Effect of transverse magnetic field on axial magnetic surfaces of a three-turn stellarator perturbed by an equilibrium plasma

Abstract

The question of maintaining plasma equilibrium in a three-turn stellarator by means of an external transverse field H⊥ is investigated in an ideal magnetohydrodynamic model as a first approximation with respect to β, where β is the ratio of the gas-kinetic pressure of the plasma to the magnetic pressure. An “island” structure of the paraxial magnetic surfaces is observed under conditions of precise compensation and slight undercompensation of the homogeneous component of the plasma magnetic field by the field H⊥. The optimum conditions are found for controlling the position of the magnetic axis with an external transverse field. Relations are obtained for estimating the maximum equilibrium pressure of the plasma in a three turn stellarator in the presence of an external transverse magnetic field.

Structure of symmetry restoring interactions: A modified BCS plus rotational approach for a schematic model space

“…and in order to recover the rotational invariance of the problem we can construct effective residual interactions which, as it has been shown in [6][7][8][9][10], should be added to the Hamiltonian (8).…”

“…We shall follow, hereon, the procedure which has been outlined in [6][7]. Thus we can define an effective symmetry restoring interaction from the commutator (9), namely:…”

“…As far as the treatment of the pairing force is concerned, we can take the Hamiltonian (26) as a good one, for each value of the rotational frequency, since in dealing with intrinsic excitations we can guarantee the decoupling of the collective rotation [6][7]. In other words we can consider it as an "effective" spherical model Hamiltonian once the correspondence between time reversed partners, like (a~, a;) and (C~, C~) pairs, is established.…”

“…Out of the many attempts which have been reported we have selected the so-called symmetry restoring technique, which has been proposed long ago by Pyatov et al [6][7], since it offers, in our opinion, some interesting possibilities. The aim of this note is mainly focussed on the discussion of the structure of residual forces which can approximately restore number and rotational symmetries spontaneously broken by the selection of a deformed basis.…”

“…The aim of this note is mainly focussed on the discussion of the structure of residual forces which can approximately restore number and rotational symmetries spontaneously broken by the selection of a deformed basis. Recently this problem has been reviewed by Szymanski et al [II] and we think that some common features are exhibited by this technique and the above mentioned one, due to Pyatov et al [6][7]. Because of our interest in the formal implicancies of the problem we have not organized the material of this note on numerical basis.…”