Abstract
TypeI Edge Localised Modes (ELMs) have been mitigated in MAST through the application of , and 6 resonant magnetic perturbations. For each toroidal mode number of the nonaxisymmetric applied fields, the frequency of the ELMs has been increased significantly, and the peak heat flux on the divertor plates reduced commensurately. This increase in ELM frequency occurs despite a significant drop in the edge pressure gradient, which would be expected to stabilise the peelingballooning modes thought to be responsible for typeI ELMs. Various mechanisms which could cause a destabilisation of the peelingballooning modes are presented, including pedestal widening, plasma rotation braking, three dimensional corrugation of the plasma boundary, and the existence of radially extended lobe structures near to the Xpoint. This leads to a model aimed at resolving the apparent dichotomy of ELM control, which is to say ELM suppression occurring due to the pedestal pressure reduction below the peelingballooning stability boundary, whilst the reduction in pressure can also lead to ELM mitigation, which is ostensibly a destabilisation of peelingballooning modes. In the case of ELM mitigation, the pedestal broadening, 3d corrugation, or lobes near the Xpoint degrade ballooning stability so much that the pedestal recovers rapidly to cross the new stability boundary at lower pressure more frequently, whilst in the case of suppression, the plasma parameters are such that the particle transport reduces the edge pressure below the stability boundary, which is only mildly affected by negligible rotation braking, small edge corrugation or short, broad lobe structures.
This work was partly funded by the RCUK Energy Programme under Grant EP/I501045 and the European Communities under the contract of Association between EURATOM and CCFE. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
I. INTRODUCTION
II. EFFECT OF RESONANT MAGNETIC PERTURBATIONS IN MAST HMODES
III. THE EFFECT OF ROTATION BRAKING ON EDGE STABILITY
IV. THE EFFECT OF THREEDIMENSIONAL CORRUGATION OF THE PLASMA BOUNDARY ON EDGE STABILITY
V. THE EFFECT OF LOBE STRUCTURES NEAR THE XPOINT ON EDGE STABILITY
VI. A MODEL FOR THE EFFECT OF RMPS ON ELM STABILITY
VII. CONCLUSIONS
Key Topics
 Edge localized modes
 50.0
 Toroidal plasma confinement
 27.0
 Plasma pressure
 16.0
 Plasma diagnostics
 13.0
 Macroinstabilities
 10.0
H05H1/02
Figures
The (a) coil in the invessel coils, (b) lineaveraged 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 threefold increase in the ELM frequency, and a 10% decrease in the plasma density is caused by the RMPs.
The (a) coil in the invessel coils, (b) lineaveraged 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 threefold 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 (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 singlenull plasma.
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 singlenull 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 flattop by 0.3 s.
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 flattop by 0.3 s.
The radial profile of the toroidal rotation frequency as simulated by MARSQ 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 radial profile of the toroidal rotation frequency as simulated by MARSQ 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 peelingballooning 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 pedestaltop rotation speeds when RMPs are applied compared to the initial rotation velocity.
The growth rate of n = 3, n = 10, and n = 15 peelingballooning 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 pedestaltop 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 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 freeboundary 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 qprofile.
The midplane boundary as a function of toroidal angle as modelled by the VMEC freeboundary 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 qprofile.
The infiniten 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 oddparity 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.
The infiniten 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 oddparity 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.
Highspeed visible camera images obtained with a HeII filter near the Xpoint during an interELM period of Hmodes in MAST when (a) n = 3, (b) n = 4, and (c) n = 6 RMPs are applied.
Highspeed visible camera images obtained with a HeII filter near the Xpoint during an interELM period of Hmodes in MAST when (a) n = 3, (b) n = 4, and (c) n = 6 RMPs are applied.
Finiten peelingballooning 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.
Finiten peelingballooning 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 peelingballooning 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 RMPinduced plasma braking, 3d corrugation of the plasma boundary and lobes near the Xpoint 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 RMPinduced particle transport means that the operational point now sits in the stable region, hence an absence of ELMs.
A model for how RMPs affect ELM behaviour illustrated in peelingballooning 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 RMPinduced plasma braking, 3d corrugation of the plasma boundary and lobes near the Xpoint 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 RMPinduced particle transport means that the operational point now sits in the stable region, hence an absence of ELMs.
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