversion channels in weakly collisional Vlasov plasmas.
In the paper, gridless particle techniques are presented in order to solve problems involving electrostatic, collisionless plasmas. The method makes use of computational particles having the shape of spherical shells or of rings, and can be used to s tudy cases in which the plasma has spherical or axial symmetry, respectively. As a computational grid is absent, the technique is particularly suitable when the plasma occupies a rapidly changing space region.
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $tto -infty$ to asymptotic dynamics as $tto +infty$. The main novelty is the construction of modified wave operators, but we also obtain a new simple proof of modified scattering. Our analysis is guided by the Hamiltonian structure of the Vlasov-Poisson system. Via a pseudo-conformal inversion we recast the question of asymptotic behavior in terms of local in time dynamics of a new equation with singular coefficients which is approximately integrated using a generating function.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا