Liouville's Theorem in the galaxy?

As you might remember, the Liouville's Theorem in statistical mechanics and Hamiltonian mechanics states that "the phase space distribution function is constant along the trajectories of a system". In other words the density in phase space remains constant along a dynamic trajectory.

Now, suppose that we have an isotropic distribution of energetic charged particles hitting our galaxy (lets assume that the galaxy is a sphere of radius R). These particles will be deflected by the magnetic field of the galaxy and some of them will hit the Earth. So, we get a new distribution of charged particles at Earth, which is not isotropic anymore.

But then an interesting question comes to mind. Does the Liouville's Theorem remain true in this case? Is our new non-uniform distribution conserved in the 6-dimensional phase space? Has the momenta changed in a way to cancel out the changes in the canonical coordinates?

What do you think?