Numerical Study of Field-reversed Configurations: The Formation and Ion Spin-up
Authors: E.V. Belova, R.C. Davidson, H. Ji, M. Yamada, C.D. Cothran, M.R. Brown, and M.J. Schaffer
Date of PPPL Report: June 2005
Published in: Nuclear Fusion 46 (2006) 162-170
Results of three-dimensional numerical simulations of field-reversed configurations (FRCs) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs, and the new FRC formation method by counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n = 1 tilt mode, where n is the toroidal mode number. The n = 2 and n = 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux, and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good qualitative agreement with results from the SSX-FRC experiment. The simulations show formation of an FRC in about 20–30 Alfvén times for typical experimental parameters. The growth rate of the n = 1 tilt mode is shown to be significantly reduced compared to the MHD growth rate due to the large plasma viscosity and field-line-tying effects.