Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion
- CEA, DAM, DIF, F-91297 Arpajon (France)
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 the Vlasov equation is 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 by Crawford and Hislop [Ann. Phys. (NY) 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.
- OSTI ID:
- 21560290
- Journal Information:
- Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 83, Issue 5; Other Information: DOI: 10.1007/BF02162154; (c) 2011 American Institute of Physics; ISSN 1539-3755
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ADVECTION
ASYMPTOTIC SOLUTIONS
BENCHMARKS
BOLTZMANN-VLASOV EQUATION
COMPUTERIZED SIMULATION
CONVERGENCE
DEFORMATION
DISPERSION RELATIONS
EIGENVALUES
EQUILIBRIUM
HERMITE POLYNOMIALS
NONLINEAR PROBLEMS
PERIODICITY
PHASE SPACE
STABILITY
VELOCITY
VORTICES
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MASS TRANSFER
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
POLYNOMIALS
SIMULATION
SPACE
VARIATIONS