Quasi‐perpendicular shocks: Length scale of the cross‐shock potential, shock reformation, and implication for shock surfing

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Abstract
One‐dimensional (1‐D) full particle simulations of almost perpendicular supercritical collisionless shocks are presented. The ratio of electron plasma frequency ωpe to gyrofrequency Ωce, the ion to electron mass ratio, and the ion and electron β (β = plasma to magnetic field pressure) have been varied. Due to the accumulation of specularly reflected ions upstream of the shock, ramp shocks can reform on timescales of the gyroperiod in the ramp magnetic field. Self‐reformation is not a low ωpe/Ωce process but occurs also in (ωpe/Ωce)2 ≫ 1, low β simulations. Self‐reformation also occurs in low ion β runs with an ion to electron mass ratio mi/me = 1840. However, in the realistic mass ratio runs, an electromagnetic instability is excited in the foot of the shock, and the shock profile is considerably changed compared to lower mass ratio runs. Linear analysis based on three‐fluid theory (incident ions, reflected ions, and electrons) indicates that the instability is a modified two‐stream instability between the decelerated solar wind electrons and the solar wind ions on the whistler mode branch. In the reforming low ion β shocks, part of the potential drop occurs at times across the foot, and part of the potential (∼40%) occurs over a few (∼4) electron inertial lengths in the steepened up ramp. Self‐reformation is a low ion β process and disappears for a Mach 4.5 shock at/or above βi ≈ 0.4. It is argued that the ion thermal velocity has to be an order of magnitude smaller than the shock velocity in order for reformation to occur. Since according to these simulations only part of the potential drop occurs for relatively short times over a few electron inertial lengths, it is concluded that coherent shock surfing is not an efficient acceleration mechanism for pickup ions at the low β heliospheric termination shock.