Energy dissipation and entropy in collisionless plasma

It is well known that collisionless systems are dissipation free from the perspective of particle collision and thus conserve entropy. However, processes such as magnetic reconnection and turbulence appear to convert large-scale magnetic energy into heat. In this paper, we investigate the energization and heating of collisionless plasma. The dissipation process is discussed in terms of fluid entropy in both isotropic and gyrotropic forms. Evolution equations for the entropy are derived and they reveal mechanisms that lead to changes in fluid entropy. These equations are verified by a collisionless particle-in-cell simulation of multiple reconnecting current sheets. In addition to previous findings regarding the pressure tensor, we emphasize the role of heat flux in the dissipation process.

Figure 1

Snapshots of isotropic fluid entropy for electrons (top) and ions (bottom) at different simulation times ${\mathrm{\Omega }}_{ci}t=50$ (left), 100 (middle), and 200 (right). Black contour lines represent magnetic field lines.

Figure 2

Energy budget of the simulation. The top panel shows the evolution of magnetic energy (dot-dashed black), ion kinetic energy (solid blue), and electron kinetic energy (dashed red). The second panel from top shows the ion (solid blue) and electron (dashed red) thermal energy. The third panel shows the ion (solid blue) and electron (dashed red) bulk flow energy. All energies in these panels are normalized to the initial magnetic energy. In the bottom panel, the rates of change in ion (solid blue) and electron (dashed red) thermal energy are shown.

Figure 3

Rate of change of the fluid entropy for electrons (left panels) and ions (right panels). The solid black lines in the top panels represent the rate of change of the fluid entropy. The convection term, Pi-D, and heat flux terms are evaluated separately and shown in the bottom panels. The sum of the three terms is displayed as the dashed blue curves in the top panels.

Figure 4

Rate of change of the CGL fluid entropy for electrons (left panels) and ions (right panels). The solid black lines in the top panels represent the rate of change of the CGL entropy $S^c$ while the dot-dashed black lines represent the regular fluid entropy $S$. The convection term and two other terms (see text for details) are evaluated separately and shown in the bottom panels. The sum of the three terms is displayed as the dashed blue curves in the top panels.