Consideration of the relationship between Kepler and cyclotron dynamics leading to prediction of a nonmagnetohydrodynamic gravity-driven Hamiltonian dynamo

Conservation of canonical angular momentum shows that charged particles are typically constrained to stay within a poloidal Larmor radius of a poloidal magnetic flux surface. However, more detailed consideration shows that particles with a critical charge-to-mass ratio can have zero canonical angular momentum and thus can be both immune from centrifugal force and not constrained to stay in the vicinity of a specific flux surface. Suitably charged dust grains can have zero canonical angular momentum and in the presence of a gravitational field will spiral inwards across poloidal magnetic surfaces toward the central object and accumulate. This accumulation results in a gravitationally-driven dynamo, i.e., a mechanism for converting gravitational potential energy into a batterylike electric power source.