A low-dimensional model system for quasi-periodic plasma perturbations

Abstract

Larger scale plasma instabilities not leading to an immediate termination of a discharge often result in periodic nonlinear perturbations of the plasma. A minimal possible model is formulated for description of the system with drive and relaxation processes which have different time scales. The model is based on two equations: the first being responsible for the relaxation dynamics and the second for the drive. The model can be generalized to describe the pellet injection.

Axisymmetric oscillations at L–H transitions in JET: M-mode

“…Similar phenomena have been reported and discussed at JET and elsewhere [2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], usually concentrating on electrostatic fluctuation measurements in similar frequency ranges. This is a rapidly advancing field, references [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] may not include all the latest or relevant results, but are representative.…”

“…Numerous theoretical and modelling studies are available on Limit Cycle Oscillations as explanations for either ELMs or dithering transitions [5,6,10,13]. Generally the interpretations focus on Limit Cycle Oscillations in predator-prey electrostatic turbulence and transport models: a complex interaction between zonal flows, E r , turbulence, GAMs, Reynolds stress, mean flows and transport.…”

“…This is a rapidly advancing field, references [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] may not include all the latest or relevant results, but are representative. Reference [20] presents a good global view of previous studies.…”

Magnetic structure and frequency scaling of limit-cycle oscillations close to L- to H-mode transitions

“…While the early I-phase with regular pulsations can be successfully modelled with the majority of the LCO models (especially the model presented in reference [29]), the transition into the intermittent phase is not covered. To our knowledge, the intermittent (or chaotic) state is discussed only in the model derived from MHD equations described in reference [35]. The chaotic solution follows from the structure of the equation system which has similarities to the Lorenz model known from chaos theory.…”

“…LCO models derived from particle and heat transport equations [2,33] or momentum transport equations [34] without involving zonal flows can likewise describe the experimental findings. In addition, models derived purely from magnetohydrodynamic (MHD) equations can produce the same LCOs dynamics [35], and several other models, mainly derived for the description of ELM cycles, have LCO solutions (for a review see e.g. reference [36]).…”