If the current sheet between adjacent twisted magnetic flux tubes is sufficiently thin, the electron flow velocity becomes comparable to the Alfv\'en velocity and can destabilize collisionless Alfv\'en waves. The threshold for instability in force-free plasmas is calculated for both inertial and kinetic Alfv\'en-wave regimes. When there is strong magnetic shear, unstable kinetic Alfv\'en waves can resonantly accelerate ions to energies much higher than the electron temperature.
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Paul M. Bellan (1999) studied this question.
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