Physics of saturation of collisionless tearing mode as a function of guide field

Abstract

The tearing instability has been the subject of much study in space and laboratory plasmas and is thought to play a role as an onset mechanism for reconnection at the magnetotail and at the magnetopause. However, the nonlinear evolution is not completely understood. Here we employ a combination of theory and full particle simulations, including one for realistic mass ratio, to address the saturation of a single, linearly unstable tearing mode as a function of guide field. For the parameter regime considered, we find no agreement with any of the previous theories of tearing mode saturation. There are marked differences in the electron behavior and the associated saturation mechanism in the antiparallel (zero guide field) and finite guide field cases. Electrons become nongyrotropic and also develop temperature anisotropies in the antiparallel case, whereas they remain isotropic in the presence of a guide field. In the antiparallel limit there are two competing saturation mechanisms. One is due to preferential parallel heating of electrons which leads to a saturation amplitude of ws ∼ 2.9 ρe, where ρe is the electron gyroradius in the asymptotic magnetic field and ws is the half‐width of the magnetic island. The other saturation mechanism is electron trapping in the magnetic island which leads to a saturation amplitude comparable to the singular layer thickness (ΔNS). Electron parallel heating is usually the dominant saturation mechanism. However, in the presence of sufficiently fast electron pitch angle scattering, caused either by current‐aligned Weibel instability or turbulence, the second saturation mechanism due to trapping becomes dominant. In the presence of a guide field, the only saturation mechanism is electron trapping which leads to a saturation amplitude of ws ∼ 1.8 ρeG in the strong guide field and ws ∼ (2ρeGΔNS)1/2 in the intermediate regime. Here ρeG is the electron gyroradius in the guide field. The predicted saturation amplitudes for all cases, including the antiparallel regime, are much smaller than the thickness of the magnetopause current layer. Thus a single tearing mode saturates at too small of an amplitude to be of relevance to reconnection in the magnetosphere.