b Limit Disruptions in Tokamaks
Kleva, Guzdar

The most serious impediment to the practical utilization of tokamaks as fusion reactors is the limitation on the plasma thermal pressure imposed by disruptions. The ratio b of the thermal pressure to the pressure of the confining magnetic field provides a measure of the efficiency of a magnetic confinement fusion reactor. Operation at high b is very desirable because it yields a large fusion reaction rate relative to the cost of the confining magnetic field. However, experimental attempts to increase the ratio b beyond a critical limit b_c have been thwarted by an abrupt, catastrophic loss of confinement. Not only do these disruptions limit b and, therefore, limit the efficiency of a tokamak, but the disruptions themselves can cause serious damage to the reactor. Displayed below are results from 3D MHD simulations performed on the T3E machine at NERSC.

The figure above shows three-dimensional isosurfaces of the pressure as the instability develops along ridges dominantly aligned along the ambient magnetic field.

The figure on the right is a poloidal projection of the pressure that shows the hot plasma fingers as they reach the wall. Our nonlinear simulations of tokamak stability reproduce the salient features of the disruptive loss of confinement. High b toroidal equilibria are linearly unstable to ballooning modes that grow on the pressure gradient on the large R side of the magnetic axis, where R is the major radius of the torus. The convection cells associated with the unstable ballooning modes transport the thermal energy toward the wall at large R in hot plasma ridges whose two-dimensional projection in the poloidal plane resembles fingers. As the hot central plasma is transported out in R in fingers, the average pressure gradient is reduced so that it no longer completely balances the Lorentz force of the confining magnetic field. As a result, there is a small net inward force in R caused by the unbalanced Lorentz force. At lower bthis force generates an axisymmetric flow that opposes the growth of the fingers to the wall at large R, thereby stabilizing the plasma nonlinearly and maintaining confinement. However, as b increases the growth rate of the plasma fingers towards the wall becomes so rapid that there is insufficient time for the self-consistently generated axisymmetric flow to halt their progress before they strike the wall, and confinement is lost.

Recent papers dealing with disruptions in tokamaks:

• b Limit Disruptions in Tokamaks, R.G. Kleva and P.N. Guzdar, Phys. Rev. Lett. 80, 3081 (1998).

• Nonlinear Stability Limit in High b Tokamaks, R.G. Kleva and P.N. Guzdar, Phys. Plasmas 7, 1163 (2000).

This research is supported by the U.S. Department of Energy.