### Theory Weekly Highlights for September 2003

##### September 26 2003

In collaboration with Dr. S.A. Galkin, the numerical problem that has prevented the 2D MHD stability code TWIST-R from producing well-behaved linear resistive MHD solutions has been resolved. A solution for a toroidal equilibrium test case was obtained with the expected behavior and exhibiting a finite jump in the logarithmic derivative of the perturbed flux at the singular surface. Benchmarking of this solution against the PEST-III code is underway - this requires accurately extracting the large and small solution components of the eigen-function in a form comparable with the PEST-III solution. Several other relatively minor numerical problems, related to the calculation of numerical coefficients with singular behavior near the magnetic axis, also remain to be resolved. It is expected that the TWIST-R code will then be able to produce robust numerical solutions for arbitrary values of the Mercier index.

##### September 19 2003

In collaboration with K. Comer of U. Wisconsin, Madison, progress was made in developing a new formulation, originally suggested by S. Cowley (UCLA and Imperial College), of the problem of finding stability boundaries with respect to variations in equilibrium parameters. As a particular parameter is varied, the sign of the inner product of the perturbed potential energy matrix with the original eigenvector determines whether stability is degraded or improved. This approach has been implemented with a modified version of the GATO code to obtain the potential energy and original eigenfunction. The code has been applied to variations in wall position where the approach works well, and to variations in aspect ratio where the second order terms are found to be large so that only small excursions are possible. A detailed analysis of each of the neglected terms is underway. This approach is expected to provide information of the stability in the immediate neighborhood of any equilibrium from a single stability run.

##### September 12 2003

The GYRO code has been used to evaluate possible turbulent dynamo action in the tokamak neoclassical current-voltage relation with realistic core simulations of a DIIID L-mode. There are two types of dynamo EMF: one which comes from fluctuations in the parallel electric field of the turbulence, and a second from divergence of magnetic flutter radial flow of current. The first yields a spatially averaged EMF much smaller than experimental errors in the inductive EMF. While the second drives little or no net current, it appears to drive very large current density spikes (and dips) near low order rational surfaces on the scale of a few ion gyroradius (and below the resolution of the MSE diagnostic.) The effect on tearing modes and NTM stability is being investigated. Fred Hinton will discuss this work in an invited APS 2003 talk.

##### September 05 2003

A new Magnetized-Target Inertial Fusion Energy (MTIFE) concept proposed by F. Thio (DOE) has been investigated in detail, which may solve the problem of the lack of adequate standoff distance between the driver and the site of explosive energy release, This has been a longstanding concern with most MTIFE concepts. The idea uses a spherically symmetric plasma liner to adiabatically compress and heat a magnetized plasmoid to fusion ignition conditions. The imploding liner is created by the intersection of multiple ~ 70 plasma jets launched from the periphery of the blast chamber with high velocity ~ 100 km/s, and high number density ~ 10^{20}/cc. The jets need to be highly supersonic, with a Mach number > 50 in order to obtain a ~ 10,000 fold amplification of the liner shell density and momentum-flux-density near the compressed target plasma. Future work will examine the fusion energy gain of this concept. If economically attractive gains of ~10 can be attained, the fusion energy yield will be ~ 1-2 GJ, which is easily containable, in contrast to the prohibitively large 100 GJ yields expected for the conventional MTIFE approach. The production of highly supersonic plasma jets on the larger scale might also open a new window into the physics of high Mach number astrophysical jets.

**Disclaimer**

These highlights are reports of research work in progress and are accordingly subject to change or modification