Field ripple behavior in helical systems

Abstract

Numerical studies were undertaken to elucidate the field ripple behavior on the magnetic axis, g ax , and on the last closed magnetic surface, g lc , as a function of the transverse magnetic field B z in helical magnetic system models with l ¼ 2,3 polarity. The models are similar to some heliotrons/torsatrons now in operation such as LHD and U-3M that have no additional longitudinal magnetic field coils. In the investigated B z range, the existence of closed magnetic surface configuration in the regime B z ¼ B zm with a minimal field ripple has been revealed. The main features of these configurations are the zero value of the minor radius of the magnetic axis (plane magnetic axis) in the l ¼ 2 system and the minimal minor radius of the bifurcation line of inner separatrix of the maximum developed inner island structure in the l ¼ 3 system. At B z range boundaries, the g lc values begin to decrease and the g ax values continue to increase.

The basic regime characteristics of thel= 2 torsatron with additional longitudinal magnetic field coils

“…One method implies a change in the basic helical line law [4]; the other involves a change in the conductor turn packing in the poles of the helical windings [8]. The B zm value is also Characteristics of the l = 2 torsatron 257 independent of the parameter K φ and can be considered as a fundamental definition of the basic regime.…”

“…This means that the magnetic surface configuration with the minimum field ripple value γ ax has a non-planar magnetic axis and is shifted inwards in the torus a little more deeply than the magnetic surface configuration with the planar magnetic axis, R 0ax < R 0axm . Against the background of results [4] for the ideal model of the l = 2 torsatron magnetic system without ACs, these peculiar properties demand apparently separate consideration. The calculations have shown that the regime with the planar magnetic axis (r ax = 0) is realized at B zm = 0.509.…”

“…The transition to this regime is realized by varying the value of the compensating magnetic field B z . Numerical calculations for the models of helical magnetic systems have shown that, in l = 2 torsatron magnetic systems without ACs, the magnetic surface configuration shifted inwards has some peculiarities, which are assumed to bear a direct relationship to the fact of an experimentally observed increase in the energy plasma confinement time τ E [4]. Firstly, this is a decrease in the field ripple γ = B max /B min (B max and B min are the maximum and minimum values respectively of the magnetic field modulus) on the magnetic axis (γ ax ) and at the last closed magnetic surface (LCMS) (γ lc ) as the magnetic surface configuration shifts inwards in the torus.…”

“…Firstly, this is a decrease in the field ripple γ = B max /B min (B max and B min are the maximum and minimum values respectively of the magnetic field modulus) on the magnetic axis (γ ax ) and at the last closed magnetic surface (LCMS) (γ lc ) as the magnetic surface configuration shifts inwards in the torus. Moreover, in the considered model of the magnetic system [4] a certain value of the compensating magnetic field B z = B zm exists at which γ ax and γ lc are minimal.…”

Magnetic Field of Helical Currents Flowing Over the Surface of a Non-Circular Torus

“…Это означает, что вы-бранный комбинированный закон навивки винтовых обмоток обеспечивает режим конфигурации маг-нитных поверхностей с центрированной плоской магнитной осью. Необходимая для реализации этого режима величина наложенного однородного поперечного компенсирующего магнитного поля B z /B 0 = 0,34 [6], где B 0 -величина тороидального компонента магнитного поля, создаваемого на круго-вой оси тора винтовыми обмотками. Средний радиус последней замкнутой магнитной поверхности r lc /R 0 = 0,12.…”