Abstract
An explicit symplectic integration scheme which describes the self-consistent wave particle interaction is developed. The integrator does not split the hamiltonian trivially into a kinetic and potential part. The integrator yields accurate growth rates for the gentle-bump instability even when the timestep is of the order of the inverse plasma frequency. This represents up to a tenfold reduction in computation compared to conventional schemes. The integrator is generalizable to arbitrary order without increase in storage requirements, but tests show that when the accuracy requirements are of the order of a few percent, the second-order method is the most efficient.
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