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EXACT SOLUTION TO LINEAR VLASOV EQUATION AND DISCUSSIONS ON LANDAU DAMPING,INSTABILITIES AND RESONANT INTERACTIONS

Hao Cai

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Abstract

The exact solution to the linearized Vlasov equation has been obtained. We have dis-cussed the singularities of the integrand and compared Landau's treatment with ours. It ispointed out that the Landau damping is related to the phase dispersion of the disturbanceswith different velocities, and the unstable solutions are probably caused by the bunchingeffects, which seems to have nothing to do with the wave-particle energy exchange. Thelinear Vlasov equation is not likely a suitable basis for the description of the resonant inter-action between particles and their self-consistent field since it maintains the conservation ofthe particles' kinetic energy but breaks down the total energy conservation.

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What this paper is about

The exact solution to the linearized Vlasov equation has been obtained. We have dis-cussed the singularities of the integrand and compared Landau's treatment with ours. It ispointed out that the Landau damping is related to the phase dispersion of the disturbanceswith different velocities, and the unstable solutions are probably caused by the bunchingeffects, which seems to have nothing to do with the wave-particle energy exchange. Thelinear Vlasov equation is not likely a suitable basis for the description of the resonant inter-action between particles and their self-consistent field since it maintains the conservation ofthe particles' kinetic energy but breaks down the total energy conservation.

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Available abstract

The exact solution to the linearized Vlasov equation has been obtained. We have dis-cussed the singularities of the integrand and compared Landau's treatment with ours. It ispointed out that the Landau damping is related to the phase dispersion of the disturbanceswith different velocities, and the unstable solutions are probably caused by the bunchingeffects, which seems to have nothing to do with the wave-particle energy exchange. Thelinear Vlasov equation is not likely a suitable basis for the description of the resonant inter-action between particles and their self-consistent field since it maintains the conservation ofthe particles' kinetic energy but breaks down the total energy conservation.

Key concepts: Landau damping, Vlasov equation, Physics, Gravitational singularity, Dispersion relation, Conservation law, Classical mechanics, Quantum electrodynamics

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