Generalized Kinetic Current-Sheet Equilibria

The well-studied equilibrium distribution of the Harris current-sheet $[1]$ has long been a mainstay for the initialization of kinetic magnetic-reconnection simulations, typically with the addition of a uniform current-free background plasma. The Harris equilibrium was generalized by Yamada et al.~$[2]$ to include an electrostatic field. Here we present further generalizations of the Harris equilibrium that are exact stationary solution of the Vlasov-Maxwell equations for fields that vary in only one dimension: ${\bf B}=B_z(y)\hat z+B_x(y)\hat x$, and ${\bf E}=-(d\phi/dy)\hat y$. These generalizations allow for (1) Non-Maxwellian distributions, including distributions where the current is carried by velocity-space skew rather than drift; (2) Electrostatic fields that asymptotically vanish far from the current sheet; (3) Magnetic fields that rotate in the $x$--$z$ plane in association with a bifurcated current profile. Methods for implementing these new equilibria to initialize kinetic reconnection simulations will be addressed. \\[4pt] [1] E.~G.~Harris, \textit{Il Nuovo Cimento}, \textbf{23}, 115 (1962).\\[0pt] [2] M.~Yamada, H.~Ji, S.~Hsu, T. Carter, R.~Kulsrud, and F. Trintchouk, \textit{Phys.~Plasmas}, \textbf{7}, 1781 (2000).