Extended MHD Study of Interchange Modes in Spheromaks

Extended MHD effects on pressure driven interchange modes are studied in decaying spheromak equilibria. Equilibria at conditions relevant to high temperature SSPX[Hooper et al., Nucl. Fus. 1999] discharges are ideal interchange unstable. Extended MHD introduces drifts which have a stabilizing effect, reducing the linear growth rate, on the high-n modes. However, extended MHD has a mixed effect on the low-n modes. The low-n modes have the greatest impact on confinement. In some cases extended MHD is destabilizing, increasing the growth rate, while in other cases extended MHD is stabilizing. A cylindrical screw-pinch model that approximates decaying spheromaks, is studied to better understand the lack of stabilization on the low-n modes. The extended MHD effects reduce the growth rate at small Hall parameter (di/a), but a second instability exists at finite Hall parameter. The second mode grows at a rate comparable to the MHD interchange mode. The diamagnetic heat flux (q∗) has an important stabilizing effect, delaying the onset of the second mode. In calculations that neglect the diamagnetic heat flux, the second mode is dominant at experimentally relevant Hall parameters, and its growth rate exceeds the MHD growth rate. However, including the diamagnetic heat flux delays the onset of the second mode. Here significant stabilization is observed at experiential conditions for Suydam parameters Ds . 1.0. This is four times the marginal ideal stable condition. An extended MHD dispersion relation for the gravitational interchange mode[Zhu et al., Phys. Rev. Lett. 2008] is analyzed to understand the nature of the second instability. The inclusion of the twofluid Ohm’s law introduces an ion drift wave. The ion drift wave can interact with the gravitational interchange mode producing a second instability.