Vlasov Equation In Magnetic Field

Details Vlasov Equation In Magnetic Field Vlasov Equation In Magnetic Field

1998-07-02

arxiv.org/abs/math-ph/9807002v2

Journal of Physics A, 32 (1999)5835-5844

Physics

Mathematical Physics

15 pages

Scientific paper

10.1088/0305-4470/32/31/308

The linearized Vlasov equation for a plasma system in a uniform magnetic field and the corresponding linear Vlasov operator are studied. The spectrum and the corresponding eigenfunctions of the Vlasov operator are found. The spectrum of this operator consists of two parts: one is continuous and real; the other is discrete and complex. Interestingly, the real eigenvalues are infinitely degenerate, which causes difficulty solving this initial value problem by using the conventional eigenfunction expansion method. Finally, the Vlasov equation is solved by the resolvent method.

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