Ion heating by kinetic cross-field streaming instability due to reflected ions at a quasiperpendicular shock

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Abstract
The present paper shows that the reflected ion at a supercritical quasiperpendicular shock wave can excite a purely growing m9de propagating parallel to the ambient magnetic field (k∥B0). To discuss the ion heating by such an unstable mode, the self‐consistent quasilinear kinetic equation is solved with the assumption that the present purely growing mode is the dominant unstable mode in the system. In the quasilinear analysis of the instability, two particular cases are considered—the case of low initial ion beta [βi(0)=0.1] and that of a high initial ion beta [βi(0)=1]. For each case of low and high initial betas, two values of initial turbulence level are used. One corresponds to δB2(0)/B20=0.1 and the other corresponding to δB2(0)/B20 =0.1. It is shown that for both low and high beta cases, the ion heating at the shock becomes more efficient for a higher value of δB2(0)/B20.