Heat pump via charge incompressibility in a collisional magnetized multi-ion plasma

Stratification due to ion-ion friction in a magnetized multiple-ion species plasma is shown to be accompanied by a heat pump effect, transferring heat from one ion species to another as well as from one region of space to another. The heat pump is produced via identified heating mechanisms associated with charge incompressibility and the Ettingshausen effect. Besides their academic interest, these effects may have useful applications to plasma technologies that involve rotation or compression.

Figure 1

Charge incompressibility in crossed magnetic and gravitational fields. Initially the plasma slab has uniform density and temperature. As external force is applied, the total ion charge density is conserved locally. In contrast, in incompressible fluid, the number density is conserved instead.

Figure 2

The evolution of (a) H density; (b) ${}^4\mathrm{He}$ density; (c) H temperature; (d) ${}^4\mathrm{He}$ temperature in the MITNS simulation of two-ion-species plasma slab. The net ion density is increasing at the top, but the Ettingshausen effect causes the net heat flow to be from top to bottom. Gravitational potential increases from zero to $m_{p}gL=2T_0$; the initial $\beta$ is ${10}^{-3}$; the system size is 20 proton gyroradii; and the proton inverse Hall parameter is ${\nu }_{pp}/{\mathrm{\Omega }}_p\sim 0.05$ (for characteristic parameters). Density and temperature units are arbitrary. The potential ${\mathrm{\Phi }}_s$ is shaped like the segment of a sine curve from minimum to maximum.

Figure 3

Maximum spatial variation of temperature $\mathrm{\Delta }T$ versus hydrogen fraction in H-He plasma. The simulation results are with diffusive heat flux ${\mathbf{q}}^T$ (blue) and without ${\mathbf{q}}^T$ (red). The prediction of Eq. (8) is the black line. Points represent values of $m_{p}gL/T_0$ ($0.01,0.1,1$), all overlapping. See the Appendix for more information on the simulations shown here.