Chaotic scattering of pitch angles in the current sheet of the magnetotail

Abstract

The process of pitch angle scattering by a current sheet is studied using the modified Harris field model. The relationship between the incoming asymptotic pitch angle αin and the outgoing asymptotic pitch angle αout is studied from first principles by numerically integrating the equation of motion. We give evidence that charged particles undergo chaotic scattering by the current sheet. For fixed αin, it is shown that αout exhibits sensitive dependence on the energy parameter Ĥ in certain energy ranges. For fixed Ĥ in the same energy ranges, αout sensitively depends on αin. For other energy values, αout does not show sensitive dependence on αin for most phase angles. The latter energy values occur at the resonance values given by the previously identified relationship Ĥ1/4 ∼ N + 0.6. Thus αout exhibits no significant sensitivity near these resonance energies. This conclusion applies to a range of αin centered at αin = 0 (i.e., field aligned in the asymptotic region). A distribution of αin is mapped from the asymptotic region to the midplane, and it is found that the resulting particle distribution should have beam structures with well‐collimated pitch angles near each resonance energy value. Implications for the particle distribution functions in the Earth's magnetotail are discussed.