Compressibility and cyclotron damping in the oblique Alfvén wave

Abstract

Compressibility, magnetic compressibility, and damping rate are calculated for the obliquely propagating Alfvén shear wave in high‐ and low‐beta Vlasov plasmas. There is an overall increase in compressibility as beta is reduced from β = 1 to β≪1. For high obliquity θ and low frequency (ω≪Ωp) the compressibility C follows a k² wave number dependence; for high θ and low β the approximation C(k) ≈ kn² ≡ (kVA/Ωp)² holds for wave numbers up to the proton cyclotron resonance, where Ωp is the proton cyclotron frequency and VA is the Alfvén velocity. Strong proton cyclotron damping sets in at kn of the order of unity; the precise kn position of the damping cutoff increases with decreasing β and increasing θ. Hence compressibility can exceed unity near the damping cutoff for high‐θ waves in a low‐β plasma. The magnetic compressibility of the oblique Alfvén wave also has a k² dependence and can reach a maximum value of the order of 10% at high wave number. It is shown that Alfvén compressibility could be the dominant contributor to the near‐Sun solar wind density fluctuation spectrum for k>10−2 km−1 and hence might cause some of the flattening at high wave number seen in radio scintillation measurements. This would also be consistent with the notion that the observed density spectrum inner scale is a signature of cyclotron damping.