Collisionless resistivity in a bifurcated current sheet

Abstract

The collisionless resistivity due to charged particle chaos in spatially inhomogeneous magnetic fields is calculated for two frequently observed magnetotail current sheets, the X line, and a bifurcated current sheet (BCS) over varying strengths of cross-tail electric field. The calculation is done for two charged species, protons and O + ions, found in the magnetotail specially during active times. Chaotic behavior of the particles is studied for the chaos parameter ≈ 1 defined by Buchner and Zelenyi (1989) as the square root of minimum radius of curvature to the maximum particle gyroradius. The surface of section plot and maximal Lyapunov exponents are analyzed to compare the particle behavior in the two magnetic field topologies. It is found that the particle behavior in a BCS is chaotic around the two humps located at ±z 0 and that the configuration is more chaotic than the X line (maximum Lyapunov exponent for X line is around 0.25 compared to 0.34 for BCS). The collisionless resistivity is calculated using the technique developed by Numata and Yoshida (2003). The method relies on a phenomenological equivalence between the particle loss rate from the chaos region and rate of change of momentum in the chaos region under steady state conditions. Rapid decay of the particles from the chaos region is modeled with exponential fits, and it is found that a double exponent is needed for O + ions in an X line and for both species in the BCS. The resistivity thus calculated is found to be 9-10 orders of magnitude higher than the Spitzer resistivity.

Chaos-induced resistivity in different magnetic configurations

“…Following Numata & Yoshida (2003), Andriyas &Spencer (2014), andShang et al (2017), the anomalous resistivity due to the chaotic motion of particles may be calculated from the "average" acceleration of particles along the acceleration electric field, α, and the relative escape rate of particles from the chaos region, β, which are defined by the following expressions…”

Chaos-induced resistivity in different magnetic configurations

“…Following Numata & Yoshida (2003), Andriyas &Spencer (2014), andShang et al (2017), the anomalous resistivity due to the chaotic motion of particles may be calculated from the "average" acceleration of particles along the acceleration electric field, α, and the relative escape rate of particles from the chaos region, β, which are defined by following expressions…”