The kinetic Alfvén wave is studied in a cylindrical force-free plasma with self-consistent magnetic fields. This equilibrium represents a reversed field pinch or a spheromak. The stability of the wave is found to depend on the ratio of the electron drift velocity to the Alfvén velocity. This ratio varies inversely with the square root of the plasma line density. The critical line density using the Spitzer–Harm electron distribution function is found for reversed field pinches with deuterium plasmas to be approximately 2×1018 and is 5×1017 m−1 in spheromaks with hydrogen plasmas. The critical line density is in reasonable agreement with experimental data for reversed field pinches.
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Meyerhofer et al. (1984) studied this question.