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A formulation for computation of a class of collision-free plasmas in two dimensions

The restrictions imposed are that the magnetic field is everywhere in the x direction, and that no quantity varies with x, but several interesting instabilities can still occur. After some discussion of objectives, a fluid-like formulation is pursued, in which the pressure anisotropy is retained, but higher moments neglected. It shows a resonance at twice the gyrofrequency, and for electrons the constraint on the time step would be unacceptable, so they should be treated more crudely. Then the dispersion equation shows only two modes, which appear sufficiently harmless for us to proceed to computations.