MAST Tokamak Research Articles

Plasma surrogate modelling using Fourier neural operators

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier neural operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (Mean Squared Error in the normalised domain ≈10−5 ). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations, and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e. cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full (available) duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

Effect of collisionality on the microinstabilities in the Globus-M spherical tokamak

Simulations of the microtearing instability developing in plasma of the Globus-M spherical tokamak were performed using the GENE gyrokinetic code in the flux-tube linear approximation mode. Under the effect of the instability, the magnetic islands form on the scale of the ion Larmor radius, and the magnetic field fluctuations occur that generate electron heat fluxes. The ion heat fluxes as well as the fluxes associated with the electrostatic fluctuations are negligible. The maximum growth rate of the microtearing instability is reached at a collision frequency within the experimental range of the collision frequency variation, within which the BT × τE ∝ ν*−0.4±0.1 scaling calculations were performed [1]. In similar calculations performed at the MAST tokamak, the growth rate decreases with decreasing collisionality in the entire range of the collision frequency variation, within which the BT × τE ∝ ν*−0.82 scaling calculations were performed [2]. This can explain why the dependences of energy confinement time on the collision frequency obtained for the MAST&NSTX and the Globus-M tokamaks are different.

Experimental constraint on the radial mode number of the geodesic acoustic mode from multi-point Langmuir probe measurements in MAST Ohmic plasma

Reciprocating Mach probe data is used to estimate the radial wave number of oscillatory zonal flows in Ohmic MAST plasma. An intermittent ∼10 kHz mode, previously identified as a geodesic acoustic mode (GAM), is detected in the wavelet decomposition and windowed spectra of plasma potential fluctuations of the MAST tokamak edge plasma. Two-points phase differencing technique is then applied to probe pins with radial and poloidal separations giving an estimate of the radial wave number at the desired range of frequencies. The phase velocity of propagation and an estimate of the shearing rate of the GAM is obtained. We measure the radial mode number range kr ≈ 0.3–1.0 cm−1 and a radial propagation speed of up to ∼1 km s−1. The GAM shearing rate is an order of magnitude smaller than the growth rate of drift-like turbulence. These results are consistent with the estimates obtained previously from multi-fluid numerical simulations of GAM in MAST.

Test of electrical resistivity and current diffusion modelling on MAST and JET

Experiments have been carried out on the MAST and JET tokamaks intended to compare the electrical resistivity of the plasma with theoretical formulations. The tests consist of obtaining motional stark effect (MSE) measurements in MHD-free plasmas during plasma current ramp-up (JET and MAST), ramp-down (MAST) and in stationary state (JET and MAST). Simulations of these plasmas are then performed in which the current profile evolution is calculated according to the poloidal field diffusion equation (PFDE) with classical or neoclassical resistivity. Synthetic MSE data are produced in the simulations for direct comparison with the experimental data. It is found that the toroidal current profile evolution modelled using neoclassical resistivity did not match the experimental observations on either device during current ramp-up or ramp-down as concluded from comparison of experimental and synthetic MSE profiles. In these phases, use of neoclassical resistivity in the modelling systematically overestimates the rate of current profile evolution. During the stationary state however, the modelled toroidal current profile matched experimental observations to a high degree of accuracy on both devices using neoclassical resistivity. Whilst no solution to the mismatch in the dynamic phases of the plasma is proposed, it is suggested that some physical process other than MHD which is not captured by the simple diffusive model of current profile evolution is responsible.

Experimental observations and modelling of intrinsic rotation reversals in tokamaks

The progress made in understanding spontaneous toroidal rotation reversals in tokamaks is reviewed and current ideas to solve this ten-year-old puzzle are explored. The paper includes a summarial synthesis of the experimental observations in AUG, C-Mod, KSTAR, MAST and TCV tokamaks, reasons why turbulent momentum transport is thought to be responsible for the reversals, a review of the theory of turbulent momentum transport and suggestions for future investigations.

Calculating fusion neutron energy spectra from arbitrary reactant distributions

The Directional Relativistic Spectrum Simulator (DRESS) code can perform Monte-Carlo calculations of reaction product spectra from arbitrary reactant distributions, using fully relativistic kinematics. The code is set up to calculate energy spectra from neutrons and alpha particles produced in the D(d, n)3He and T(d, n)4He fusion reactions, but any two-body reaction can be simulated by including the corresponding cross section. The code has been thoroughly tested. The kinematics calculations have been benchmarked against the kinematics module of the ROOT Data Analysis Framework. Calculated neutron energy spectra have been validated against tabulated fusion reactivities and against an exact analytical expression for the thermonuclear fusion neutron spectrum, with good agreement. The DRESS code will be used as the core of a detailed synthetic diagnostic framework for neutron measurements at the JET and MAST tokamaks.

Effect of toroidal Alfvén eigenmodes on fast particle confinement in the spherical tokamak Globus-M

In experiments with neutral beam injection at the early stage of a Globus-M discharge, instabilities were observed that were excited by fast ions in the frequency range of 50–200 kHz, which were identified as toroidal Alfvén eigenmodes (TAE) (Petrov et al., Plasma Phys. Rep., vol. 37, 2011, pp. 1001–1005). In contradiction with the NSTX and MAST tokamaks, a regime of TAE generation was realized with strongly developed single modes. Magnetic measurements with fast Mirnov probes have shown that most of the modes have toroidal number $n=1$. The influence of the modes on the fast particle confinement was recorded by means of a tangentially directed neutral particle analyser (NPA) and neutron detector. Hydrogen and deuterium were used as target plasma and injected beam for study of the isotopic effect. At deuterium injection into the deuterium plasma, TAE led to the neutron rate dropping by 25 %, whereas NPA fluxes of high energy dropped by 75 %. At hydrogen injection, the drop in the measured NPA fluxes did not exceed 25 %.

The appearance and propagation of filaments in the private flux region in Mega Amp Spherical Tokamak

The transport of particles via intermittent filamentary structures in the private flux region (PFR) of plasmas in the MAST tokamak has been investigated using a fast framing camera recording visible light emission from the volume of the lower divertor, as well as Langmuir probes and IR thermography monitoring particle and power fluxes to plasma-facing surfaces in the divertor. The visible camera data suggest that, in the divertor volume, fluctuations in light emission above the X-point are strongest in the scrape-off layer (SOL). Conversely, in the region below the X-point, it is found that these fluctuations are strongest in the PFR of the inner divertor leg. Detailed analysis of the appearance of these filaments in the camera data suggests that they are approximately circular, around 1–2 cm in diameter, but appear more elongated near the divertor target. The most probable toroidal quasi-mode number is between 2 and 3. These filaments eject plasma deeper into the private flux region, sometimes by the production of secondary filaments, moving at a speed of 0.5–1.0 km/s. Probe measurements at the inner divertor target suggest that the fluctuations in the particle flux to the inner target are strongest in the private flux region, and that the amplitude and distribution of these fluctuations are insensitive to the electron density of the core plasma, auxiliary heating and whether the plasma is single-null or double-null. It is found that the e-folding width of the time-average particle flux in the PFR decreases with increasing plasma current, but the fluctuations appear to be unaffected. At the outer divertor target, the fluctuations in particle and power fluxes are strongest in the SOL.

Development of an ITER prototype disruption mitigation valve

Disruptions in tokamaks seem to be unavoidable. Consequences of disruptions are (i) high heat loads on plasma-facing components, (ii) large forces on the vacuum vessel, and (iii) the generation of runaway electron beams. In ITER, the thermal energy of the plasma needs to be evenly distributed on the first wall in order to prevent melting, forces from vertical displacement events have to be minimized, and the generation of runaway electrons suppressed. Massive gas injection using fast valves is a concept for disruption mitigation which is presently being explored in many tokamaks. Fast disruption mitigation valves based on an electromagnetic eddy current drive have been developed in Jülich since the 1990s and models of various sizes have been built and are in operation in the TEXTOR, MAST, and JET tokamaks. A disruption mitigation valve for ITER is of necessity larger with an estimated injected gas volume of ∼20kPam3[7] for runaway electron suppression and all materials used have to be resistant to much higher levels of neutron and gamma radiation than in existing tokamaks. During the last 5 years, the concept for an ITER prototype disruption mitigation valve has been developed up to the stage that a fully functional valve could be built and tested. Special emphasis was given to the development and functional testing of some critical items: (i) the injection chamber seal, (ii) the piston seal, (iii) the eddy current drive, and (iv) a braking mechanism to avoid too fast closure of the valve, which could damage the injection chamber seal. The concept of the valve will be introduced and detailed solutions and testing results for the critical items presented.

Pellet fuelling with edge-localized modes controlled by external magnetic perturbations in MAST

The fuelling of plasmas by shallow frozen pellets with simultaneous mitigation of edge-localized modes (ELM) by external magnetic perturbation is demonstrated on the MAST tokamak. In these plasmas post-pellet particle loss is dominated by ELMs. It is shown that the size of post-pellet ELMs can be controlled by external magnetic perturbations. Post-pellet ELMs remove particles from a large part of the pellet deposition zone including the area with positive density gradient. The mechanism explaining this peculiarity of particle loss is suggested.

The radial electric field as a measure for field penetration of resonant magnetic perturbations

In this paper we introduce a new indirect method for identifying the radial extent of the stochastic layer due to applying resonant magnetic perturbations (RMPs) in H-mode plasmas by measuring the spin-up of the plasma near the separatrix. This spin-up is a predicted consequence of enhanced electron loss, due to magnetic stochastization (Kaveeva et al 2008 Nucl. Fusion 48 075003). We find that in DIII-D H-mode plasmas with n = 3 RMPs applied for edge localized mode suppression, the stochastic layer is limited to the outer 5% region in normalized magnetic flux, ΨN. This is in contrast to vacuum modelling predictions where this layer can penetrate up to 20% in ΨN. Theoretical predictions of a stochastic radial electric field, Er component exceed the experimental measurements by about a factor 3 close to the separatrix, suggesting that the outer region of the plasma is weakly stochastic. Linear response calculations with M3D-C1, a resistive two-fluid model, show that in this outer 5% region, plasma response often reduces the resonant magnetic field components by 67% or more in comparison with vacuum calculations. These results for DIII-D are in reasonable agreement with results from the MAST tokamak, where the magnetic field perturbation from vacuum field calculations needed to be reduced by 75% for agreement with experimental measurements of the x-point lobe structures (Kirk et al 2012 Phys. Rev. Lett. 108 255003).

Fast ion transport induced by saturated infernal mode

Tokamak discharges with extended weak-shear central core are known to suffer from infernal modes when the core safety factor approaches the mode ratio. These modes can cause an outward convection of the well-passing energetic ions deposited in the core by fusion reactions and/or neutral beam injection. Convection mechanism consists in collisional slowing down of energetic ions trapped in the Doppler-precession resonance with a finite-amplitude infernal mode. Convection velocity can reach a few m/s in modern spherical tori. Possible relation of this transport with the enhanced fast ion losses in the presence of “long lived modes” in the MAST tokamak [I. T. Chapman et al., Nucl. Fusion 50, 045007 (2010)] is discussed.

Measurement and control of the fast ion redistribution on MAST

Previous experiments on MAST and other tokamaks have indicated that the level of fast ion redistribution can exceed that expected from classical diffusion and that this level increases with beam power. In this paper we present a quantification of this effect in MAST plasmas using a recently commissioned scanning neutron camera. The observed fast ion diffusivity correlates with the amplitude of n = 1 energetic particle modes, indicating that they are the probable cause of the non-classical fast ion diffusion in MAST. Finally, it will be shown that broadening the fast ion pressure profile by the application of neutral beam injection at an off-axis location can mitigate the growth of these modes and result in the classical fast ion behaviour.

Experimental signatures of critically balanced turbulence in MAST.

Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).

Effect of resonant magnetic perturbations on ELMs in connected double null plasmas in MAST

The application of resonant magnetic perturbations (RMPs) with a toroidal mode number of n = 3 to connected double null plasmas in the MAST tokamak produces up to a factor of 9 increase in edge-localized mode (ELM) frequency and reduction in plasma energy loss associated with type-I ELMs. A threshold current for ELM mitigation is observed above which the ELM frequency increases approximately linearly with current in the coils. The effect of the RMPs is found to be scenario dependent. In one scenario the mitigation is only due to a large density pump out event and if the density is recovered by gas puffing a return to type-I ELMs is observed. In another scenario sustained ELM mitigation can be achieved irrespective of the amount of fuelling. Despite a large scan of parameters complete ELM suppression has not been achieved. The results are compared with modelling performed using either the vacuum approximation or including the plasma response. The requirement for a resonant condition, that is an optimum alignment of the perturbation with the plasma, is confirmed by performing a scan in the pitch angle of the applied field.

A fast, magnetics-free flux surface estimation and q-profile reconstruction algorithm for feedback control of plasma profiles

The flux surfaces' layout and the magnetic winding number q are important quantities for the performance and stability of tokamak plasmas. Normally, these quantities are iteratively derived by solving the plasma equilibrium for the poloidal and toroidal flux.In this work, a fast, non-iterative and magnetics-free numerical method is proposed to estimate the shape of the flux surfaces by an inward propagation of the plasma boundary shape, as can be determined for example by optical boundary reconstruction described in Hommen (2010 Rev. Sci. Instrum. 81 113504), toward the magnetic axis, as can be determined independently with the motional Stark effect (MSE) diagnostic. Flux surfaces are estimated for various plasma regimes in the ITER, JET and MAST tokamaks and are compared with results of CRONOS reconstructions and simulations, showing agreement to within 1% of the minor radius for almost all treated plasmas.The availability of the flux surface shapes combined with the pitch angles measured using MSE allow the reconstruction of the plasma q-profile, by evaluating the contour-integral over the flux surfaces of the magnetic field pitch angle. This method provides a direct and exact measure of the q-profile for arbitrary flux surface shapes, which does not rely on magnetic measurements. Results based on estimated flux surface shapes show agreement with CRONOS q-profiles of better than 10%. The impact of the shape of the flux surfaces on the q-profile, particularly the profiles of elongation and Shafranov shift, and offsets in plasma boundary and the magnetic axis are assessed.OFIT+ was conceived for real-time plasma profile control experiments and advanced tokamak operation, and provides quickly and reliably the mapping of actuators and sensors to the minor radius as well as the plasma q-profile, independent of magnetic measurements.

РЕЖИМЫ РАБОТЫ МОДИФИЦИРОВАННОЙ УСТАНОВКИ Т-15

Transport calculations of the operational regimes for the constructed modified T-15 device are presented. The Canonical Profiles Transport Model (CPTM), verified with JET and MAST tokamaks, is used in the simplified version: Te, Ti and current density diffusion equations are solved with the fixed plasma density n profile. L- and H- modes are described by the appropriate modeling of the boundary conditions for the temperatures and plasma density, confirmed by JET experiment. The absorbed power density profile is determined by the simple formulas. The results are presented as graphics and tables, which can be easily used in order to cre ate the scientific device programs, to develop diagnostics or to define the position of the device in modern tokamak experiments.

Effect of resonant magnetic perturbations with toroidal mode numbers of 4 and 6 on edge-localized modes in single null H-mode plasmas in MAST

The application of resonant magnetic perturbations (RMPs) with a toroidal mode number of n = 4 or n = 6 to lower single null plasmas in the MAST tokamak produces up to a factor of 5 increase in edge-localized mode (ELM) frequency and reduction in plasma energy loss associated with type-I ELMs. A threshold current for ELM mitigation is observed above which the ELM frequency increases approximately linearly with current in the coils. Despite a large scan of parameters, complete ELM suppression has not been achieved. The results have been compared with modelling performed using either the vacuum approximation or including the plasma response. During the ELM mitigated stage clear lobe structures are observed in visible-light imaging of the X-point region. The size of these lobes is correlated with the increase in ELM frequency observed. The characteristics of the mitigated ELMs are similar to those of the natural ELMs suggesting that they are type-I ELMs which are triggered at a lower pressure gradient. The application of the RMPs in the n = 4 and n = 6 configurations before the L–H transition has little effect on the power required to achieve H-mode while still allowing the first ELM to be mitigated.

H-mode access by pellet fuelling in the MAST tokamak

Access into H-mode is studied in the MAST tokamak when plasma is fuelled by cryogenic pellets. It is shown that pellet fuelling from the high-field side allows access to H-mode in plasmas heated by neutral beams. Simple and two-stage L–H transitions are identified. The results of comparison of the L–H transitions with pellet injection with transitions where plasmas are fuelled solely by gas puffing depend on the gas puff geometry: fuelling by high-field side gas leads to an L–H transition at the density comparable to the transition with pellet injection. In contrast low-field gas can completely prevent the L–H transition.

Interaction between a low-frequency electrostatic mode and resonant magnetic perturbations in MAST

A strong ≈10 kHz mode is detected in both potential and density fluctuations of the edge plasma of the MAST tokamak using a reciprocating probe. The mode is radially localized, with outer limit ≈2 cm inside the separatrix, and is affected on application of resonant magnetic perturbations generated by external coils. A shift in frequency with plasma rotation is found, and a rapid suppression of the mode is observed when it can couple to the imposed n = 3 magnetic perturbations in the rotating frame. Non-linear coupling to high wave number turbulence is evident, and an increase in power of turbulence fluctuations is seen after suppression. These observations are then interpreted in the context of known low-frequency plasma modes present in the toroidal configuration. A possibility that the observed mode is a geodesic acoustic mode is considered and motivated by observations.