The (a) coil in the in-vessel coils, (b) line-averaged electron density, (c) the emission in MAST discharge 27205 without RMPs, and (d) the emission in MAST discharge 27204 with maximum n = 6 RMP applied. A clear three-fold increase in the ELM frequency, and a 10% decrease in the plasma density is caused by the RMPs.
The (a) electron pressure at the pedestal top, (b) electron pressure pedestal width in flux space, (c) the electron temperature against the electron density, and (d) the electron pressure gradient as a function of time after the previous ELM for a series of MAST shots both without applied RMPs and when an n = 6 field is applied. The data in the first 10% of the ELM cycle are ignored. The RMPs cause a reduction in density, leading to a decrease in pressure and pressure gradient, as well as a significant increase in the pedestal width.
The edge stability diagram constructing by varying edge pressure, α and current density, j and reconstructing many different equilibria and testing stability to modes. The stability boundary is assessed when the mode growth rate drops below , though the qualitative boundary is unaffected when the marginal point is taken at zero growth rate, or below half of the ion diamagnetic frequency. 34 The star represents the experimental equilibria and the boundary using the pressure profile with and without n = 4 RMPs has been assessed for a MAST single-null plasma.
The radial profile of the toroidal rotation velocity as measured by charge exchange recombination spectroscopy in 10 ms time intervals for MAST discharges 27654 (n = 3 RMP), 27846 (n = 4 RMP), and 27204 (n = 6 RMP). In each case, the RMP field is turned on at 0.28 s and reaches flat-top by 0.3 s.
The radial profile of the toroidal rotation frequency as simulated by MARS-Q in 10 ms time intervals for MAST discharges (a) 27654 (n = 3 RMP), (b)27846 (n = 4 RMP), and (c) 27204 (n = 6 RMP). In each case, the edge rotation is fixed throughout. The vertical dashed lines are the rational surfaces.
The growth rate of n = 3, n = 10, and n = 15 peeling-ballooning modes as a function of rotation velocity at the pedestal top. The rotation profile is fixed and takes a modified tanh profile shape across the pedestal region. Also shown are the saturated pedestal-top rotation speeds when RMPs are applied compared to the initial rotation velocity.
The electron density radial profile in the pedestal region as measured by the Thomson scattering diagnostic for discharges with and without an n = 6 RMP applied. When the RMP is applied (red line), the pedestal width clearly increases and the position of the outboard midplane moves out by approximately 5 cm. The inboard position is unaffected.
The midplane boundary as a function of toroidal angle as modelled by the VMEC free-boundary 3d equilibrium code for different applied fields in MAST. The boundary shows a clear periodic corrugation in addition to the negligible n = 12 toroidal field ripple. The displacement is maximised when the parity of the applied field is resonant with the equilibrium q-profile.
The infinite-n ballooning mode stability parameter as a function of toroidal flux, focusing on the pedestal region, for an axisymmetric case and for the most unstable toroidal position when an odd-parity n = 3 RMP is applied. The application of the RMPs leads to a 3d corrugation of the plasma boundary, which in turn leads to increased ballooning mode drive in certain toroidal locations.
High-speed visible camera images obtained with a HeII filter near the X-point during an inter-ELM period of H-modes in MAST when (a) n = 3, (b) n = 4, and (c) n = 6 RMPs are applied.
Finite-n peeling-ballooning stability boundaries for a MAST single null plasma with axisymmetric lobes present as observed experimentally under application of RMPs. The star represents the experimental equilibrium prior to an ELM before applying the RMPs, with the triangle the operational parameters after RMPs are applied.
A model for how RMPs affect ELM behaviour illustrated in peeling-ballooning stability space, viz. current density against normalised pedestal pressure gradient. In a typical type I ELMing plasma, an ELM is triggered when the pressure and current profiles (black star) reach the corner of the stability boundary (black line). When RMPs are applied, the enhanced particle transport leads to a reduction in the pressure, and commensurate reduction in the pedestal bootstrap current. In the case of RMP mitigation, the combined effect of RMP-induced plasma braking, 3d corrugation of the plasma boundary and lobes near the X-point is to significantly degrade ballooning stability, indicated by the ballooning boundary moving to lower normalised pressure gradients (blue line). The pedestal recovers to this lower stability boundary more rapidly after the previous ELM, and so the ELM frequency increases. In the case of ELM suppression, the ballooning boundary is not as degraded (red line), and the RMP-induced particle transport means that the operational point now sits in the stable region, hence an absence of ELMs.
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