Representation of the third adiabatic invariant in the flow form and some consequences of its conservation on examples of specific axial magnetic systems.

The dynamics of invariant magnetic surfaces is considered using examples of magnetic systems of axial symmetry. In the system formed by two turns with current, an internal trap (probcotron) and an external trap (dipole) are isolated. For the perturbation vector satisfying the condition of conservation of the third invariant, the dynamics of non-interacting particles moving in the plane of the magnetic equator is considered in drift approximation. The results obtained are extended to the equator of a geomagnetic trap in which the external disturbing field is set by an annular current. It is shown that in the limited magnetosphere of the Earth, in the approximation of the constancy of the third invariant, the real effect of the ring current on plasma dynamics differs from the generally accepted model calculations performed on the basis of dipole representations of the geomagnetic field. At the same time, it is not the magnetic flux that makes practical sense, but only its change, equal to the difference between the final and initial values of the fluxes calculated according to the real field parameters. For the main phase of a particular magnetic storm, the minimum energy values of charged particles in radiation belts, which they must have in order to satisfy the condition of preserving the third adiabatic invariant, are estimated.

V.V. Bogdanov. Representation of the third adiabatic invariant in the flow form and some consequences of its conservation on examples of specific axial magnetic systems. \\Geomagnetism and aeronomy. Volume 59, No.4, pp. 449-469. DOI: 10.1134/S0016794019040072