A particle model for magnetotail neutral sheet equilibria

Previous studies of forced current sheet equilibria, that is, x ‐independent current sheets with a constant B z = B n and a constant, uniform electric field E y (Eastwood, 1972, 1974; Hill, 1975; Francfort and Pellat, 1976; Lyons and Speiser, 1985) are numerically and analytically extended to the regime υ D /υ T ≲ 1 and B n /( 4π n b υ T ²) ≲ 1, where υ D = cE y /B n , υ T the proton thermal velocity, and n b is the value of the number density outside the current sheet (at the simulation boundary). Such equilibria may be applicable to the thin current sheets observed in the current disruption region of the magnetotail during substorm growth phase and to the magnetotail neutral sheet. It is found that the current and thickness of the forced current sheet are controlled by the motions of the individual protons. For κ A ≪ 1 and υ D /υ T ≳ 1, we numerically verify the scaling for the current sheet half thickness, a ∼ (υ D /υ T ) −4/3 λ b (Francfort and Pellat, 1976), where λ b = ( m i c ²/4π n b e ²) 1/2 and κ A is the value of κ = ( R min /ρ max ) 1/2 in the self‐consistent current sheet for protons of average energy ( R min is the minimum field line radius of curvature and ρ max is the maximum gyroradius). The magnetic field outside the current sheet B x0 is given by eB x0 / m i c = υ D /λ b (Hill, 1975). It is further found that if the degree of pitch angle scattering is treated as a variable parameter, there is a peak value of the current corresponding to zero isotropization of the distribution as it passes through the field reversal. The maximum reduction in the net current (or equivalently, the reduction in B x0 ) due either to nonlinear particle dynamics (chaos) or to pitch angle scattering wave‐particle interactions is by a factor of .This maximum reduction in the current can be achieved by particle nonlinear dynamics for values of κ A near 1 in the regime υ D /υ T ≳ 1. Rather than an anomalous resistivity, the most important effect arising from the particle nonlinear dynamics is a catastrophic loss of equilibrium near κ A = 1. This feature is due to the inability of proton trajectories with κ ≳ 1 to balance the gradient of the magnetic pressure and to set a length scale in the z direction. The signatures of this process, expressed in terms of the current sheet distribution function, the external distribution function, and the magnetic field structure, are charted. These signatures could be used to determine, through satellite observation, if the abrupt loss of equilibrium observed in our model can result in a disruption in the cross‐tail current.