Rotation dynamics and stability of collisional edge layers in tokamak plasmas

Abstract

An earlier neoclassical transport theory for a collisional edge layer with steep radial gradients in the toroidal damping timescale is extended, to include also the faster poloidal damping timescale. In order to determine the stability behaviour of poloidal and toroidal rotations in a tokamak plasma, a two-timescale analysis is applied. It is observed that the poloidal and toroidal spin-up tendencies are strongly coupled by nonlocal interactions, although these evolve essentially on different timescales. Effects of charge exchange interactions, neutral beam injection, and a radial polarization current on both rotation speeds are consistently included in the model.

Magnetic confinement theory summary

“…[40]) has been extended by Kalupin [41], emphasizing the role of the density gradient length, L n , and finding ped ∝ n −1 ; the results are similar to those predicted by the model of Guzdar et al [42]. Since the transition and barrier formation are generally thought to be associated with plasma flows, the time-dependent solutions of the coupled, non-linear system of equations for temperature gradients and the poloidal and toroidal velocities have been investigated by both Fukuyama [43] and Daybelge [44]. Fukuyama included both neo-classical and turbulent transport, where the latter can be suppressed by shear in the radial electric field shear; in particular, this can be generated by the different prescriptions for determining E r in the core and SOL.…”

“…He finds transport barriers can result [43]. Daybelge's neo-classical modelling [44], which allows for steep radial gradients, shows chaotic oscillations in the flows can also occur.…”

Summary of the magnetic confinement theory and modelling

“…see [99], where the impact of low-hybrid wave instability on runaway dynamics was considered). Daybelge discusses chaotic behaviour of edge plasma rotation [100]. He finds that a steep temperature gradient in highly collisional plasma can induce a topological change, or a global bifurcation in the phase portrait of rotation velocities.…”

Summary: theory of magnetic confinement

“…The varieties of dynamical processes that may influence the barrier formation at the edge [2] still prevent the completion of the theoretical model, and key processes are under investigation. Kasuya [9] and Daybelge [10] examined the nonlinearity of the radial electric field. A testable result is presented [9] in relation with the bifurcation driven by an electrode [11,12], and the understanding of the nonlinear response of a radial electric field was progressed.…”