Dependence of Velocity Space Loss Region ofl=2 Torsatron onεh(a)/εt(a)

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Abstract
Velocity space loss regions are studied by using constants of motion to calculate particle orbits in l =2 torsatrons. A criterion to confine a particle with v // ≃0 initially is obtained in terms of ε t ( a ), ε h ( a ) and ρ 0 , where v // is a parallel velocity, ε t ( a ) and ε h ( a ) are magnitudes of toroidal magnetic ripple and helical magnetic ripple, respectively, and ρ 0 is a normalized radius of initial position. In order to confine all particles in ρ 0 ≤0.3, ε h ( a )/ ε t ( a )≥3-3.5 is required for a model magnetic field described by both ε t ( r ) and ε r ( r ); however, ε h ( a )/ ε t ( a ) can be reduced to about 2 by improving particle confinement with appropriate side-band components corresponding to l =1 and l =3 helical fields having the same helical period number as the l =2 helical field. This result increases flexibility for designing a low aspect ratio helical system with good confinement of high energy particles.