Abstract
Abstract. We have performed 3 one-dimensional full particle electromagnetic simulations of a quasi-perpendicular shock with the same Alfvén Mach number MA~5, shock normal-magnetic field angle ΘBn=87° and ion and electron beta (particle to magnetic field pressure) of 0.1. In the first run we used an ion to electron mass ratio close to the physical one (mi/me=1024). As expected from previous high mass ratio simulations the Modified Two-Stream instability develops in the foot of the shock, and the shock periodically reforms itself. We have then self-consistently included in the simulation 10% pickup protons distributed on a shell in velocity space as a third component. In a run with an unrealistically low mass ratios of 200 the shock still reforms itself; reformation is due to accumulation of specularly reflected particles at the upstream edge of the foot. In a third run including pickup protons we used a mass ratio of 1024. The shock reforms periodically as in the low mass ratio run with a somewhat smaller time constant. The specular reflection of pickup protons results in an increase of the shock potential some distance ahead of the shock foot and ramp. The minimum scale of the cross shock potential during reformation is about 7 electron inertial length λe. We do not find any pickup proton acceleration in the ramp or downstream of the shock beyond the energy which specularly reflected ions gain by the motional electric field of the solar wind during their upstream gyration.
Highlights
It is generally accepted that interstellar neutral atoms, which are ionized in the heliosphere and picked up by the solar wind, are accelerated at the termination shock by first order Fermi acceleration, known as diffusive shock acceleration, up to several 100 MeV nucleon−1 (Pesses et al, 1981) and constitute the so-called anomalous cosmic rays (ACRs)
The shock is produced by the so-called injection method: a high-speed plasma consisting of solar wind electrons, solar wind protons, and pickup protons is injected from the left hand boundary of a one-dimensional simulation system and travels toward positive x
We have presented in this paper 3 full particle simulations of a quasi-perpendicular shock with the same Alfven Mach number MA and shock normal – magnetic field angle Bn but different ion to electron mass ratios, and with or without contribution of pickup protons
Summary
It is generally accepted that interstellar neutral atoms, which are ionized in the heliosphere and picked up by the solar. Scholer et al (2003) have performed full particle simulations of quasi-perpendicular shocks with the physical mass ratio and have found that low ion beta, βi, shocks periodically reform. The length scale of the potential during reformation cycle can, at best, get as small as about 4 electron inertial lengths λe=c/ωpe (ωpe is the electron plasma frequency) They have concluded that the MRI process is not a viable mechanism for pre-acceleration of pickup ions at the termination shock, Lipatov and Zank (1999) found such an acceleration process in their finite electron mass hybrid shock simulations where pickup protons were included. In order to achieve reasonable run times and simulation domains a ratio of ωpe/ ce=2 had to be used
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