The topology of tokamak orbits

Guiding-centre orbits in non-circular axisymmetric tokamak plasmas are studied in the constants of motion (COM) space of (v, ζ, ψ m . Here, v is the particle speed, ζ is the pitch angle with respect to the parallel equilibrium current, J || , at the point in the orbit where ψ = ψ m , and ψ m is the maximum value of the poloidal flux function (increasing from the magnetic axis) along the guiding-centre orbit. Two D-shaped equilibria in a flux-conserving tokamak having values of 1.3% and 7.7% are used as examples. In this space, each confined orbit corresponds to one and only one point, and different types of orbit (e.g. circulating, trapped, stagnation and pinch orbits) are represented by separate regions or surfaces in the space. It is also shown that the existence of an absolute minimum B in the higher- (7.7%) equilibrium results in an orbit topology dramatically different from that of the lower- case. The differences indicate the confinement of additional high-energy (v → c, within the guiding-centre approximation), trapped, co- and counter-circulating particles, with an orbit ψ m falling within the absolute B-well.