Parallel Transport on Open Magnetic Field Lines

The plasma parallel transport on open magnetic fields can become dominant, and its theory becomes especially challenging when the mean-free-path({\it{mfp}}) of the plasma is comparable to or greater than the field line length scale of B modulation. Here we present a fluid theory based on the lowest order expansion of Vlasov equation in $\rho/L$. The different roles of $\|B\|$ modulation and the two components of the parallel heat flux ($q_n$ and $q_s$, associated with the parallel and perpendicular thermal energies respectively), in determining the plasma profiles ($n$, $T_\parallel$, $T_\perp$, $\phi$, and $u_\parallel$), are elucidated by general analytical expressions and confirmed by first-principle kinetic simulations of a flux expander into absorbing walls. The parallel heat flux, calculated from kinetic theory in the long {\it{mfp}} regime, is shown to have surprising behaviors along an open field line. For example, $q_n$ can run against the parallel temperature gradient when there is significant flux expansion toward the wall. A scan from low to high collisionality is then performed to clarify the dramatic difference in plamsa profiles. This work was supported by the DOE OFES.