Radial drift invariant in long-thin mirrors

Abstract

Abstract:In omnigenous systems, guiding centers are constrained to move on magnetic surfaces. Since a magnetic surface is determined by a constant radial Clebsch coordinate, omnigenuity implies that the guiding center radial coordinate (the Clebsch coordinate) is a constant of motion. Near omnigenuity is probably a requirement for high quality confinement and in such systems only small oscillatory radial banana guiding center excursions from the average drift surface occur. The guiding center radial coordinate is then the leading term for a more precise radial drift invariant I r , corrected by oscillatory "banana ripple" terms. An analytical expression for the radial invariant is derived for long-thin quadrupolar mirror equilibria. The formula for the invariant is then used in a Vlasov distribution function.Comparisons are first made with Vlasov equilibria using the adiabatic parallel invariant. To model radial density profiles, it is necessary to use the radial invariant (the parallel invariant is insufficient for this). The results are also compared with a fluid approach. In several aspects, the fluid and Vlasov system with the radial invariant give analogous predictions. One difference is that the parallel current associated with finite banana widths could be derived from the radial invariant.

A supplemental device to return escaping particles to a magnetic mirror reactor

“…Both the open magnetic (mirror-type) and the closed magnetic (toroidal-type) systems still have instability problems that obstruct the way to a controlled fusion reactor. Mirror-type research continues in mirror hybrid reactors [11][12][13]. In hybrid reactor research, plasma confinement demands can be relaxed if the fission reaction induces strong energy multiplication.…”

Radial constant of motion for particles in magnetic mirror fields

“…In a previous study [2], restricted to magnetic drifts and thus with the E × B drift neglected, a radial invariant has been identified in symmetric long thin quadrupolar mirror vacuum fields, if, in a single bounce, the displacement of the guiding center due to magnetic drifts is small. The radial drifts then change sign on a passage through the midplane, and the radial drift becomes oscillatory, thereby avoiding a net radial drift.…”

“…Even a small ripple field (which could be associated with the discrete nature of coils) superimposed on an axisymmetric torus can cause a net radial drift and particle leakage [4,5]. Similar unfavorable consequences are seen in three-dimensional magnetic fields [2][3][4][5][6], and radial confinement in stellarators and quadrupolar mirrors are for this reason subtle to foresee. It is thus of basic importance to identify systems with a radial invariant.…”

“…However, these two invariants are not sufficient to provide radial confinement of particles, since guiding center drifts can cause a radial escape from the flux tube and thereby ruin the confinement even for a collision-free motion. One additional invariant, which implies a bounded radial motion [2], would prevent this, but it is often impossible to identify such an invariant. In certain magnetic fields, i.e.…”

“…A standard approach, compare [2], with a long thin flux tube with mid plane radius a and length 2 L is considered, where λ = a/L 1 and z = 0 is the mid plane. A vacuum magnetic scalar potential for a long thin symmetric quadrupolar mirror is…”