Particle Acceleration by Pickup Process Upstream of Relativistic Shocks

<jats:title>Abstract</jats:title> <jats:p>Particle acceleration at magnetized purely perpendicular relativistic shocks in electron–ion plasmas is studied by means of two-dimensional particle-in-cell simulations. Magnetized shocks with the upstream bulk Lorentz factor <jats:italic>γ</jats:italic> <jats:sub>1</jats:sub> ≫ 1 are known to emit intense electromagnetic waves from the shock front, which induce electrostatic plasma waves (wakefield) and transverse filamentary structures in the upstream region via stimulated/induced Raman scattering and filamentation instability, respectively. The wakefield and filaments inject a fraction of the incoming particles into a particle acceleration process, in which particles are once decoupled from the upstream bulk flow by the wakefield, and are picked up again by the flow. The picked-up particles are accelerated by the motional electric field. The maximum attainable Lorentz factor is estimated as <jats:inline-formula> <jats:tex-math> <?CDATA ${\gamma }_{\max ,e}\sim \alpha {\gamma }_{1}^{3}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> <mml:mo>,</mml:mo> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mi>α</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac38aaieqn1.gif" xlink:type="simple" /> </jats:inline-formula> for electrons and <jats:inline-formula> <jats:tex-math> <?CDATA ${\gamma }_{\max ,i}\sim (1+{m}_{e}{\gamma }_{1}/{m}_{i}){\gamma }_{1}^{2}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> <mml:mo>,</mml:mo> <mml:mi>i</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <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:msubsup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac38aaieqn2.gif" xlink:type="simple" /> </jats:inline-formula> for ions, where <jats:italic>α</jats:italic> ∼ 10 is determined from our simulation results. <jats:italic>α</jats:italic> can increase up to <jats:italic>γ</jats:italic> <jats:sub>1</jats:sub> for a weakly magnetized shock if <jats:italic>γ</jats:italic> <jats:sub>1</jats:sub> is sufficiently large. This result indicates that highly relativistic astrophysical shocks such as external shocks of gamma-ray bursts can be an efficient particle accelerator.</jats:p>