Dory–Guest–Harris instability as a benchmark for continuum kinetic Vlasov–Poisson simulations of magnetized plasmas

The Dory–Guest–Harris instability is demonstrated to be a well-suited benchmark for continuum kinetic Vlasov–Poisson algorithms. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. A fourth-order continuum kinetic algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. Second-order accurate simulations are also shown to be consistent with theoretical predictions, but require higher resolution for convergence. The Dory–Guest–Harris instability benchmark extends the scope of current standard test problems by providing a substantive means of validating continuum kinetic simulations of magnetized plasmas in higher-dimensional 3D (x,vx,vy)(x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented.