Theoretical constraints on the cross-tail width of bursty bulk flows

Abstract

The characteristic cross-tail width of bursty bulk flows (BBFs) in earth's plasma sheet was investigated at two stages of its life, one at its onset, the other when it is fully developed. Equilibrium domains with gradient of magnetic field are constructed. Interchange instability analysis of such domains yields the most unstable mode with the half wave length comparable with the observed cross-tail width of a flow burst and the inverse of growth rate comparable with its duration. The thickness of the plasma sheet for the most unstable mode is also comparable to the width of BBFs in the north–south direction. We found that viscosity, the dimension of the unstable domain, the thickness of the plasma sheet and gradient of the magnetic field together determine the most unstable mode. The ion Larmor radius plays an important role in viscosity as half effective mean free path. For a fully developed flow, however, velocity-caused pressure difference between the leading and trailing sides of a flow burst also plays a role. The equatorial cross section of flow is reshaped and its cross-tail width is changed as well. Representing the surrounding medium with empirical magnetic field and plasma models, the force balance of the fast flow is analyzed. The cross-section area of flow burst is estimated to be one to several square earth radii, and the cross-tail width of fast flow is estimated to be 1 to 3 earth radii, which is consistent with observations of BBFs.