On the compressibility effect in test particle acceleration by magnetohydrodynamic turbulence

Abstract

The effect of compressibility in a charged particle energization by magnetohydrodynamic (MHD) fields is studied in the context of test particle simulations. This problem is relevant to the solar wind and the solar corona due to the compressible nature of the flow in those astrophysical scenarios. We consider turbulent electromagnetic fields obtained from direct numerical simulations of the MHD equations with a strong background magnetic field. In order to explore the flow compressibility effect over the particle dynamics, we performed different numerical experiments: an incompressible case and two weak compressible cases with Mach number <i>M</i> = 0.1 and <i>M</i> = 0.25. We analyze the behavior of protons and electrons in those turbulent fields, which are well known to form aligned current sheets in the direction of the guide magnetic field. What we call protons and electrons are test particles with scales comparable to (for protons) and much smaller than (for electrons) the dissipative scale of MHD turbulence, maintaining the correct mass ratio <span class="equationTd"><span class="MathJax" id="MathJax-Element-1-Frame" tabindex="0" style="position: relative;" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll" altimg="eq-00001.gif"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi></mrow></msub><mo>/</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math>" role="presentation"><nobr><span class="math" id="MathJax-Span-1" style="width: 2.761em; display: inline-block;"><span style="display: inline-block; position: relative; width: 2.371em; height: 0px; font-size: 116%;"><span style="position: absolute; clip: rect(1.738em, 1002.37em, 2.83em, -1000em); top: -2.543em; left: 0em;"><span class="mrow" id="MathJax-Span-2"><span class="mrow" id="MathJax-Span-3"><span class="msub" id="MathJax-Span-4"><span style="display: inline-block; position: relative; width: 1.111em; height: 0px;"><span style="position: absolute; clip: rect(3.438em, 1000.7em, 4.147em, -1000em); top: -4.009em; left: 0em;"><span class="mrow" id="MathJax-Span-5"><span class="mi" id="MathJax-Span-6" style="font-family: STIXGeneral; font-style: italic;">m</span></span><span style="display: inline-block; width: 0px; height: 4.009em;" /><span style="position: absolute; top: -3.859em; left: 0.722em;"><span class="mrow" id="MathJax-Span-7"><span class="mi" id="MathJax-Span-8" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">e</span></span><span style="display: inline-block; width: 0px; height: 4.009em;" /></span></span><span class="mo" id="MathJax-Span-9" style="font-family: STIXGeneral;">/</span><span class="msub" id="MathJax-Span-10"><span style="display: inline-block; position: relative; width: 0.994em; height: 0px;"><span style="position: absolute; clip: rect(3.438em, 1000.7em, 4.147em, -1000em); top: -4.009em; left: 0em;"><span class="mrow" id="MathJax-Span-11"><span class="mi" id="MathJax-Span-12" style="font-family: STIXGeneral; font-style: italic;">m</span></span><span style="display: inline-block; width: 0px; height: 4.009em;" /><span style="position: absolute; top: -3.859em; left: 0.722em;"><span class="mrow" id="MathJax-Span-13"><span class="mi" id="MathJax-Span-14" style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;">i</span></span><span style="display: inline-block; width: 0px; height: 4.009em;" /></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.543em;" /></span><span style="display: inline-block; overflow: hidden; vertical-align: -0.233em; border-left: 0px solid; width: 0px; height: 1.067em;" /></span></span></span></span></span></span></nobr></span></span><span class="equationTd"><span class="formulaLabel">. For these test particles, we show that compressibility enhances the efficiency of proton acceleration, and that the energization is caused by perpendicular electric fields generated between currents sheets. On the other hand, electrons remain magnetized and display an almost adiabatic motion, with no effect of compressibility observed. Another set of numerical experiments takes into account two fluid modifications, namely, electric field due to Hall effect and electron pressure gradient. We show that the electron pressure has an important contribution to electron acceleration allowing highly parallel energization. In contrast, no significant effect of these additional terms is observed for the protons.</span></span>