We propose the heating of collisionless plasma by utilizing a spatial phase mixing by shear Alfv\'en wave resonance and discuss the application to toroidal plasma. The phase mixing takes place as a result of the nonuniform Alfv\'en speed. The approximate heating rate per cycle of the wave frequency is given by (b₀^_²μ₀)κk_⊥ where κ is the measure of the nonuniformity, k_⊥ is the wave number perpendicular to the direction of the magnetic field and the nonuniformity, and b₀ is the flux density of the applied-wave magnetic field.
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Hasegawa et al. (1974) studied this question.
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