J. M. Faustin

Sawtooth control in JET with ITER relevant low field side resonance ion cyclotron resonance heating and ITER-like wall

New experiments at JET with the ITER-like wall show for the first time that ITER-relevant low field side resonance first harmonic ion cyclotron resonance heating (ICRH) can be used to control sawteeth that have been initially lengthened by fast particles. In contrast to previous (Graves et al 2012 Nat. Commun. 3 624) high field side resonance sawtooth control experiments undertaken at JET, it is found that the sawteeth of L-mode plasmas can be controlled with less accurate alignment between the resonance layer and the sawtooth inversion radius. This advantage, as well as the discovery that sawteeth can be shortened with various antenna phasings, including dipole, indicates that ICRH is a particularly effective and versatile tool that can be used in future fusion machines for controlling sawteeth. Without sawtooth control, neoclassical tearing modes (NTMs) and locked modes were triggered at very low normalised beta. High power H-mode experiments show the extent to which ICRH can be tuned to control sawteeth and NTMs while simultaneously providing effective electron heating with improved flushing of high Z core impurities. Dedicated ICRH simulations using SELFO, SCENIC and EVE, including wide drift orbit effects, explain why sawtooth control is effective with various antenna phasings and show that the sawtooth control mechanism cannot be explained by enhancement of the magnetic shear. Hybrid kinetic-magnetohydrodynamic stability calculations using MISHKA and HAGIS unravel the optimal sawtooth control regimes in these ITER relevant plasma conditions.

Applications of the SCENIC code package to the minority ion-cyclotron heating in Wendelstein 7-X plasmas

We present SCENIC simulations of a W7X 4He plasma with 1% H minority and with an antenna model close to the design foreseen for the W7X ICRF antenna [1, 2]. A high mirror and a standard equilibrium are considered. The injected wave frequency is fixed at 33.8 MHz and 39.6MHz respectively and only fundamental minority heating is considered. Included in this calculation is a new realistic model of the antenna, where it is found that the localization of the antenna geometry tends to break the five-fold periodicity of the system. We assess the heat transfer through the toroidal periods via Coulomb collisions.

An approximate single fluid 3-dimensional magnetohydrodynamic equilibrium model with toroidal flow

An approximate model for a single fluid three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium with pure isothermal toroidal flow with imposed nested magnetic flux surfaces is proposed. It recovers the rigorous toroidal rotation equilibrium description in the axisymmetric limit. The approximation is valid under conditions of nearly rigid or vanishing toroidal rotation in regions with significant 3D deformation of the equilibrium flux surfaces. Bifurcated helical core equilibrium simulations of long-lived modes in the MAST device demonstrate that the magnetic structure is only weakly affected by the flow but that the 3D pressure distortion is important. The pressure is displaced away from the major axis and therefore is not as noticeably helically deformed as the toroidal magnetic flux under the subsonic flow conditions measured in the experiment. The model invoked fails to predict any significant screening by toroidal plasma rotation of resonant magnetic perturbations in MAST free boundary computations.

Saturated ideal kink/peeling formations described as three-dimensional magnetohydrodynamic tokamak equilibrium states

Free boundary magnetohydrodynamic equilibrium states with spontaneous three dimensional deformations of the plasma-vacuum interface are computed for the first time. The structures obtained have the appearance of saturated ideal external kink/peeling modes. High edge pressure gradients yield toroidal mode number n = 1 corrugations for a high edge bootstrap current and larger n distortions when this current is small. Deformations in the plasma boundary region induce a nonaxisymmetric Pfirsch-Schluter current driving a field-aligned current ribbon consistent with reported experimental observations. A variation in the 3D equilibrium confirms that the n = 1 mode is a kink/peeling structure. We surmise that our calculated equilibrium structures constitute a viable model for the edge harmonic oscillations and outer modes associated with a quiescent H-mode operation in shaped tokamak plasmas.

Fast particle loss channels in Wendelstein 7-X

One of the main goals of Wendelstein 7-X (W7-X) is to demonstrate the fast particle confinement properties of the quasi-isodynamic stellarator concept. Fast particle populations will be produced either by Neutral Beam Injection (NBI) or by minority Ion Cyclotron Resonant Heating (ICRH). A fraction of these particles are expected to be lost (even without collisions), despite the optimisation procedure used for the W7-X design. Confinement properties of NBI particles in W7-X were presented in the paper of Drevlak et al (2014 Nucl. Fusion 54 073002). A detailed study is presented here where the loss patterns of an NBI population are described. In particular, focussing on a high-mirror equilibrium, the confinement of fast ions with varying energy injection is studied under collisional conditions. It is found that collisions are not only responsible for classical transport losses but also enhance drift induced losses caused by trapped particles. Moreover, an asymmetry is found in the toroidal position of particle losses which can be explained by local variation in the equilibrium field. The effects of a neoclassically resolved radial electric field are also investigated. Fast particle confinement is significantly improved by the associated drift. In particular, an increasing radial electric field helps to reduce and even stop the losses due to the 3D equilibrium structure for times comparable to slowing down time.

The merits of ion cyclotron resonance heating schemes for sawtooth control in tokamak plasmas

JET experiments have compared the efficacy of low-and high field side ion cyclotron resonance heating (ICRH) as an actuator to deliberately minimise the sawtooth period. It is found that low-field side ICRH with low minority concentration is optimal for saw tooth control for two main reasons. Firstly, low-field side heating means that any toroidal phasing of the ICRH (-90 degrees, +90 degrees or dipole) has a destabilising effect on the sawteeth, meaning that dipole phasing can be employed, since tins is preferable due to less plasma wall interaction from Resonant Frequency (RI) sheaths. Secondly, the resonance position of the low field side ICRH does not have to be very accurately placed to achieve saw tooth control, relaxing the requirement for real-time control of the RF frequency. These empirical observations have been confirmed by hybrid kinetic-magnetohydrodynamic modelling, and suggest that the ICRH antenna design for ITER is well positioned to provide a control actuator capable of having a significant effect on the sawtooth behaviour.

Modeling of ion-cyclotron resonant heating in Wendelstein 7-X equilibrium

W7X stellarator 3D equilibrium has been computed with the equilibrium code ANIMEC (Anisotropic Neumann Inverse Moments Equilibrium Code). This equilibrium was used to model ICRH minority heating in 4He(H) plasma with the 3D full-wave code LEMan (Low frequency ElectroMagnetic wave propagation). The coupled power spatial distribution is shown for different resonance positions within the range of frequencies foreseen for the ICRH antenna. It is found that for the high mirror equilibrium examined, the antenna frequency can be chosen to optimise the power deposition in the plasma core while limiting the absorption at the edge.

ICRH induced particle losses in Wendelstein 7-X

Fast ions in W7-X will be produced either by neutral beam injection (NBI) or by ion-cyclotron resonant heating (ICRH). The latter presents the advantage of depositing power locally and does not suffer from core accessibility issues (Drevlak et al 2014 Nucl. Fusion 54 073002). This work assesses the possibility of using ICRH as a fast ion source in W7-X relevant conditions. The SCENIC package is used to resolve the full wave propagation and absorption in a three-dimensional plasma equilibrium. The source of the ion-cyclotron range of frequency (ICRF) wave is modelled in this work by an antenna formulation allowing its localisation in both the poloidal and toroidal directions. The actual antenna dimension and localization is therefore approximated with good agreement. The local wave deposition breaks the five-fold periodicity of W7-X. It appears that generation of fast ions is hindered by high collisionality and significant particle losses. The particle trapping mechanism induced by ICRH is found to enhance drift induced losses caused by the finite orbit width of trapped particles. The inclusion of a neoclassically resolved radial electric field is also investigated and shows a significant reduction of particle losses.

Free boundary equilibrium in 3D tokamaks with toroidal rotation

The three-dimensional VMEC equilibrium solver has been adapted to numerically investigate the approximate toroidal rotation model we have derived. We concentrate our applications on the simulation of JET snakes and MAST long-lived modes under free boundary conditions. Helical core solutions are triggered when exceeds a threshold value, typically 2.7% in JET-like plasmas. A large plasma current and edge bootstrap current can drive helical core formations at arbitrarily small in which the ideal saturated internal kink coexists with an ideal saturated external kink structure of opposite phase. The centrifugal force linked with the rotation has the effect of displacing the plasma column away from the major axis, but does not alter significantly the magnitude of the edge corrugation of the plasma. Error field correction coil currents in JET-like configurations increase the outer midplane distortions by 2 cm. The edge bootstrap current enhances the edge modulation of the plasma driven by the core snake deformations in MAST.