Ion Constants of Motion in the Orbitron Fusion Device

The Orbitrap is an electrostatic ion trap with a quadro-logarithmic electrostatic potential well between an inner, spindle-shaped cathode and an outer barrel-shaped anode. The shape of the potential well gives confined ions an axial harmonic oscillation whose period depends on the ion charge-to-mass ratio, but not its radial location, making the Orbitrap ideal for mass spectrometry. In the Orbitron fusion device, Orbitrap ion confinement is combined with magnetron radial electron confinement by applying an axial magnetic field. The Hamilton-Jacobi equation for the Orbitron with a homogeneous magnetic field is separable in standard cylindrical coordinates (r, θ, z), and thus, the corresponding action variables (Jr, pθ, Jz) are conserved. Canonical perturbation theory about the potential well minimum is compared with an implicit orbit solver using CVODE. The onset of adiabatic breakdown due to a single diagnostic port in the anode is explored by varying the port diameter. The present work has elucidated the proper phase-space and Vlasov-space coordinates for an orbit-averaged Fokker-Planck code, presently under development.