Description of Research Projects
MHD stability of Internal Kink Mode and sawteeth, and interaction with fast ions: theory and JET experiments
A long mean free path treatment of energetic ions, and their effects on the MHD instability known as the internal kink mode, has demonstrated the possibility that certain populations of fast ions can affect tokamak stability in an extremely useful way. Our work has shown precisely the features in phase space of a fast ion distribution required to control undesirable tokamak instabilities. The mechanism that links the fast ion dynamics and MHD stability has been subsequently validated in dedicated experiments at JET. This area of research has paved the way for performance limiting and potentially disruption causing neo-classical tearing modes to be avoided. Experimental validation of the theory has been achieved, and exploited to avoid NTMs in ITER relevant scenarios.
Integrated modelling of ICRH in 2D and 3D configurations
Optimal modelling of ICRH requires the integration of an equilibrium code, and a wave propagation code and a guiding centre code. With the generalisation of pressure anisotropy in all of these codes, we have been able to self-consistently model the extreme anisotropic heating effect of ICRH. The recently developed code SCENIC (published under this name in Computer Physics Communications) has been applied to JET tokamak experiments with minority heated Helium-3 thereby assisting predictions of the effect of ICRH on sawtooth control and NTM avoidance. In addition to similar predictions applied to ITER, the code has been applied to a weakly 3-dimensional stellarator system. We have also led an effort to include the effect of the heated energetic ions on the anisotropic tokamak and stellarator equilibrium during the heating simulations.
Kinetic-MHD theory and the effects of energetic ions on tokamak stability limits
MHD stability control will be one of the main challenges for the successful operation of ITER. Indeed the MHD model is considered to provide necessary stability criteria for magnetic fusion plasmas. In turn, the stability threshold for interchange instabilities provides a necessary criteria for MHD stability. It has long been known that kinetic corrections to ideal MHD can provide important stabilisation effects. The most obvious are FLR corrections in the layer region close to a rational surface. These diamagnetic effects can increase continuum damping through enhancing the perpendicular plasma inertia. Meanwhile, kinetic corrections in a collisionless plasma associated with parallel dynamics are treated by replacing the adiabatic equation of state with a moment equation obtained from the linearized collisionless drift kinetic equation. We have recently developed a general treatment of the parallel dynamics associated with collisionless wave-particle interaction, with results applied to the challenging application of interchange modes. We have obtained a solution to the drift kinetic equation that is simultaneously valid through the inner layer of the rational surface, and the outer region. It is seen that stability depends on an inseparable combination of modified FLR effects (enhanced inertia) in the layer region, and wave-particle interaction, and consequent stabilisation, in the outer region.
Turbulence driven by tokamak micro-instabilities, and interaction with energetic ions
Turbulence is an inevitable feature of tokamak plasmas. Meanwhile,energetic ions are required in order to heat the plasma to the temperatures required for fusion to take place. Since the future tokamak ITER will have a large population of energetic (fusion produced) alpha particles, it is of interest to simulate the interaction between energetic ions and turbulence generated from micro-instabilities, and in particular, to see if turbulence could affect the confinement properties of the energetic ions. We have concluded that turbulence phenomena could indeed, under certain conditions, transport energetic particles away from the hot plasma core, thus affecting the efficiency of plasma heating, and potentially plasma burn in a future reactor. The work has identified the conditions for which this takes place, both for energetic ions generated from auxiliary heating, and for fusion alpha particles. It has been found that if the separation in energy between the fuel plasma and the alpha particles is sufficiently large, then the confinement of alpha particles should remain excellent.
Toroidal plasma rotation in tokamaks and its effect on MHD stability
The motion of a plasma can, under certain conditions, reach sonic speeds along the direction of toroidal symmetry in a tokamak. Our interest in this area has been to model the stability of such toroidally rotating plasmas. The work brings together analytical theory, self consistent integration of numerical codes, and experimental data. Each of these have been compared favourably. In particular, we have led an effort to try to correct a mistake commonly made in the literate concerning strong toroidal flows in which the centrifugal effect of the rotating plasma had only been partially accounted for. By analytical analysis employing algebraic reduction software, we have been able to switch the correcting terms on and off, and in this way compare with various full numerical code platforms. This work has led to a number of papers, and to recognition of the issue of self-consistent plasma rotation and its effect in tokamaks. In related work, this collaboration has recently demonstrated that a Kelvin-Helmholz-like MHD instability exists in toroidal tokamak plasmas. By using analytic techniques and self-consistent MHD codes we were able to quantify the degree of velocity shear in the toroidal plasma motion required to trigger the instability, and also a window of operation stable to both external kink modes and Kelvin-Helmholz modes.
Linear MHD stability of scenarios with low magnetic shear (hybrid scenarios)
Spherical tokamaks can tolerate a large ratio of plasma energy relative to magnetic energy. Stability thresholds of some instabilities appear to be broadly governed by ideal magnetohydrodynamics. The so called long lived mode, which is frequently observed to limit plasma operation in MAST, has recently been linked to the infernal mode, previously found in MHD codes and modelling analysis. In connection to this, we have made progress in forming an analytic description of the infernal mode. This work has been extended to include the effects of resistivity, sheared plasma rotation, diamagnetic effects and viscosity. Convenient stability thresholds and growth rates can be obtained, including the derivation of rapid growth of linear resistive modes associated with small magnetic shear.
Non-linear MHD coupling of resistive and ideal instabilities in tokamaks
A great deal of research effort has gone into controlling the sawtooth instability. The reason for this is that sawtooth oscillations can trigger dangerous instabilities known as NTMs. These latter instabilities drive magnetic reconnection via the finite resistivity of a fusion plasma, and in analogy with solar flares, NTMs can cause a disruption, or plasma termination, which is intolerable for a next step reactor like ITER. The non-linear-resistive MHD code XTOR has been employed for the task of identifying the mechanism that drives rapidly growing NTMs from sawteeth. Comparisons have been made with the linear analytical studies mentioned earlier. In addition, the XTOR code has been employed in the ideal limit, in order to investigate non-linear saturated (time invariant) MHD states following linear MHD instability. Excellent comparisons have been made between the saturated state of and n=1 instability calculated with XTOR with 3D helical equilibria generated from hybrid scenarios which have safety factor close to unity over an extended region.
Theory of 3D helical plasma configurations in a nominally axisymmetric tokamak
Pioneering work using tools usually adopted for 3D stellarator physics has identified that a plasma in a toroidally axisymmetric tokamak configuration can generate a non-axisymmetric structure in the plasma core, and that this can be at a lower (preferred) energy state than the usual axisymmetric state. This work has explained a number of previously unexplained experimental phenomena, including the snake instability. The internal 3D structures are also similar to long lived modes observed during hybrid scenario operation in tokamaks. That these structures can be constructed in the ANIMEC equilibrium code enables the effects of fast ion transport in the presence of long lived modes to be assessed more self-consistently.
Exact guiding centre drift of particles with 3D time varying fields
We have improved the accuracy of the guiding centre formulation adopted in the VENUS-LEVIS code, to include anisotropic pressure, and the full vector potential of time varying magnetic fields. Subsequently, the code has been reformulated from a canonical phase space representation into a general Lagrangian representation. This has allowed particles to be followed exactly with any coordinate system, thus permitting the most convenient coordinate system to be chosen, according to the application. Additional work in this area includes an investigation into the effect of pressure anisotropy on the toroidal magnetic drift, both numerically with the VENUS code, and analytically.
Exact guiding centre drift of particles in helical equilibria
The 3D helical equilibria generated from the ANIMEC code provide a convenient platform for establishing the transport of fast ions in the presence of infernal modes that can occur in hybrid scenarios. Using the VENUS-LEVIS code we have been able to demonstrate that neutral beam ions are ejected from the core of the plasma due to the 3D helical core. These results compare favourably with the measured loss of fast ions in the core of the plasma when long lived modes are significant in spherical tokamaks.
Stellarator stability with anisotropic pressure equilibrium
A model for the effect of anisotropy developed at SPC has enabled our suite of 3D codes to be modified to include the physics of anisotropy. In particular, both a bi-Maxwellian distribution model, and a variable injection angle slowing down distribution function for fast particles that drive pressure anisotropy in the equilibrium state has been implemented in the fixed and free boundary versions of the VMEC code. The free boundary version has been renamed ANIMEC. These models allow an accurate description of plasmas, particularly those subjected to Ion Cyclotron Resonance Heating. The bi-Maxwellian model has also been incorporated into the wave code LEMan, the stability code TERPSICHORE and the guiding centre code VENUS, and this in turn has enabled the stability of anisotropic 3D systems to be assessed, and for the ICRH code SCENIC to be developed. Fluid-MHD stability analysis of the LHD heliotron has been investigated with both fast ion anisotropic distribution function models.