The drift Hamiltonian in a magnetic field with a separatrix

In a plasma equilibrium, the simplest coordinates to use for the calculation of particle drift trajectories are magnetic coordinates. Unfortunately, these coordinates are singular on a magnetic separatrix, which makes their use impractical in this region. Here a coordinate system that is nonsingular on a magnetic separatrix while retaining most of the attractive features of magnetic coordinates is developed. In particular, a simple expression for the Hamiltonian for particle drift trajectories is obtained and a simple prescription for making quantities, such as the electric potential, constant on the magnetic surfaces is given