Damping of long‐wavelength kinetic Alfvén fluctuations: Linear theory

The full electromagnetic linear dispersion equation for kinetic Alfvén fluctuations in a homogeneous, isotropic, collisionless, Maxwellian electron‐proton plasma is solved numerically in the long‐wavelength limit. At propagation sufficiently oblique to the background magnetic field B o , the wave number dependence of the damping rate of such modes is summarized by an analytic expression which scales as k ⊥ 2 k ∥ where the subscripts denote directions relative to B o . This damping progressively (although not monotonically) increases with increasing electron and proton β , corresponding to four distinct damping regimes: nonresonant, electron Landau, proton Landau, and proton transit‐time damping.