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We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwellsystems for collisionless plasmas. The linearized systems can be written asseparable Hamiltonian systems with constraints. By using a general theory forseparable Hamiltonian systems, we recover the sharp linear stability criteriaobtained previously by different approaches. Moreover, we obtain theexponential trichotomy estimates for the linearized Vlasov-Maxwell systems inboth relativistic and nonrelativistic cases.

Linear instability of Vlasov-Maxwell systems revisited-A Hamiltonian approach