Control of resistive wall modes in the spherical tokamak

Abstract

In this work, the MARS-F/K codes (Liu Y Q et al 2000 Phys. Plasmas 7 3681 & Liu Y Q et al 2008 Phys. Plasmas 15 112503) are utilized to model the passive and active control of the n=1 (n is the toroidal mode number) resistive wall mode (RWM) in a spherical tokamak (aspect ratio A=1.66). It is found that passive stabilization of the RWM gives a relatively small increase in normalized beta above the no-wall limit, relying on toroidal plasma flow and drift kinetic resonance damping from both thermal and energetic particles. Results of active control show that with the flux-to-voltage control scheme, which is the basic choice, a proportional controller alone does not yield complete stabilization of the mode. Adding a modest derivative action, and assuming an ideal situation without any noise in the closed-loop, the RWM can be fully stabilized with the axial plasma flow at 5% of the Alfven speed. In the presence of sensor signal noise, success rates exceeding 90% are achieved, and generally increase with the proportional feedback gain. On the other hand, the required control coil voltage also increases with feedback gain and with the sensor signal noise.

Role of electrostatic perturbation on kinetic resistive wall mode with application to spherical tokamak

“…Figures 1(b) and (d) shows that the MARS-K computed δW k , for both the real and imaginary parts, converges to a finite value at large E × B rotation frequency. The converged δW k recovers the CGL limit, which is indicated by the horizontal dashed lines in the plots and is computed via a separate code implementation specifically for the CGL limit, with fluidlike terms as shown in equations ( 15), ( 16) and (19). Note also that the imaginary part of δW k vanishes at the CGL limit, as expected.…”

“…The updated code is then utilized to investigate the RWM stability, and the associated high-β plasma response to externally applied three-dimensional (3D) field perturbations, for a spherical tokamak (ST) plasma from the MAST experiment [16]. The RWM, being often driven by high plasma pressure (exceeding the so-called Troyon no-wall limit [17]), is an important MHD instability in MAST-U [18] as well as future reactor-scale ST devices such as STEP [19]. An unstable lown (typically n = 1) RWM, not well controlled either by active means (e.g.…”

Plasma control for the step prototype power plant

“…For constant values of toroidal field and plasma current, increasing the normalised beta β N will be doubly helpful as an increase in pressure will increase the fusion power while an increased pressure gradient will increase the bootstrap current thereby reducing the required current drive power. Operation at high values of β N may result in RWMs becoming unstable [20]. These modes have toroidal mode numbers n ⩾ 1, with n = 1 and n = 2 being most relevant here.…”

“…A possible arrangement of such RWM coils is shown in green in figure 14. Further details of the work to design an active RWM stabilisation system, which will be very similar to the system needed for vertical stabilisation, can be found in [20].…”

“…The plan to operate at high plasma pressure, means that 'Resistive Wall Modes' (RWMs) may be unstable. To assure that such modes can be stabilised, a fast closed loop control system based on a set of 3D RWM coils is included in the STEP prototype design [20].…”