Guiding-center Hamiltonian for large gyroexcursion particles in mirror configurations

An explicit expression is derived for the guiding-center Hamiltonian K, an expression valid for particles having gyroexcursion ρ comparable to the system size, such as the high-energy ring particles in the Berta experiment. The form of K is quite simple. It depends on the magnetic field strength B and its radial derivatives, evaluated at an average radius of the particle from the symmetry axis, and it allows for a slow, but otherwise arbitrary, variation of B along the axis. The adiabatic invariant of the gyromotion is related not to the full kinetic energy of the particle normal to the field, as is μ≡(1/2)mv⊥2/B in small-ρ theories, but rather to the small additional kinetic energy due to the radial wobble of the particle about a constant-radius orbit.