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On the dynamics of infinitely many charged particles with magnetic confinement. (English) Zbl 1150.82016

A physical system consting of many charged particles with the same mass \(m=1\) and the same electric charge \(q=1\), confined by an external magnetic field in an unbouded cylindrical conductor infinitely extended in the direction of its symmetry axis is considered. It is assumed that charged particles mutually interact via the Coulomb force and the proper magnetic field has a singularity. The existence, uniqueness and quasi-locality of the motion of charged particles in the three dimensional case are proved. Additionally a non-trivial bound on the growth of the velocity of each particle is found.

MSC:

82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
70F45 The dynamics of infinite particle systems
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