1998 Annual Report
Fusion Energy Sciences

Stellarator Optimization

L. P. Ku, D. Monticello, and A. Reiman, Princeton Plasma Physics Laboratory

A cutaway view of a two-field-period, aspect ratio 2.1 stellarator showing the last closed flux surface.
Contours of magnetic field strength on the last closed flux surface of the configuration shown in the left figure, demonstrating the good toroidal symmetry.

Research Objectives

To identify compact stellarator configurations that have low aspect ratio, good quasi-axisymmetry, and high magnetohydrodynamics (MHD) stability beta limit.

Computational Approach

We have constructed a configuration optimizer in which the state variables are the Fourier harmonics representing the plasma boundary, and the objective functions are measures of the quasi-axisymmetry and growth rates of the ballooning and kink modes. Constraints such as plasma beta, aspect ratio, profile of rotational transform, etc. can be imposed. The plasma surface is deformed to generate the desired rotational transform, and the quasi-axisymmetry and the stability of the plasma are maximized. The program finds paths to an optimal state using quadratic programming or chi-square minimization techniques. Evaluation of the gradient of the objective functions involves equilibrium calculations, mapping the resulting equilibria to the so-called Boozer magnetic coordinates, and performing stability calculations in the Boozer space. On the Cray C90, each complete function call for the stability calculations takes about 2.5 minutes of CPU time and 35 MW of memory for 33 flux surfaces with about 400 modes. A typical run involves about 600 function calls.

Accomplishments

We have been pursuing the design of compact stellarator configurations with aspect ratios (R/a) in the range of 2-4, comparable to those of tokamaks. To provide good particle drift trajectories, we have focused on configurations that are close to quasi-axisymmetric. A wide range of configurations have been studied. These configurations have the fraction of the rotational transform generated externally ranging from 20% to about 50%, and with beta up to 7%.

We have explored the MHD and transport properties of these configurations. Methods of stabilizing the external kink modes without a conducting wall have been found. The two illustrations show the boundary shape and the magnetic field strength of a two-field-period, aspect ratio 2.1 stellarator. This configuration has about 40% of the rotational transform generated by the external coils; the remaining 60% is supplied by the bootstrap current.

Significance

Stellarators are magnetically confined fusion devices with confinement properties similar to those of tokamaks. Both devices have toroidally nested closed magnetic surfaces created by helical (toroidal plus poloidal) magnetic fields. Unlike tokamaks, stellarators primarily use currents in external coils, rather than in the plasma itself, to confine and stabilize the plasma.

Large stellarator experiments are under way in Europe and Japan, and a smaller experiment is under construction at the University of Wisconsin. These programs are important because the similarities and differences between stellarators and tokamaks can be used to improve our understanding of toroidal confinement and to develop an improved reactor concept. Recent studies have shown that stellarators may be competitive with tokamaks as reactors.

Stellarators with improved performance have been designed in recent years by running fast three-dimensional computer codes. Spectral methods have raised the accuracy of the codes to a level where they provide a reliable simulation of the physics. Improvement and further development of these codes will provide us with even more powerful tools to search for interesting and attractive configurations in a very complex and multi-dimensional space.


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