Structure of kinetic Alfvén waves with small transverse scale length

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Abstract
This analytical study illustrates the spatialpattern of kinetic Alfvén waves excited by a current-modulating disk whose dimension a, transverse to the confining magnetic field, is comparable to the ion sound gyroradius c s /Ω i , where c s is the sound speed and Ω i the ion cyclotron frequency. The radial structure of the wave azimuthal magnetic field is found to consist of four regions: a Bessel function behavior for r<a, a near null at r≅a, and a driven Airy pattern for r≫a which merges onto the 1/r asymptotic region. The pattern spreads at an angle given by tan θ=(ω/Ω i )(c s /v A )/2.6, where ω is the modulation frequency and v A is the Alfvén speed. This behavior arises because there is a maximum value at finite k ⊥ for the ratio of the perpendicular to parallel group velocity, which differs from the cone spreading [G. J. Morales et al., Phys. Plasmas 1, 3765 (1994)] associated with inertial Alfvén waves.

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