Non-MHD gravity-driven Hamiltonian dynamo for driving astrophysical jets

Conservation of canonical angular momentum $P_{\phi }=m_{\sigma }r^{2}\dot{\phi}+\ (2\pi )^{-1}q_{\sigma } \psi (r,z,t)$ shows that charged particles are typically constrained to stay within a poloidal Larmor radius of a poloidal magnetic flux surface $\psi (r,z,t) $. However, more detailed consideration shows that particles with a critical charge to mass ratio can have zero canonical angular momentum and so 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 [1], i.e., a mechanism for converting gravitational potential energy into a battery-like electric power source. \newline \newline [1] P. M. Bellan, Phys. Plasmas 14, Art. No. 122901, 2007