UCLA BPPL - Field Reversed Configurations

A Helmholtz coil is inserted into a uniform high-electron beta plasma. A current is pulsed through the coil so as to produce a field opposite to and stronger than the uniform background magnetic field. The field-reversed configuration (FRC) contains two cusp null points on axis.

EMHD vortex

Schematic diagram of the plasma device with field-reversed configuration produced by a Helmholtz coil.

After establishing this initial field topology, the current is rapidly switched off, and the free relaxation of the FRC, now only carried by electron currents, is studied. The FRC is not stabilized by any conducting boundaries. It relaxes without destructive tilting instabilities. The FRC elongates, slightly tilts, and precesses around B0. The behavior is explained by the self-consistent behavior of field lines frozen into the electron fluid flow as follows: The toroidal electron flow rotates the magnetic field lines which creates toroidal fields at the ends of the FRC. These toroidal fields are produced by axial currents which close in poloidal loops. The associated electron flows convect the field lines axially outward which elongates the FRC. Thus, twisting and stretching of field lines are always coupled in EMHD.

Directional antenna

(a) Measured magnetic field vectors and (b) calculated field lines (contours of constant poloidal flux) for an EMHD FRC.

When the FRC is tilted, the toroidal electron flow not only twists the field lines but convects the entire tilted FRC topology toroidally. This results in a precession motion which is observed for the first time. It is best demonstrated by calculating the magnetic moment m of the toroidal current loop and observing it rotate as the FRC decays. The tip of the vector m traces out a 3-D hodograph which can be viewed stereoscopically.

Directionality of antenna

3-D hodograph of the magnetic moment of an EMHD FRC. The vector m performs a precession as the FRC freely relaxes.

The stability of the FRC to tilting is a topic of current research. The FRC appears unstable since the magnetic moment is not aligned with the external field. In a single fluid (or solid), the magnetic moment would rotate until aligned with the external field. But in an EMHD fluid, the ions are essentially immobile, and only the electrons are coupled to the magnetic field. The torque on the electrons cannot rotate the electron fluid since it is bound by space charge forces to the immobile ions. In ideal, uniform EMHD plasmas, the electric and magnetic forces exactly balance, -neE + J × B = 0, implying no rotation of the electrons. A small rotation is observed, possibly due to pressure gradients, breakdown of EMHD near null points, turbulence, etc. Observationally, the tilt decreases with increasing size of the FRC. Further research is needed in this field.