Modeling Liner Compression of FRCs: Obstacles and Advances

Compression of a field-reversed configuration (FRC) by an imploding solid liner is a possible path to magnetized target fusion. It is critical to the success of such experiments to perform full-up multidimensional computational simulations of them. However, there are numerous difficulties in performing those simulations. The interacting physical processes involved introduce disparate time scales. For example, the FRC itself has near-vacuum buffer-field regions that have extremely high Alfven velocity, while the implosion of the liner proceeds at a much slower pace. These strongly differing time scales impose stringent accuracy requirements. The lifetime of an FRC of sufficient density to provide interesting fusion output is on the order of 10 ms while the implosion times of liners of sufficient thickness to survive acceleration to the requisite velocity are somewhat longer than 20 ms. Hence, the FRC must be formed and translated into the liner after the liner implosion begins, so that the FRC formation fields may perturb the liner. Our previous simulations of the experiment have addressed formation separately from the liner implosion and merged the FRC into the liner simulation, preventing proper assessment of this issue. Experimental success hinges on realizing the magnetic inhibition of thermal conduction to prevent loss of plasma energy. Our previous simulations of the final stages of FRC compression have often failed because of inaccuracy in the numerical treatment of the parallel flux. The Rayleigh Taylor instability of the inner surface of the liner during final stages of compression may ultimately limit the performance of this system and must be assessed computationally. However, the modes that grow are those with crests parallel to the FRC's magnetic field, and are not present in the 2-d azimuthally symmetric simulations used for design of the FRC formation and liner implosion. We have made significant progress on these issues. First, we have performed fully integrated, simultaneous simulations of liner implosion and FRC formation on the same grid. These simulations address the generation of rotation in the FRC as well as perturbations of the liner. Second, we have developed a mixed-order numerical treatment of the anisotropic heat conduction that has proven both more robust and more accurate. The improvement has enabled us to run more simulations for design purposes. Finally, we have begun to perform 3-d simulations of the final stages of compression, beginning from the self-consistent state of the 2-d axisymmetric simulation, perturbed in a mass, energy, momentum, and flux conserving .