I like the initial description and review of HMC, quite compact, and somewhat makes it clearer why the proposal is symmetric, since it reduces to an absolute value of a determinant of a Jacobian being there, which is 1 due to HMC volume-preservation qualities. Unfortunately it cites a 1995 reference for that filled with measure theory ...
The reason why it's called "magnetic" is because they're able to make the connection to a magnetic field in physics.
Experiments are based on Gaussians, since this is mostly a theoretical work.
(I won't be able to go through this paper too much.)