Abstract
We discuss the motion of a relativistic test charge moving toward a strong increasing magnetic field when the dominant forces controlling the particle's motion are the magnetic mirroring effect and synchrotron radiation. Equations of motion are established and greatly simplified when the magnetic field has a power-law dependence on distance. The final fate of the particle is either being bounced by the magnetic mirror or gyrating in the lowest Landau orbit while coasting indefinitely with finite forward velocity. Which final fate the test particle ends up in is qualitatively determined by the mirror to radiation ratio |$\zeta\equiv(3m^3c^6/4e^4B^3)(\hat B \cdot \nabla B)$|. The distinct regions in the phase space occupied by these two classes of solutions are sought and various astrophysical applications discussed.
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