The
Field-Reversed Configuration (FRC) is a compact toroid with little or no
toroidal field. It offers a unique fusion reactor potential because of its
compact and simple geometry, translation properties, and high plasma beta.
These attractive features have motivated extensive experimental and theoretical
research on FRCs. At the present time there are at least six active FRC and ion
ring experiments in the United States, including Los Alamos National
Laboratory, Princeton Plasma Physics Laboratory, the University of Washington,
Cornell University, UC Irvine, and Swarthmore College. One of the most
important scientific issues in FRC research is the stability of the FRC
configuration with respect to low-*n *(toroidal mode number)
MHD modes.

According to an
empirical scaling based on the experimental data for prolate FRCs, stability
with respect to global MHD modes is observed for *S*/E* *< *3-4, where *E* is the separatrix elongation, and *S** is a kinetic parameter which measures
the number of thermal ion gyro-radii in the configuration. The FRC parameters
are defined as follows: The separatrix elongation *E* is the ratio of the separatrix half-length to its radius (Fig.
1); the kinetic parameter, *S**, is the ratio of the separatrix radius to
the ion skin depth (*S** is also
approximately the ratio of the separatrix radius to the ion gyroradius in the
external field). There is a clear discrepancy between the observed macroscopic
resilience of FRC plasmas in low-*S**
experiments, and the predictions of standard MHD theory that many modes should
be unstable on an MHD time scale. Resolution of this discrepancy requires
advanced theoretical and numerical studies including kinetic effects. On the
other hand, in order to achieve good plasma confinement, larger devices with *S**>100-300 are needed, and conditions
for large-*S** FRC stability are yet to
be investigated both experimentally and theoretically.

**FIGURE 1. **Contour plot of poloidal
flux for a prolate FRC configuration.

Under the auspices
of the present DOE contract, most of the theoretical work on FRCs at the
Princeton Plasma Physics Laboratory has focused on investigating a variety of
non-ideal MHD effects, including plasma flow and kinetic effects on FRC
stability properties, particularly with respect to the *n*=1 tilt
mode. A new 3D nonlinear hybrid and MHD simulation code (HYM) has been
developed at PPPL and this code has been used to study the relative roles of
various competing kinetic effects on linear stability behavior. These studies
have demonstrated that the *n=*1 tilt instability can
saturate nonlinearly in highly kinetic FRCs. Although considerable progress has
been made, particularly in describing kinetic stability properties, a complete
understanding of the observed FRC stability properties is still lacking. In
order to assess the potential of FRCs as an innovative confinement concept for
fusion energy, it remains essential to develop an improved understanding of FRC
macroscopic stability properties both in the low-*S** (kinetic) and high-*S**
(MHD-like) regimes.