A kinetic cross-field streaming instability

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Abstract
In a high‐beta plasma the so‐called modified‐two‐stream instability, which results from strongly magnetized electrons drifting relative to unmagnetized ions across a homogeneous magnetic field, is misnamed because the mode is highly kinetic, particularly when the relative streaming velocity exceeds the Alfvén speed of the plasma. This kinetic cross‐field streaming instability is investigated in detail, examining the effect of the electromagnetic terms and the stability boundaries in both low‐ and high‐beta plasmas. An approximate dispersion relation showing the relation of this mode to the whistler is derived and solutions of it are compared with those obtained from the exact dispersion relation. The kinetic mode, unlike the usual modified‐two‐stream instability, is not stabilized by electromagnetic effects when the relative electron–ion drift speed exceeds the Alfvén speed.