The Effect of Sheared Toroidal Flow on an FRC's n=2 Rotational Instability

Abstract

Summary form only given. A field reversed configuration (FRC) is observed to gain angular momentum until alpha=OmegaR/OmegaDi (rotational frequency over ion diamagnetic drift frequency) reaches a critical value, at which point an instability with azimuthal mode number n=2 develops. Questions remain as to whether the observed threshold is explained by published calculations, which assume a rigid rotor profile. Questions also remain as to the cause of the spin-up, but it necessarily involves angular momentum transport to the FRC through the outer surface. Rotation of the bulk, then, via kinematic viscosity and/or convection can entail significant velocity shear. Rotation results in centripetal acceleration supported by a magnetic field, so the instability may be interpreted as Rayleigh-Taylor (R-T). Both sheared flow and finite Larmour radius (FLR) effects are mitigating factors for the R-T instability, and are synergistic. The instability is investigated with an analytic planar R-T model of an FLR plasma with a magnetically transverse sheared flow layer. If this layer is too thin to reach the magnetic reversal axis instability is implied. Gyroviscous-flow shear coupling in this case negates the stabilizing effects of both, and rapid convection of the sheared layer to the magnetic axis is expected. Once this happens, though, the FRC is stable until the shear factor reaches a critical value when the n=2 mode becomes unstable. This model provides insight into what may be an important feature of FRC stability, although less simplified calculations are needed. Nonetheless, it can be used to tentatively predict stability characteristics of an FRC during compression by an electromagnetically imploded metal cylinder (for magnetized target fusion adiabatic compression). This is of concern since acceleration from such an implosion supplements centripetal acceleration, and alpha increases by a factor of 2.4, assuming angular momentum conservation, adiabatic compression, and the theoretical volume vs. radius scaling