Non-perturbative relativistic guiding center transformation: exact magnetic moment and the gyro-phase proposed as the Kaluza-Klein 5^th dimension

摘要

The non perturbative guiding center transformation [Di Troia C., Phys.Plasmas 22, 042103 (2015)] is extended to the relativistic regime. The singleparticle dynamic is described in the Minkowski flat space-time. The mainsolutions are obtained in covariant form: the gyrating particle solutions andthe guiding particle solution, both in gyro-kinetic as in MHD orderings. It isshown the relevance of the ideal Ohm's law in the context of the guiding centertransformation. Moreover, it is also considered the presence of a gravitationalfield. The way to introduce the gravitational field is original and based onthe Einstein conjecture on the feasibility to extend the general relativitytheory to include electromagnetism. In gyro-kinetic theory, some interestingnovelties appear in a natural way, such as the exactness of the conservation ofmagnetic moment, or the fact that the gyro-phase is treated as the nonobservable fifth dimension of the Kaluza-Klein model.