Scaling of Ion Bulk Heating in Magnetic Reconnection Outflows for the High-Alfvén-speed and Low-β Regime in Earth’s Magnetotail

Abstract We survey 20 reconnection outflow events observed by Magnetospheric MultiScale in the low- β and high-Alfvén-speed regime of the Earth’s magnetotail to investigate the scaling of ion bulk heating produced by reconnection. The range of inflow Alfvén speeds (800–4000 km s −1 ) and inflow ion β (0.002–1) covered by this study is in a plasma regime that could be applicable to the solar corona and flare environments. We find that the observed ion heating increases with increasing inflow (upstream) Alfvén speed, V A , based on the reconnecting magnetic field and the upstream plasma density. However, ion heating does not increase linearly as a function of available magnetic energy per particle, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Instead, the heating increases progressively less as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> rises. This is in contrast to a previous study using the same data set, which found that electron heating in this high-Alfvén-speed and low- β regime scales linearly with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic">V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> , with a scaling factor nearly identical to that found for the low- V A and high- β magnetopause. Consequently, the ion-to-electron heating ratio in reconnection exhausts decreases with increasing upstream V A , suggesting that the energy partition between ions and electrons in reconnection exhausts could be a function of the available magnetic energy per particle. Finally, we find that the observed difference in ion and electron heating scaling may be consistent with the predicted effects of a trapping potential in the exhaust, which enhances electron heating, but reduces ion heating.