The particle confinement criteria for axisymmetric field-reversed configurations (FRCs) are obtained from the two constants of motion, H and Po. Here, H and P ft are the total energy and canonical angular momentum of a particle.
Based on two constants of motion, H and YQ, where H is the total energy of a particle and P# is its canonical angular momentum, particle confinement criteria are derived which impose constraints on H and PQ. With no electric field at the ends of field-reversed magnetic configurations, confinement criteria for closed-field and absolute confinements are obtained explicitly, including both lower and upper bounds of Pg/q, where q is the charge of the species considered, for a class of Hill's vortex field-reversed magnetic configurations. The commonly used criterion for the Hamiltonian, H < -co 0 Pe, where co 0 = qBo/mc, is deduced from a more general form as a special case. In this special case, it is found necessary to impose a new criterion, -B 0 R w /2c < Pfl/q < 0, where R w is the wall radius and Bo is the vacuum field, which reduces the confinement region in (H, ?Q) space. With the presence of electric fields at the ends of field-reversed magnetic configurations, confinement criteria are obtained for two interesting cases. In addition to lower and upper bounds of H, both lower and upper bounds of P#/q are found. For axially confined particles, the lower bound of P#/q reduces the confinement region in (H,Pg) space and represents a new criterion. These results can be applied to calculations for field-reversed mirrors and field-reversed theta pinches.
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