  We consider the Fokker-Planck equation with a strong external magnetic field.
Global-in-time solutions are built near the Maxwellian, the global equilibrium
state for the system. Moreover, we prove the convergence to equilibrium at
exponential rate. The results are first obtained on spaces with an exponential
weight. Then they are extended to larger functional spaces, like the Lebesgue
space and the Sobolev space with polynomial weight, by the method of
factorization and enlargement of the functional space developed in [Gualdani,
Mischler, Mouhot, 2017].
