Superadiabatic and stochastic ion motion in the presence of a wave in a mirror-machine plasma

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Abstract
The method of overlapping resonances is used to determine whether a single electrostatic wave in a mirror‐machine plasma causes stochastic ion motion or its opposite, superadiabatic motion. Inclusion of the grad‐B drift velocity does not alter the result found by Rosenbluth and by Timofeev: high‐energy ions move superadiabatically and low‐energy ions move stochastically, the boundary occurring at a perpendicular kinetic energy of approximately 8 keV. Numerical calculations of ion orbits reveal large fractional changes in the magnetic moment during a bounce period; this result sheds doubt on the quantitative validity of a quasi‐linear diffusion equation, although qualitative validity may hold. Results from the 2XIIB experiment contradict the theoretical prediction of superadiabaticity. Replacement of the slab approximation used in this paper by a model including the azimuthally asymmetric quadrupole field may remove this discrepancy.