Drift orbits in the TMX and MFTF-B tandem mirrors

Drift orbits for the TMX and MFTF-B tandem-mirror designs are followed by using a long-thin expansion of the drift equations. Unexpected asymmetries in the field-line curvatures in the yin-yang end-mirror traps, caused by the transition coils between the solenoid and the yin-yang, result in an elliptical distortion of the drift surface with a/b= 1.5 at most, a perhaps tolerable deviation from omnigenity. Yushmanov-trapped particles are no worse than the bulk hot particles. Finite-beta plasma fields, coupled to the asymmetric curvature, produce sizeable banana orbits with widths comparable to the plasma radius, but these orbits are possible for only a few of the particles. Details of the transition through resonance in the solenoid are shown, including the banana shapes of the drift surfaces and the disruption of the surface in the stochastic regime. The orbits in the original design for the A-cell of MFTF-B are the most extreme; in the vacuum fields they all have an extended peanut shape that finally closes only at about 3 m. This shape is strongly non-omnigenous and suggests a hollow plasma-density profile. Finite-beta ×∇B drifts can help to minimize the radial extent of these orbits, but the strength of the vacuum curvatures makes omnigenity only marginally possible. Including ×∇ϕ drifts makes omnigenity even more unlikely for the ions, for which the ×∇B and ×∇ϕ drifts are of opposite sign, and conversely helps to omnigenize the drift surfaces of the ECRH 200-keV electrons. It is argued that not every class of particles can have good, i.e. near-omnigenous drifts, regardless of the ability of ϕ(r) to adjust to limit the radial extent of the orbits. This lack of omnigenity leaves one with no theoretical base for describing the MHD equilibrium in the original designs, but a new magnetic field design for MFTF-B A-cell has apparently completely restored omnigenous orbits.