Probing Proton versus Electron Heating and Energization during Magnetic Reconnection

Abstract The mechanisms controlling the relative heating and energization of electrons and protons during magnetic reconnection are explored. Simulations are carried out with the kglobal model, which produces bulk heating and the extended power-law distributions of both species that have been documented in observations. The simulations have been carried out with a range of proton-to-electron mass ratios and upstream temperatures to isolate the factors that control energy gain. The simulations reveal that when the upstream temperatures of the two species are equal, the proton heating and energization exceed that of electrons, and that this is a consequence of the much larger energy gain of protons on their first entry into the reconnection exhaust. The effective energy gain of protons on exhaust entry scales as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>A</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> since the protons counterstream at the Alfvén speed C A while the initial electron energy gain is smaller by the factor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Since Fermi reflection during flux rope merger dominates energy gain in large-scale reconnecting systems and the rate of energy gain is proportional to energy, protons continue to gain energy faster than electrons for the duration of the simulations, leading to temperature increments of protons exceeding that of electrons, and the nonthermal energy content of protons also exceeding that of electrons.