Author: Wrick Sengupta
Requested Type: Poster
Submitted: 2022-03-04 14:57:04
Co-authors: E. Rodriguez, R.Jorge, M. Landreman, A. Bhattacharjee
4 Ivy Lane
Princeton, NJ 08544
Magnetic shear is one of the most essential magnetohydrodynamic (MHD) equilibrium figure-of-merit. It is well known that magnetic shear plays a critical role in the theory of MHD as well as kinetic stability. Mercier (1965) obtained an analytic expression for the general on-axis rotational transform of a magnetically confined device. Mercier's formula helps us understand various ways to generate rotational transform in a stellarator. In contrast, only special cases for the on-axis magnetic shear are known. To the best of our knowledge, an analytic expression for the on-axis magnetic shear in a general three-dimensional MHD equilibrium with finite beta is unknown. This is because shear can only be obtained by going to the fourth-order in an expansion in the square root of the magnetic flux coordinate, which is challenging. In this work, we shall present the general analytical expression for the on-axis magnetic shear and compare it with special cases that exist in the literature. We shall also provide the physical interpretations of the various terms that appear in the expression for on-axis shear.
This work was supported by the U.S.Department of Energy Grant No. DE-FG02-86ER53223, the Simons Foundation/SFARI (560651, AB) and DoE Contract No DEAC02-09CH11466.