Application of benchmarked kinetic resistive wall mode stability codes to ITER, including additional physics

Abstract

Leading resistive wall mode (RWM) stability codes MARS-K [Liu et al., Phys. Plasmas 15, 112503 (2008)] and MISK [Hu et al., Phys. Plasmas 12, 057301 (2005)] have been previously benchmarked. The benchmarking has now been extended to include additional physics and used to project the stability of ITER in a realistic operating space. Due to ITER's relatively low plasma rotation and collisionality, collisions and non-resonance rotational effects were both found to have little impact on stability, and these non-resonance rotational effects will also not self-consistently affect the ITER RWM eigenfunction. Resonances between thermal ions and electrons and the expected level of ITER toroidal rotation were found to be important to stability, as were alpha particles, which are not in rotational resonance. MISK calculations show that without alpha particles, ITER is projected to be unstable to the RWM, but the expected level of alphas is calculated to provide a sufficient level of stability.

Model predictive control of resistive wall mode for ITER

“…In this scheme, the original high-order model of plasma RWM dynamics (4-5) is used. The initial state for the simulations was set so that in the modal form (7) the states of the unstable modes were set to a perturbed value of 0.5 while the states of the stable modes were set to 0, unless stated otherwise. Because we want to emphasize performance near actuator voltage constraints, the limit values are set to a relatively low value |u| ≤ 34 V. With the model (8)(9) in the modal form, the control cost 𝐐𝐐 𝐶𝐶 was tuned so that the two diagonal elements corresponding to the unstable modes were set to 10, the other diagonal elements corresponding to the stable modes were set to 10 −1 , while all non-diagonal elements were zero; the cost 𝐑𝐑 𝐶𝐶 was set to 10 −2 ⋅I27.…”

“…Using the state-space transformation of the original RWM model to the modal form and decomposition to the unstable and stable parts (7) we have tested the robustness of the closed-loop performance with the MPC controller 4 (designed using the unmodified model) in simulation with modified values of the growth rate γ and the frequency ω. When the growth rate γ is decreased, the system dynamics become less unstable.…”

“…We are most interested in practically comparing the BAP of the closed-loop system with our MPC controller and the KF with that of the system with the closely related LQG controller with EWP, which were evaluated in simulation with the full-dimensional RWM model with the PS saturation |𝐮𝐮| ≤ 34 V. Using the state-space transformation of the original RWM model to the modal form and decomposition to the unstable and stable parts (7) we explored BAP in terms of the stabilizable region of the two unstable modes, 𝜉𝜉 1 and 𝜉𝜉 2 . In Figure 16, the height represents the integral of PS power until the simulation termination at 0.5 s (for stable closed-loop responses), at grid points of an edge section of the region of the unstable dynamic states, 0.35 ≤ 𝜉𝜉 1 ≤ 0.65 and 0.35 ≤ 𝜉𝜉 2 ≤ 0.65.…”

“…But at higher plasma pressures above the no-wall βN, the RWM dynamics are still unstable. Passive stabilization may be possible by plasma rotation (via neutral-beam heating/ECCD or rotating magnetic field perturbation) or kinetic effects [4,5,6,7], however these may not be sufficient in reactor conditions expected to be suitable for exploiting nuclear fusion for commercial-scale energy production in longpulse high-βN H-mode scenarios at the fusion energy gain factor Q exceeding 5. Hence, active RWM feedback control via corrective magnetic coils, which augment the effect of the conductive wall and attempt to provide balance to the RWM magnetic disturbance, is planned for advanced ITER experiments, and is one of the important open scientific questions on the path towards fusion energy [5,8,9,10].…”

Finite-word-length FPGA implementation of model predictive control for ITER resistive wall mode control

“…A resistive wall mode (RWM) is an instability due to plasma kink at higher normalized plasma pressures βN, moderated by the presence of a resistive wall surrounding the plasma [1,2,3]. Passive RWM stabilization approaches based on plasma rotation and kinetic effects may not be sufficient [4,5]. The subject of this work is active feedback stabilization of the kink instability associated with the main non-axisymmetric (n = 1) RWM, according to the modelling expected to be dominant in ITER advanced tokamak scenarios.…”