Magnetic axis safety factor of finite β spheromaks and transition from spheromaks to toroidal magnetic bubbles
The value of the safety factor on the magnetic axis of a finite-beta spheromak is shown to be a function of beta in contrast to what was used in Bellan, Phys. Plasmas 9, 3050 (2002); this dependence on beta substantially reduces the gradient of the safety factor compared to the previous calculation. The method for generating finite-beta spheromak equilibria is extended to generate equilibria describing toroidal magnetic "bubbles," where the hydrodynamic pressure on the magnetic axis is less than on the toroid surface. This "anti-confinement" configuration can be considered an equilibrium with an inverted beta profile and is relevant to interplanetary magnetic clouds as these clouds have lower hydrodynamic pressure in their interior than on their surface.
© 2015 AIP Publishing LLC. Received 10 November 2014; accepted 3 February 2015; published online 23 February 2015. This material was based upon work supported by the U.S. Department of Energy Office of Science, Office of Fusion Energy Sciences under Award Nos. DE-FG02-04ER54755 and DE-SC0010471, by the National Science Foundation under Award No. 1059519, and by the Air Force Office of Scientific Research under Award No. FA9550-11-1-0184. The authors wish to thank an anonymous reviewer for making the valuable suggestion that Y_n Bessel solutions be allowed when r=0 is excluded from the domain.
Published - 1.4908553.pdf
Submitted - 1502.01656v1.pdf