Hydromagnetic stability of a plasma in stellarators

Abstract

It is shown that, with the help of the sufficient criterion for hydromagnetic stability of a plasma proposed by Solovev, It is possible to calculate for stellarators a non-trivial plasma pressure limit at which there is hydromagnetic plasma stability with respect to arbitrary perturbations. In the simplest case of a two-turn stellarator with a circular magnetic axis this limit has the form β ≤ (δU0/U0)(ι/2π)2.

Toroidal Contributions to the Shear and thej∥-Kink Instability in the Tokamak and Screw Pinch

“…that is, if 0~ (r/R) 2 . Because B^/BQ-R/r, the destabilizing term due to j\\, which is present in linear-pinch theory, is of higher order.…”

“…For clarity, therefore, the Tokamak rotational transform (/) is first calculated to order (r/R) 2 . To obtain the proper averaging, the formula for I is…”

“…6W has been calculated ty order (r/R) 4 . To this order, the only possible destabilizing terms are proportional to the pressure gradient; these appear if \dp/dr\z(r/R) 2 …”

Implementation of Hamada principle in calculations of nested 3-D equilibria

“…This paper was motivated by Shafranov who in 1998 attended the American Physical Society meeting. He was my former supervisor and an expert in equilibrium and stability theory of stellarators (Shafranov & Yurchenko 1969; Pustovitov & Shafranov 1990). I was especially pleased to present to him the new concept of reference magnetic coordinates (RMC) invented just two months earlier.…”

Flute instability in a Tokamak of arbitrary cross-section

“…In Ref. [1] Shafranov and Yurchenko obtained the necessary stability criterion of a plasma in an axisymmetric Tokamak of elliptical cross-section, one of the axes of which is parallel to the axis of symmetry. This stability condition, with allowance for the ballooning mode, takes the form Mi <f 1 (e)+q 1 Rf 2 (e)-/3 I f 3 (e) , 0, = 2<p>/(I/2 7 ra) 2 (1) where jo is the density of the homogeneous current, Bo the longitudinal magnetic field on the magnetic axis, p the gas-kinetic pressure of the plasma, I the total current, R the major radius of the torus, a the radius of the flowing magnetic surface, = ( L 2 -L 2 )/(L 2 L-, and L 2 being the horizontal and vertical axes of the ellipsoidal cross-section, and q : the coefficient of "triangularity" of the cross-section…”