Kinetic Alfvén wave revisited

<jats:p>We develop a series of new analytical expressions describing the physical properties of the kinetic Alfvén wave. The wave becomes strongly compressive when <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/jgra14441-math-0001.gif" xlink:title="equation image" /> is of the order of the ion inertial length. Thus, in a low‐β plasma, the kinetic Alfvén wave can be compressive at values of <jats:italic>k</jats:italic><jats:sub>⊥</jats:sub> for which the dispersion relation departs only slightly from that of the usual MHD Alfvén wave. The compression is accompanied by a magnetic field fluctuation δ<jats:italic>B</jats:italic><jats:sub>‖</jats:sub> such that the total pressure perturbation δ<jats:italic>p</jats:italic><jats:sub>tot</jats:sub> ≈ 0. Thus the wave undergoes transit‐time damping as well as Landau damping; the two effects are comparable if the ion thermal speed is of the order of the Alfvén speed. We find that the transverse electric field is elliptically polarized but rotating in the electron sense; this surprising behavior of the polarization of the Alfvén branch was discovered numerically by <jats:italic>Gary</jats:italic> [1986]. We derive a new dispersion relation which explicitly shows how the kinetic Alfvén wave takes on some properties of the large‐<jats:italic>k</jats:italic><jats:sub>⊥</jats:sub> limit of the slow mode. We also derive approximate dispersion relations valid for a multi‐ion plasma with differential streaming. We suggest that the kinetic Alfvén wave may be responsible for the flattening of density fluctuation spectra observed at large wavenumbers in the corona and in the solar wind. We also find that our derived properties of the kinetic Alfvén wave are consistent with its presence in the dissipation range of MHD turbulence [<jats:italic>Leamon et al.</jats:italic>, 1998a, b].</jats:p>