Admissible Equilibria of Non-neutral Plasmas in a Malmberg-Penning Trap

Abstract

A ''parallel current constraint'' is derived, that in combination with the Poisson equation allows one to select admissible equilibria of non-neutral plasmas in a Malmberg-Penning trap in the presence of a nonuniform and nonaxisymmetric magnetic field. Asymmetry-induced currents (analogous to the PfirschSchlüter currents in Tokamaks) appearing in a non-neutral plasma even in the absence of magnetic drifts are explicitly computed in the case of a uniformly tilted magnetic field. The radial confinement of non-neutral plasmas in Malmberg-Penning (MP) traps is provided by a strong axial magnetic field. This field is assumed to be uniform in most theories that deal with plasma confinement. However, small perturbations of the magnetic field may play a crucial role in the transport of non-neutral plasmas in this kind of confinement devices [1]; see also the review paper [2] and references therein for further discussion of the problem of non-neutral plasma transport. On the other hand, it is well known that an accurate treatment of the plasma transport requires at first an analysis of the plasma equilibrium, as it is demonstrated by established theories for quasineutral plasma confined, e.g., in tandem mirrors [3].It may be wondered whether an equilibrium of a nonneutral plasma exists in an asymmetric magnetic field, since an asymmetry leads in general to plasma expansion. A positive answer to this question implies that the equilibrium is referred to a time interval shorter than the expansion time m . If the asymmetry is small, the latter is expected to be at least greater then the axial bounce time of the particles inside the trap b and the plasma azimuthal rotation time 2=! E , i.e., m ) ð b ; 2=! E Þ. In general, m / À2 , where the parameter characterizes the smallness on the magnetic field inhomogeneity. At this stage it can be assumed that $ B=B, where B represents the difference of the actual magnetic field from an ideal uniform magnetic field B Ã ¼ B Ã e z directed along the symmetry axis of the cylindrical confinement device. For the small values achieved in existing devices the expansion time can therefore be quite large, and for a shorter time interval, t ( m , it is possible to consider a slowly evolving plasma column as being in a static equilibrium.Systematic studies of nonaxisymmetric equilibria in a MP trap have been started in Refs. [4,5]. In Ref.[4] the equilibrium of a non-neutral plasma column in a weakly tilted magnetic field was simulated numerically. In Ref. [5] an electrostatic asymmetry was introduced by azimuthally sectored electrodes, and the analytical treatment was limited to the case of a cold plasma with a stepwise radial density profile. Later on, three-dimensional numerical particle-in-cell simulations of the non-neutral plasma equilibrium with quadrupole or mirror magnetic perturbations have been reported in Ref. [6]. However, similar numerical simulations are hardly able to uncover fine-structure effects that limit plasma lifetime in existing and future facilities designed to achieve im...

Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with quadrupole field errors

“…1 for a localized magnetic quadrupole; for a constant quadrupole, it is equal to ͑ 2 / 2−L 2 / 8͒h 0 . 5,6 As it follows from the discussion in Sec. Azimuthal sweep of the streamline patterns are shown in Fig.…”

“…5,6 In an ideally axisymmetric Malmberg-Penning trap, the electric current has the merely azimuthal component caused by the charged plasma rotation. These currents can be thought of as an analog of the Pfirsch-Schlüter currents in tokamaks 8 or the Stupakov currents in tandem mirrors; 9,10 however, they have a different origin.…”