Magnetic Field Amplification and Particle Acceleration in Weakly Magnetized Transrelativistic Electron–Ion Shocks

Abstract We investigate the physics of quasi-parallel transrelativistic shocks propagating in weakly magnetized plasmas by means of long-duration two-dimensional particle-in-cell simulations. The structure of the shock precursor is shaped by a competition between the Bell instability and the Weibel (filamentation) instability. The Bell instability is dominant at relatively high magnetizations ( σ ≳ 10 −3 ), whereas the Weibel instability prevails at lower magnetizations ( σ ≲ 10 −4 ). Shocks with precursors shaped by Bell modes efficiently accelerate ions, converting a fraction ε i ∼ 0.2 of the upstream flow energy into downstream nonthermal ion energy. The maximum energy of nonthermal ions exhibits a Bohm scaling in time, as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:mi>t</mml:mi> </mml:math> . A much smaller fraction ε e ≪ 0.1 of the upstream flow energy goes into downstream nonthermal electrons in the Bell regime. On the other hand, when the precursor is dominated by Weibel modes, the shock efficiently generates both nonthermal ions and electrons with ε i ∼ ε e ∼ 0.1, albeit with a slower scaling for the maximum energy, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> . Our results are applicable to a wide range of transrelativistic shocks, including the termination shocks of extragalactic jets, the late stages of gamma-ray burst afterglows, and shocks in fast blue optical transients.