Effect of Vacuum Magnetic Well on Magnetohydrodynamic Stability in Heliotron-E-like Configurations with High Shear

The v acuum magnetic field o f the H elio tron-E device [1, 2] is a high-shear 1 = 2 stellarator with a large average magnetic hill, a high rotat ional t ran s ­ fo rm at the p lasm a b o undary , and a p lanar magnetic axis. Previous ideal m agne tohyd ro ­ dynam ic (M H D ) stability com puta t ions o f freeb o u n d a ry m odes with low values o f the toroidal m ode n u m b e r n show that a limiting average ßvalue o f c r~ 2 % can be estimated [ 3 6 ] in agreem ent with experimental results [1]. In the numerical w ork a b road pressure profile has been assum ed (ß 0 ~ 1.35 cr-value is 1 .4% . As show n in [6], the s tabilization o f the most un ­ stable n = 1, m = 1 mode is mainly caused by the increase o f shear at the resonant t = 1 surface by varying the to ro ida l field ra the r than by deepening o f the m agnetic well. So the critical /7-limit in­ creases as the toroidal field increases because the resonant t = 1 surface is shifted to the high-shear region. T h e H elio tron-E device has the fea ture [6] tha t w ith in certain limits the to ro ida l field and thus the twist can be varied. Effects due to the shaping o f the pressure profile on the M H D stability have been stud ied in [3]. In the present paper, the effect o f an axisym ­ metric q u a d ru p o le field, which produces a vacuum m agnetic well in Heliotron-E-like configurations, on unstab le ideal M H D modes in finite-/? equilibria is investigated. The asym ptotic S TE P code [7] was