The plasma equilibrium in a linear trap at β ≈ 1 (or above the mirror-instability threshold) under the topology-conservation constraint evolves into a kind of diamagnetic "bubble". This can take two forms: either the plasma body greatly expands in radius while containing the same magnetic flux, or, if the plasma radius is limited, the plasma distribution across flux-tubes changes, so that the same cross-section contains a greatly reduced flux. If the magnetic field of the trap is quasi-uniform around its minimum, the bubble can be made roughly cylindrical, with radius much larger than the radius of the corresponding vacuum flux-tube, and with non-paraxial ends. Then the effective mirror ratio of the diamagnetic trap becomes very large, but the cross-field transport increases. The confinement time can be found from solution of the system of equilibrium and transport equations and is shown to be τ E ≈ √ τ τ ⊥ . If the cross-field confinement is not too degraded by turbulence, this estimate in principle allows construction of relatively compact fusion reactors with lengths in the range of a few tens of meters. In many ways the described here diamagnetic confinement and the corresponding reactor parameters are similar to those claimed by the FRCs.
The relativistic guiding center dynamics of charged particles is described in terms of noncanonical variables. The gyrokinetic transformation is obtained using the perturbative Lagrangian approach with a fully relativistic, four-dimensional covariant formulation. It is shown that the definition of the ignorable gyrophase (as well as those of the magnetic moment and the gyrocenter energy) is not unique, and allows for several free functions in the gyrokinetic transformation. This freedom can be interpreted as a choice of the reference frame. One of these frames, namely that moving with the relativistic version of the E_×B_-drift velocity, generates the simplest and intuitive description.
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