An analytic solution of high-beta equilibrium in a large aspect ratio tokamak

Cowley, S. C. ; Kaw, P. K. ; Kelly, R. S. ; Kulsrud, R. M. (1991) An analytic solution of high-beta equilibrium in a large aspect ratio tokamak Physics of Fluids B, 3 (8). pp. 2066-2077. ISSN 0899-8221

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An analytic solution of the high-beta (ε βpq2/ε»1) equilibrium of a large aspect ratio tokamak is presented. Two arbitrary flux functions, the pressure profile p(φ) and the safety factor profile q(φ), specify the equilibrium. The solution splits into two asymptotic regions: the core region where β is a function of the major radius alone and a narrow boundary layer region adjoining the conducting wall. The solutions in the two regions are asymptotically matched to each other. For monotonic pressure profiles, the Shafranov shift is equal to the minor radius. For beta much bigger than 1, the solution contains a region (in place of the magnetic axis) of zero magnetic field and constant pressure. At high beta the quantity βI, which is essentially proportional to the pressure over the total current squared, is largely independent of pressure. The important ramifications of limited βI for high-beta reactors are discussed. Generalizations to shaped cross sections and hollow pressure profiles are outlined. The problem of equilibrium reconstruction in the high-beta regime is also considered.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
ID Code:25143
Deposited On:01 Dec 2010 12:03
Last Modified:04 Jun 2011 04:19

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