Influence of helical magnetic field satellite harmonics and of the radial electric field on charged particle motion in torsatrons

Abstract

Collisionless charged particle motion in torsatrons is studied with the use of a longitudinal adiabatic invariant and numerical integration of the guiding centre drift equations. Emphasis is placed on investigating the influence of satellite harmonics of the helical magnetic field and the radial electric field on particle confinement. From this standpoint, the particle orbits, the limiting cycles of equations of particle motion, and the shape and size of regions in phase space in which the particle orbits lie are considered as a function of the device parameters. A comparison is made of magnetic configurations of various types differing in the number of helical field periods, in the inhomogeneity ratio ϵt/ϵl and in their sets of satellite harmonics. The characteristics of the configurations compared are close to the parameters of actual torsatrons: Heliotron E, ATF and Uragan-2M

Transport and confinement properties of stellarators/heliotrons with the multiple-toroidicity magnetic fields

“…[14][15][16][17][18][19][20] To verify conclusions concerning the high-order Nу2 harmonics effects on charged particle confinement, formulated in the previous section, we shall find the adiabatic invariants of particle motion for all stellarator configurations, as considered in the paper. For a stellarator magnetic field described by model ͑10͒, the IG.…”

“…Since for such particles, the values of the trapping parameters q 2 are nearly zero, in the process of a drift, the fraction of the contours of the q 2 ϭ0 curves, closed in the confinement volume, can reproduce the fraction of confined deeply trapped particles quite well. 18 Analysis of the character of the q 2 ϭ0 curves in different stellarator-type configurations shows the following ͑Figs. 6 and 7͒.…”

“…That is why the search for methods of the controlling of the stellarator device parameters, from the viewpoint of improving the rippletrapped particle confinement, have continued to be an important subject of investigation for more than three decades. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] In recent years, these investigations were crowned with a success in the discovery of the quasi-symmetric stellarator configurations with confinement properties similar to those of an axisymmetric tokamak. [21][22][23][24][25][26][27] The Helical-Axis Advanced Stellarator ͑Helias͒, proposed by Nuehrenberg and Zille, 23,24 is an example of a configuration of the quasihelically symmetric type, [21][22][23][24][25][26][27] in which the magnetic-field strength on the given flux surface depends only on the helical coordinate, i.e., BϵB(,ϪM ) where M is an integer, and is the toroidal flux.…”

New Approach to Transport Improvement in a Helical Magnetic Axis System by Introduction of Effective Toroidal Curvature

“…Following the method done by Smirnova [9], we consider the dependence of the particle confinement properties of a given device on its parameters. For this purpose it is convenient to use the longitudinal adiabatic invariant J k ϵ R y k dl (y k is the velocity parallel to B) of a particle trapped in a helical ripple well.…”

Reduction of the direct losses of charged particles in a torsatron with additional toroidal field coils

“…Owing to the moderate aspect ratio and the unfavourable winding law of helical conductors [12], the standard configuration of the URAGAN-2M torsatron (with equal currents in all TF coils) is characterized by prompt direct losses of helically trapped particles that exceed the indirect losses in the low collisionality regime [5]. Thus, the main purpose of the present Letter is the investigation of the effect of the unbalanced currents in the TF coils on the direct particle losses in the URAGAN-2M torsatron.…”