Global thermal equilibrium for non-neutral plasma in non-uniform field traps with cylindrical symmetry

The confinement of a non-neutral plasma in a global thermal equilibrium state is known to

be possible in the uniform magnetic field of a Penning-Malmberg trap [1]. The distribution

function of a global thermal equilibrium state is obtained by maximizing the plasma entropy

subject to fixed values for the total number of particles, total energy and total canonical angular

momentum [2]. If a non-neutral plasma arrives in this state, there is no theoretical limit on the

confinement time. We generalize the theory of these states to include cylindrical symmetric traps

with non-uniform magnetic fields. We construct configurations that enable the confinement of

a plasma with the topology of a torus in a magnetic dipole field. Such a configuration also

confines a neutral plasma for a finite amount of time, making it an attractive candidate for the

creation of an electron-positron pair plasma [3].

[1] S. A. Prasad and T. M. O’Neil. "Finite length thermal equilibria of a pure electron plasma column," Phys.

Fluids 22, 278 (1979).

[2] T. O’Neil and D. H. Dubin, Thermal equilibria and thermodynamics of trapped plasmas with a single sign of

charge, Physics of Plasmas 5, 2163 (1998).

[3] M. R. Stoneking et al. "A new frontier in laboratory physics: magnetized electron–positron plasmas." Journal

of Plasma Physics 86.6 (2020).