Elena Belova and Stephen Jardin,
Princeton Plasma Physics Laboratory

Research Objectives

The objective is to determine the gross stability of the field-reversed configuration (FRC). This is a plasma confinement configuration that is relatively simple to make and has some desirable features from a fusion reactor perspective. These configurations have been made in the laboratory and show some signs of stability for short times. However, analysis of the configuration with fluid equations, i.e., in the magnetohydrodynamic (MHD) approximation, shows that they should be unstable to a number of different modes. Our objective is to use a more accurate description of the plasma by including particle orbit effects and to see if this would improve the theoretical predictions of stability.

Computational Approach

The approach is to use a hybrid MHD code that treats the electrons as a cold fluid and the ions as particles. The particle ion motion is described by the Lorenz force equations with the standard leapfrog scheme used for the time advance. The electric field is calculated from the electron momentum equation neglecting the inertial term. The fluid equations are advanced on a finite-difference mesh in a cylindrical coordinate system, while the particle pushing is done on a Cartesian grid. In contrast to previous work, the method is utilized to reduce numerical noise in the simulations.

Accomplishments

	Snapshots showing a 2D slice of the constant pressure contours during the evolution of a tilt-instability in a field-reversed configuration. This was a 3D MHD simulation of an E = 3.7 prolate configuration with elongation of 3.7. Times are normalized to the Alfven-wave transit time. Including particle orbit effects was found to slow down but not completely stabilize this mode.

The potentially unstable modes can be categorized by their dominant Fourier component about the symmetry axis. The n = 1 mode is normally the most unstable. The mode has a tilt-like structure. Elongated FRC with E > 1 are called prolate, and those with E < 1 are called oblate. We have found that the tilt mode is mostly internal to the configuration for prolate until it has grown to large amplitude, and then it suddenly acts to destroy the configuration. For the oblate configuration, the mode is external from the beginning and involves substantial distortion of the plasma boundary. We find that the effects of particle orbits are especially important for the prolate configuration, and that they can reduce the growth rate of the tilt mode by an order of magnitude or more. Also, the tilt mode in the prolate configuration is very difficult to measure experimentally because of its largely internal nature.

Significance

Publications

W. Park, E. V. Belova, G. Y. Fu, X. Z. Tang, H. R. Strauss, and L. E. Sugiyama, "Plasma simulation studies using multilevel physics models," Phys. Plasmas 6, 1796 (1999).

E. Belova and S. C. Jardin, "Numerical study of global stability of the field-reversed configuration," Bull. Am. Phys. Soc. 44, 85 (1999).