A novel quiescent quasi-steady state of a toroidal electron plasma

The existence of a novel quiescent quasi-steady state of the toroidal electron cloud is reported. This is achieved by first constructing a maximum entropy mean-field solution for pure electron plasma at zero-inertia limit ( rho <overbar></mml:mover> L / L -> 0, where rho <overbar></mml:mover> L is average electron Larmor radius and L is typical mean spatial gradient length scale), which is then used as "seed" solution to a high fidelity 3D3V PIC solver, at finite density of pure electron plasma in small aspect ratio toroidal configuration. The electron cloud is shown to attain a quiescent quasi-steady state satisfying full equations of motion and hence accurate to all orders in rho <overbar></mml:mover> L / L, with far superior confinement properties as compared to typical initial condition used in today's laboratories. Salient features include the absence of center of charge motion, naturally shaped centrally peaked density, and potential concentric surfaces. The variation of temperatures T <overbar></mml:mover> parallel to ( R , t ) and T <overbar></mml:mover> perpendicular to ( R , t ) (averaged over the toroidal direction) with major radius R is reported for the first time for a toroidal electron plasma. For the small aspect ratio of O(1) considered here, the temperature profiles are such that T <overbar></mml:mover> parallel to ( R , t ) and T <mml:mo><overbar></mml:mover> <mml:mo>perpendicular to <mml:mo stretchy="false">( R <mml:mo>, t <mml:mo stretchy="false">) fall with R as 1 <mml:mo>/ R 2 and 1 <mml:mo>/ R 3, respectively. Our solution to this long-standing problem of finding a quiescent quasi-steady of a toroidal charge cloud may have direct relevance to not only pure electron plasma but also to pure ion plasma.