Three-turn helical magnetic configuration with shear and minimum B̄

Abstract

The authors investigate the magnetic configuration of a three-turn helical magnetic field through which an axial current flows and which has three spatial magnetic axes. It is shown that, near the spatial axes, the cross-sections of the magnetic surfaces are ellipses lying in the planes perpendicular to the axes. The parameter values for which the configuration concerned possesses, near one of the spatial axes, an angle of torsion of the magnetic field lines, shear and minimum average magnetic field is considered.

Plasma equilibrium in configurations with a helical magnetic axis with allowance for toroidality

“…To describe a toroidal Vintotron configuration we shall take as one of the co-ordinate axes a helical line, on a torus of minor radius r Q and major radius R, forming a complete loop and making S. turns around the torus [ 12]. The value of r. determines the position of the magnetic axis of a straight Vintotron [7][8][9][10].…”

“…The sign of A determines the orientation of the ellipses relative to the principal normal. Both the numerical value and the sign of A depend on the basic parameters adopted for the Vintotron [7][8][9][10].…”

“…The coefficient A depends on the following three basic parameters of the Vintotron [7][8][9][10]: e -the tangent of the angle of inclination of the helical conductor; B x /B 0 -the ratio between the amplitudes of the helical magnetic field and the longitudinal field, and J/I the ratios of the currents in the helical conductor and in the central rod [7][8][9] or I1/I2 the ratios of the currents in the helical conductors [10]. Hence, if e and B x /B 0 are constant, while J/I (or I1/I2) varies in the range of a few tenths to a few units, we can obtain the value of A for which conditions (4.…”

“…In the present work we estimate the equilibrium values for /3 for toroidal traps with a spatial magnetic axis, such as can be produced by different combinations of the magnetic fields from helical conductors with an axial current 1 [7][8][9] or from helical conductors with various currents [9][10]. In this paper we shall refer to traps of the same type as Vintotrons.…”

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This paper is a study of plasma equilibrium in Vintotrons toroidal traps with a spatial magnetic axis established by various combinations of magnetic fields from helical conductors [7][8][9][10]. The authors determine the displacement of the vacuum magnetic axis in the presence of a plasma as a function of the relationship between the curvature of the helical magnetic axis, the curvature of the torus and a parameter characterizing the ellipticity of the-vacuum magnetic surfaces.

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