Ion thermalization and wave excitation downstream of Earth's bow shock: A theory for Cluster observations of He 2+ acceleration

It has been well documented that the plasma immediately downstream of Earth's quasi‐perpendicular bow shock, which consists of reflected protons and directly transmitted ions with large temperature anisotropies ( T ⊥ / T z ), is unstable to the excitation of ion cyclotron waves. These waves in turn scatter the protons and ions to marginal stability. Using Cluster data following the inbound shock crossing at 1717:48 UT on 31 March 2001, we investigate the joint evolution of the proton and helium distribution functions. Within a short distance downstream of the shock the perpendicular heating of helium is faster than the parallel heating, so that the temperature anisotropy of helium first increases near the shock before decreasing farther downstream. The observed spectra of magnetic fluctuations, which are dominated by left‐hand circularly polarized waves, display one peak at < gα (He 2+ gyrofrequency), just downstream of the shock, and two peaks with a slot near ≈ gα , farther downstream, where is wave frequency in hertz. We present a quasi‐linear theory that accounts for the observed long‐time decrease of the He 2+ temperature anisotropy and the excited wave spectrum. The predicted temperature anisotropy and the general shape of the excited wave spectrum match the observations remarkably well. Nevertheless, certain features of the observations, such as the large amplitude of the lower‐frequency peak and very low amplitude of the higher‐frequency peak just downstream of the shock, require further work.