M. Fitzgerald

Identifying the impact of rotation, anisotropy, and energetic particle physics in tokamaks

In this paper we study the effects of poloidal and toroidal rotation, and anisotropy in tokamaks. To resolve these effects from uncertainties in the data, we introduce a Bayesian inference framework which calculates the magnetic configuration probabilistically using motional Stark effect and magnetic data. Drawing on these calculations, we compute the poloidal and toroidal Mach numbers in MAST for a discharge with good rotation data. Our calculations confirm that the poloidal Mach number Ms,θ = vθ/vi × B/Bθ is near zero (with vθ and vi the poloidal and thermal velocity, respectively), even on the outboard side where the scaling of poloidal field strength Bθ to total field B is large. In contrast, the toroidal rotation of this plasma reaches a Mach number of 0.5 on axis. The impact of the toroidal rotation on the equilibrium reconstructions of the plasma is however small: it acts to increase the radius of the magnetic axis by ≈1%, and lower the central safety factor by ≈5%. In comparison, corrections to make the pressure profile consistent with internal measurements such as charge exchange recombination spectroscopy and Thomson scattering have a much larger impact. In other work we compute the level of anisotropy from a TRANSP simulation of a neutral beam-heated MAST discharge. This shows a large level of anisotropy, with p⊥/p∥ ≈ 1.7, sufficient to boost the central safety factor by 15%. For this discharge, which is representative of many MAST discharges, the effect of anisotropy and consistent pressure profiles is more pronounced than the toroidal rotation of the plasma.

EFIT tokamak equilibria with toroidal flow and anisotropic pressure using the two-temperature guiding-centre plasma

A new force balance model for the EFIT magnetohydrodynamic equilibrium technique for tokamaks is presented which includes the full toroidal flow and anisotropy changes to the Grad–Shafranov equation. The free functions are poloidal flux functions and all non-linear contributions to the toroidal current density are treated iteratively. The parallel heat flow approximation chosen for the model is that parallel temperature is a flux function and that both parallel and perpendicular pressures may be described using parallel and perpendicular temperatures. This choice for the fluid thermodynamics has been shown elsewhere to be the same as a guiding-centre kinetic solution of the same problem under the same assumptions. The model reduces identically to the static and isotropic Grad–Shafranov equation in the appropriate limit as different flux functions are set to zero. An analytical solution based on a modified Soloviev solution for non-zero toroidal flow and anisotropy is also presented. The force balance model has been demonstrated in the code EFIT TENSOR, a branch of the existing code EFIT++. Benchmark results for EFIT TENSOR are presented and the more complicated force balance model is found to converge to force balance similarly to the usual EFIT model and with comparable speed.

Analysing the impact of anisotropy pressure on tokamak equilibria

Neutral beam injection and ion cyclotron resonance heating induce pressure anisotropy. The axisymmetric plasma equilibrium code HELENA has been upgraded to include anisotropy and toroidal flow. We have studied, using both analytical and numerical methods, the determining factors for anisotropic equilibria and their impact on flux surfaces, the magnetic axis shift, and the displacement of pressure and density contours from the flux surface. With p∥/p⊥ ≈ 1.5, p⊥ can vary by 20% on the s = 0.5 flux surface, in a MAST-like (MAST: Mega Amp Spherical Tokamak) equilibrium. We have also re-evaluated the widely applied approximation to the anisotropy in which p* = (p∥ + p⊥)/2, the average of the parallel and perpendicular pressures, is taken as the approximate isotropic pressure. We show that an isotropic reconstruction can yield a correct p* only by giving an incorrect RB. We find the reconstructions of the same MAST discharge with p∥/p⊥ ≈ 1.25 using isotropic and anisotropic models to have a 3% difference in a toroidal field and a 66% difference for a poloidal current.

Fast particle modifications to equilibria and resulting changes to Alfvén wave modes in tokamaks

We quantify the impact of poloidal and toroidal rotation, anisotropy and energetic particle pressure produced by neutral beam injected energetic particles on the magnetic configuration and wave modes in tokamaks. Specifically, we focus on the class of spherical tokamaks, for which the impact of neutral beam heating is larger due to the relatively low toroidal field and large trapped particle fraction. Recently, (Hole et al 2011 Plasma Phys. Control. Fusion 53 074021) we have used Bayesian inference techniques to compute rotating MAST equilibria, and thereby compute toroidal and poloidal Mach numbers and their uncertainties, as well as computed MAST anisotropic equilibria in the presence of neutral beam heating. Motivated by this work, we compute the impact of rotation and anisotropy on magnetohydrodynamic (MHD) waves of the plasma. Specifically, we determine how a change in q profile due to rotation and anisotropy could affect frequency scalings of the Alfven continuum, Alfven gap modes and compressional Alfven eigenmodes. We also use Bayesian inference to infer energetic particle pressure, and compare the result with the inferred pressure from high-fidelity TRANSP simulations.

Energetic Geodesic Acoustic Modes Associated with Two-Stream-like Instabilities in Tokamak Plasmas

An unstable branch of the energetic geodesic acoustic mode (EGAM) is found using fluid theory with fast ions characterized by their narrow width in energy distribution and collective transit along field lines. This mode, with a frequency much lower than the thermal GAM frequency ω_{GAM}, is now confirmed as a new type of unstable EGAM: a reactive instability similar to the two-stream instability. The mode can have a very small fast ion density threshold when the fast ion transit frequency is smaller than ω_{GAM}, consistent with the onset of the mode right after the turn-on of the beam in DIII-D experiments. The transition of this reactive EGAM to the velocity gradient driven EGAM is also discussed.

Resolving the wave–particle–plasma interaction: advances in the diagnosis, interpretation and self-consistent modelling of waves, particles and the plasma configuration

The purpose of this review is to present the state-of-the-art in diagnosis, interpretation and modelling of waves, particles and the magnetic configuration in fusion plasmas. Knowledge of the magnetic configuration underpins all confinement, stability and transport physics, as well as being an essential prerequisite for the inference of plasma parameters from many diagnostics. As the effect of fast particles become important enough to modify the macroscopic variables of the plasma, the macroscopic fluid equations for equilibrium need to be modified to encapsulate the effects of pressure anisotropy, particle and heat flow. We present a review of such modifications in tokamak geometry, and review probabilistic validation techniques of different equilibrium models. In the last decade new spectral tools have also emerged to characterize the linear behaviour of waves and wave-modes, such as SVD, Fourier-SVD, data-mining and the bispectrum. An emerging trend is the use of statistics to characterize the nonlinear wave population of the plasma from wave field data. Finally, progress is reported on developments in understanding the physics of wave–particle resonant interactions, and the emerging science of the wave–particle–plasma interaction.

The impact of energetic particles and rotation on tokamak plasmas

We discuss two contributions that elucidate the impact of energetic particles and rotation on tokamak plasmas: FLOW-M (M. J. Hole and G. Dennis, Plasma Phys. Control. Fusion 51, 035014, 2009), a generalisation of the ideal MHD flow code FLOW to multiple quasi-neutral fluids, and recent work on steady poloidal and toroidal bulk flows in tokamak plasmas [K. G. McClements and M.J. Hole, Phys. Plasmas 17, 082509 (2010)]. Hole and Dennis have generalized ideal MHD to consider multiple quasi-neutral fluids, each in thermal equilibrium and each thermally insulated from each other such that no population mixing occurs. Kinetically, such a model may be able to approximate the ion or electron distribution function in regions of velocity phase space with a large number of particles, at the expense of more weakly populated phase space, which may have uncharacteristically high temperature and hence pressure. As magnetic equilibrium effects increase with the increase in pressure, this work constitutes an upper limit to the effect of energetic particles. McClements and Hole have examined the effects of poloidal and toroidal flows on tokamak plasma equilibria in the MHD limit. Transonic poloidal flows, of the order of the sound speed multiplied by the ratio of poloidal magnetic field to total field B?/B, can cause the (normally elliptic) Grad-Shafranov (G-S) equation to become hyperbolic in part of the solution domain. The discontinuity in variables produced by this transition indicates a breakdown in the validity of the MHD model in tokamak plasmas. It is pointed out that the range of poloidal flows for which the G-S equation is hyperbolic increases with plasma beta and B?/B, thereby complicating the problem of determining spherical tokamak plasma equilibria with transonic poloidal flows. When the assumption of isentropic flux surfaces is replaced with the more tokamak-relevant one of isothermal flux surfaces, a simple expression can be obtained for the variation of density on a flux surface when poloidal and toroidal flows are simultaneously present. Combined with Thomson scattering measurements of density and temperature, this expression could be used to infer information on poloidal and toroidal flows on the high field side of a tokamak plasma, where direct measurements of flows are not generally possible.

Stabilization of sawteeth with third harmonic deuterium ICRF-accelerated beam in JET plasmas

Sawtooth stabilisation by fast ions is investigated in deuterium (D) and D-helium 3 (He3) plasmas of JET heated by deuterium Neutral Beam Injection combined in synergy with Ion Cyclotron Resonance Heating (ICRH) applied on-axis at 3rd beam cyclotron harmonic. A very significant increase in the sawtooth period is observed, caused by the ICRH-acceleration of the beam ions born at 100 keV to the MeV energy range. Four representative sawteeth from four different discharges are compared with Porcellis model. In two discharges, the sawtooth crash appears to be triggered by core-localized Toroidal Alfven Eigenmodes inside the q = 1 surface (also called “tornado” modes) which expel the fast ions from within the q = 1 surface, over time scales comparable with the sawtooth period. Two other discharges did not exhibit fast ion-driven instabilities in the plasma core, and no degradation of fast ion confinement was found in both modelling and direct measurements of fast ion profile with the neutroncamera. The developed sawtooth scenario without fast ion-driven instabilities in the plasma core is of high interest for the burning plasmas. Possible causes of the sawtooth crashes on JET are discussed.

Fusion product studies via fast ion D–D and D–3He fusion on JET

Dedicated fast ion D-D and D-He-3 fusion experiments were performed on JET with carbon wall (2008) and ITER-like wall (2014) for testing the upgraded neutron and energetic ion diagnostics of fusion ...

MHD normal mode analysis with equilibrium pressure anisotropy

This work was funded by the Australian Research Council through Grant Nos. DP1093797 and FT0991899. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 633053 and from the RCUK Energy Programme [grant number EP/I501045].