Alfvén Wave Damping from Finite Gyroradius Coupling to the Ion Acoustic Mode

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Abstract
The collisionless damping of shear Alfvén waves in the limit of low frequency and small but finite Larmor radius is discussed. Because the averaging of the wave electric field over the Larmor circle (the so‐called finite cyclotron radius effect) creates a small difference in the transverse velocities of the ions and electrons, a longitudinal electric field appears in the Alfvén wave which is responsible for the transfer of the wave energy into the thermal motion of the “resonant” particles V z = ω/k z . Numerical solutions (in the complex ω plane) of the dispersion relation for two wave modes have been obtained: the shear Alfvén mode and the least damped Fried and Gould ion acoustic mode. The normalized damping rate (Im ω)/(Re ω) has been computed for both waves, and it is shown that the damping factor for the Alfvén wave is maximal when the Alfvén velocity is equal to the real part of the phase velocity of the ion acoustic wave. Moreover, there exists a particular direction of propagation with respect to the magnetic field for which both the Alfvén and the least damped ion acoustic waves have the same Landau damping. The damping factor for the ion acoustic wave is a minimum for this particular mode and it is shown that at low values of the electron‐to‐ion temperature ratio T e /T i (T e /T i ≲ 2) , the critical drift velocity necessary for instability occurs at a much lower velocity than is usually predicted.