Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry
- CEA, IRFM, F-13108, Saint-Paul-lez-Durance (France)
The bounce-action-angle coordinates (J,{zeta}) for charged particles trapped in an axisymmetric dipole magnetic field are constructed by perturbation analysis. First, the lowest-order bounce-action-angle coordinates (J{sub 0},{zeta}{sub 0}) are derived for deeply trapped particles in the harmonic-oscillator approximation. Next, the Lie-transform perturbation method is used to derive higher-order anharmonic action-angle corrections (J=J{sub 0}+{epsilon}{sub t}J{sub 1}, {zeta}={zeta}{sub 0}+{epsilon}{sub t{zeta}1}), where the dimensionless parameter {epsilon}{sub t{identical_to}}(s{sub b}/r{sub e}){sup 2}<<1 is defined as the ratio of the turning-point distance |s{sub b}| (measured from the equator) along a magnetic field line labeled by the equatorial distance r{sub e}. Explicit expressions (with anharmonic corrections) for the canonical parallel coordinates s(J,{zeta}) and p{sub ||}(J,{zeta}) are presented, which satisfy the canonical identity {l_brace}s,p{sub ||{r_brace}{identical_to}}1. Lastly, analytical expressions for the bounce and drift frequencies (which include anharmonic corrections) yield excellent agreement with exact numerical results.
- OSTI ID:
- 21421276
- Journal Information:
- Physics of Plasmas, Vol. 17, Issue 10; Other Information: DOI: 10.1063/1.3486554; (c) 2010 American Institute of Physics; ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Yang-Mills fields on CR manifolds
Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry