Estimation of orbit island width from static magnetic island width, using safety factor and orbit pitch

Abstract

In order to account for the effect of field perturbations on the transport of fast ions in integrated codes used for the simulation of operational scenarios, it is crucial to develop computationally efficient reduced transport models. Such modeling efforts may greatly benefit from a simple method that determines the width of the island-like structures, which are produced by resonant perturbations in the phase space of the fast ion guiding centers and are known to play a key role for fast ion transport enhancement. In this paper, we present a method for estimating the widths of such ‘orbit islands’ for passing particles in the presence of static magnetic perturbations. The method consists of mapping the boundaries of magnetic islands from magnetic flux space () into the canonical angular momentum space () of the fast ions. As a working example, we consider co-passing neutral beam (NB) ions subject to a resonant magnetic perturbation (RMP) in a KSTAR tokamak plasma. The estimated orbit island width deviates by less than 25% from the value obtained from Poincaré plots of the actual guiding center trajectories, even when the magnetic drifts are large (here, up to 50% of the minor radius). Our analysis also shows that most of the fast ion transport can be attributed to the effect of isolated islands, which means that stochastization of particle trajectories due to resonance overlaps does not play a major role in the case studied here. The island mapping method proposed here eliminates the need to compute and analyze Poincaré maps of particle trajectories, so that computation times can be reduced tremendously by several orders of magnitude. A further speed-up may be achieved by the development of a method for estimating the width of magnetic islands under realistic conditions.

Simulations tackle abrupt massive migrations of energetic beam ions in a tokamak plasma

“…It should be noted that the energetic ions are not trapped in magnetic islands but in drift orbit islands. These are influenced by the electric and magnetic drifts of the charged particles and have different existence conditions, spatial locations and widths than magnetic islands 37 , 38 .…”

Efficient estimation of drift orbit island width for passing ions in a shaped tokamak plasma with a static magnetic perturbation

“…In a first attempt to reduce the amount of calculations needed, we have recently introduced a mapping from poloidal magnetic flux space (ψ p ) into canonical toroidal angular momentum space (P φ ) via the safety factor profile q(ψ p ) and its drift-kinetic counterpart, the orbit pitch parameter h(P φ |E, µ, σ ∥ ) (sometimes referred to as 'kinetic safety factor'). 6 Using such a mapping, we have proposed a procedure for estimating the width of fast ion orbit islands from the width of magnetic islands [26]. The computational cost was substantially reduced, since the kinetic Poincaré maps were replaced by a set of one-dimensional pitch profiles h(P φ |E, µ, σ ∥ ), which require test particles to be traced for only one poloidal transit.…”

“…In the above-mentioned KSTAR scenario, the estimation errors lay within 25% (see. figure 12 of [26]). This is more accurate than existing analytical estimates, but there is still room for improvement.…”

“…These shortcomings of our previous method [26] are eliminated in the present work, where we incorporate Hamiltonian techniques to calculate the widths of both magnetic islands [28] and orbit islands. To solve the equations of phase-space flow lines of passing ions near the resonant surface, a suitable set of straight orbit coordinates (equivalent to straight-fieldline coordinates [29]) is introduced, where the poloidal angle ϑ is selected such that the unperturbed guiding center orbits are straight on the unperturbed drift surface spanned by θ and the geometric toroidal angle φ.…”

“…The slope of the guiding center trajectory corresponds to the above-mentioned orbit pitch parameter h(P φ |E, µ, σ ∥ ). Although the construction of such coordinates generally requires the numerical integration of the flow lines, we speed this step up with the use an approximate but fairly accurate formula [equation ( 45) below], which we have already used in our previous work [26] to calculate the orbit pitch with minimal computational effort. The main remaining shortcoming of the new method presented here is that we still rely on a perturbative treatment, where a simple superposition of unperturbed and perturbed fields is assumed.…”