T. C. Hender

Culham Centre for Fusion Energy, Abingdon, ENG, United Kingdom

Are you T. C. Hender?

Claim your profile

Publications (148)272.25 Total impact

  • Article: Strong toroidal effects on tokamak tearing mode stability in the hybrid and conventional scenarios
    [show abstract] [hide abstract]
    ABSTRACT: The hybrid scenario is thought to be an important mode of operation for the ITER tokamak. Analytic and numerical calculations demonstrate that toroidal effects at finite β have a strong influence on tearing mode stability of hybrid modes. Indeed, they persist in the large aspect ratio limit, R/a → ∞. A similar strong coupling effect is found between the m = 1, n = 1 harmonic and the m = 2, n = 1 harmonic if the minimum safety factor is less than unity. In both cases the tearing stability index, Δ' increases rapidly as β approaches ideal marginal stability, providing a potential explanation for the onset of linearly unstable tearing modes. The numerical calculations have used an improved version of the T7 code (Fitzpatrick et al 1993 Nucl. Fusion 33 1533), and complete agreement is obtained with the analytic theory for this demanding test of the code.
    Plasma Physics and Controlled Fusion 01/2012; 54(2):025009. · 2.42 Impact Factor
  • Source
    Article: Modelling of plasma response to resonant magnetic perturbation fields in MAST and ITER
    [show abstract] [hide abstract]
    ABSTRACT: The resonant magnetic perturbation (RMP) fields, including the plasma response, are computed within a linear, full toroidal, single-fluid resistive magnetohydrodynamic (MHD) model, and under realistic plasma conditions for MAST and ITER. The response field is found to be considerably reduced, compared with the vacuum field produced by the magnetic perturbation coils. This field reduction relies strongly on the screening effect from the toroidal plasma rotation. Computations also quantify three-dimensional (3D) distortions of the plasma surface, caused by RMP fields. A correlation is found between the computed mode structures, the plasma surface displacement and the observed density pump-out effect in MAST experiments. Generally, the density pump-out tends to occur when the surface displacement peaks near the X-points.
    Nuclear Fusion 06/2011; 51(8):083002. · 4.09 Impact Factor
  • Article: Macroscopic stability of high β MAST plasmas
    [show abstract] [hide abstract]
    ABSTRACT: The high-beta capability of the spherical tokamak, coupled with a suite of world-leading diagnostics on MAST, has facilitated significant improvements in the understanding of performance-limiting core instabilities in high performance plasmas. For instance, the newly installed motional Stark effect diagnostic, with radial resolution <25 mm, has enabled detailed study of saturated long-lived modes in hybrid scenarios. Similarly, the upgraded Thomson scattering system, with radial resolution <10 mm and the possibility of temporal resolution of 1 µs, has allowed detailed analysis of the density and temperature profiles during transient activity in the plasma, such as at a sawtooth crash. High resolution charge exchange recombination spectroscopy provided measurement of rotation braking induced by both applied magnetic fields and by magnetohydrodynamic (MHD) instabilities, allowing tests of neoclassical toroidal viscosity theory predictions. Finally, MAST is also equipped with internal and external coils that allow non-axisymmetric fields to be applied for active MHD spectroscopy of instabilities near the no-wall beta limit. MAST has been able to operate above the pressure at which the resonant field amplification is observed to strongly increase. In order to access such high pressures, the resistive wall mode must be damped, and so numerical modelling has focused on assessing the kinetic damping of the mode and its nonlinear interaction with other instabilities. The enhanced understanding of the physical mechanisms driving deleterious MHD activity given by these leading-edge capabilities has provided guidance to optimize operating scenarios for improved plasma performance.
    Nuclear Fusion 06/2011; 51(7):073040. · 4.09 Impact Factor
  • Article: Survey of disruption causes at JET
    [show abstract] [hide abstract]
    ABSTRACT: A survey has been carried out into the causes of all 2309 disruptions over the last decade of JET operations. The aim of this survey was to obtain a complete picture of all possible disruption causes, in order to devise better strategies to prevent or mitigate their impact. The analysis allows the effort to avoid or prevent JET disruptions to be more efficient and effective. As expected, a highly complex pattern of chain of events that led to disruptions emerged. It was found that the majority of disruptions had a technical root cause, for example due to control errors, or operator mistakes. These bring a random, non-physics, factor into the occurrence of disruptions and the disruption rate or disruptivity of a scenario may depend more on technical performance than on physics stability issues. The main root cause of JET disruptions was nevertheless due to neo-classical tearing modes that locked, closely followed in second place by disruptions due to human error. The development of more robust operational scenarios has reduced the JET disruption rate over the last decade from about 15% to below 4%. A fraction of all disruptions was caused by very fast, precursorless unpredictable events. The occurrence of these disruptions may set a lower limit of 0.4% to the disruption rate of JET. If one considers on top of that human error and all unforeseen failures of heating or control systems this lower limit may rise to 1.0% or 1.6%, respectively.
    Nuclear Fusion 04/2011; 51(5):053018. · 4.09 Impact Factor
  • Source
    Article: Non-linear instability at large vertical displacements in the MAST tokamak
    [show abstract] [hide abstract]
    ABSTRACT: Data from forced Vertical Displacement Event (VDE) experiments in the Mega Ampère Spherical Tokamak (MAST) indicate that the plasma is highly destabilized above z displacements of ~0.4 m. Previous work investigating the plasma response to vertical plasma perturbations in MAST had found it to be more non-linear than an equivalent conventionally shaped tokamak. Further investigation into the stability of the plasma at high z displacements is done using a linear vertical stability code. Theoretically it is found that the plasma becomes ideally unstable from z ~ 0.8 m, corresponding to a significant acceleration of the vertical position experimentally.
    Plasma Physics and Controlled Fusion 02/2011; 53(3):035018. · 2.42 Impact Factor
  • Article: Effects of a resistive wall on magnetohydrodynamic instabilities
    [show abstract] [hide abstract]
    ABSTRACT: The paper presents linear and non-linear MHD calculations to examine the effect of a finite conductivity (resistive) wall on plasma stability. At a limiting safety factor qψ of approximately 2 in the tokamak and generally in the RFP, ideal modes are found, with a growth rate that varies inversely with the wall time constant. Resistive tearing modes can also be destabilized by a finite conductivity wall, but sufficiently fast plasma rotation can in turn stabilize these instabilities. It is shown that, non-linearly, the eddy currents driven in the resistive wall, by rotating MHD activity, produce a torque which opposes and slows the plasma rotation. This effect can be particularly strong in the RFP and leads to mode lock times which are shorter than in the tokamak.
    Nuclear Fusion 01/2011; 29(8):1279. · 4.09 Impact Factor
  • Article: Plasma stored energy and momentum losses during large MHD activity in JET
    [show abstract] [hide abstract]
    ABSTRACT: Substantial losses of plasma stored energy and toroidal ion momentum are observed in JET during large amplitude oscillating or quasi-stationary MHD activity when mode coupling effects become important. The degradation in the diamagnetic stored energy due to low m,n MHD modes increases with amplitude, reaching ΔW/W > 30% at a mode amplitude of r/Bθ > 0.4%. Favourable comparisons are made with the degradation in the incremental energy confinement time during such MHD activity as predicted by Chang and Callen. The reduction in the plasma ion toroidal momentum, from charge exchange measurements on C 6+ ions, depends on the extent of mode coupling within the plasma and on the oscillation frequency of the n = 1 mode. When r/Bθ > 0.1% for more than about 300 ms, toroidal coupling between low m,n modes together with coupling of the plasma ions to the modes by a force equilibrates the toroidal ion rotation frequency with the MHD oscillation frequency over substantial regions of the plasma, depending on the radius of the rational q surface of the coupled MHD mode. This ion mode coupling force becomes particularly apparent when the mode frequency drops to nearly zero and the ion toroidal rotation frequency also drops to zero within 100–300 ms, despite continued neutral beam injection. In such cases, the toroidal ion momentum appears to be lost electromagnetically via the MHD modes to the external structure or to fixed stray fields of the tokamak, while the plasma stored energy losses must be accounted for by other processes.
    Nuclear Fusion 01/2011; 30(2):205. · 4.09 Impact Factor
  • Article: Disruptions in JET
    [show abstract] [hide abstract]
    ABSTRACT: In JET, both high density and low-q operation are limited by disruptions. The density limit disruptions are caused initially by impurity radiation. This causes a contraction of the plasma temperature profile and leads to an MHD unstable configuration. There is evidence of magnetic island formation resulting in minor disruptions. After several minor disruptions, a major disruption with a rapid energy quench occurs. This event takes place in two stages. In the first stage there is a loss of energy from the central region. In the second stage there is a more rapid drop to a very low temperature, apparently due to a dramatic increase in impurity radiation. The final current decay takes place in the resulting cold plasma. During the growth of the MHD instability the initially rotating mode is brought to rest. This mode locking is believed to be due to an electromagnetic interaction with the vacuum vessel and external magnetic field asymmetries. The low-q disruptions are remarkable for the precision with which they occur at qψ = 2. These disruptions do not have extended precursors or minor disruptions. The instability grows and locks rapidly. The energy quench and current decay are generally similar to those of the density limit.
    Nuclear Fusion 01/2011; 29(4):641. · 4.09 Impact Factor
  • Article: Toroidal internal kink stability in tokamaks with ultra flat q profiles
    R.J. Hastie, T.C. Hender
    [show abstract] [hide abstract]
    ABSTRACT: Linear stability properties of the ideal internal kink mode in toroidal geometry are calculated for equilibria in which the q(r) profile is very flat and q ≈ 1 in the core region of the plasma. Marginal stability criteria and growth rates are calculated analytically in the large aspect ratio limit and compared with numerical results from the FAR code. The theory is developed for m = n = 1 modes and for higher m (= n) modes. The temperature perturbation due to adiabatic expansion in the linear phase of the 1/1 mode is calculated and compared with experimental data, showing that the predictions from ideal MHD theory cannot account for the observed temperature increase on JET. Comparison with collisionless theory suggests that the observed temperature increase can be accounted for by compression of the trapped particles.
    Nuclear Fusion 01/2011; 28(4):585. · 4.09 Impact Factor
  • Article: Large amplitude quasi-stationary MHD modes in JET
    [show abstract] [hide abstract]
    ABSTRACT: Oscillating MHD modes in JET are often observed to slow down as they grow and generally stop rotating (lock) when the amplitude exceeds a critical value, then continue to grow to large amplitudes (r/Bθ ~ 1%). The mode can grow early in the current rise or after perturbations, such as a pellet injection or a large sawtooth collapse, and maintain a large amplitude throughout the remainder of the discharge. Such large amplitude quasistationary MHD modes can apparently have profound effects on the plasma, including stopping central ion plasma rotation, reducing the amplitude and changing the shape of sawteeth, flattening the temperature profile around resonant q surfaces and reducing the stored energy. Perhaps most important, large amplitude locked modes are precursors to most disruptions. Some large amplitude modes can be avoided by proper programming of the q evolution. The apparent reasons for the mode locking in a particular location are discussed and a comparison with theory is made.
    Nuclear Fusion 01/2011; 28(6):1085. · 4.09 Impact Factor
  • Article: Finite beta effects on tearing modes in the tokamak
    T.C. Hender, R.J. Hastie, D.C. Robinson
    [show abstract] [hide abstract]
    ABSTRACT: Details are given of a numerical study of finite-beta tearing modes in the tokamak. The linear compressible resistive MHD equations are solved in full toroidal geometry with no ordering assumptions. The results show a strong stabilizing effect as beta is increased, arising from the average curvature within the resistive layer. This stabilizing effect is particularly pronounced for high conductivity temperatures and small aspect ratios.
    Nuclear Fusion 01/2011; 27(9):1389. · 4.09 Impact Factor
  • Article: Resistive wall mode control code maturity: progress and specific examples
    [show abstract] [hide abstract]
    ABSTRACT: Two issues of the resistive wall mode (RWM) control code maturity are addressed: the inclusion of advanced mode damping physics beyond the ideal MHD description, and the possibility of taking into account the influence of 3D features of the conducting structures on the mode stability and control. Examples of formulations and computational results are given, using the MARS-F/K codes and the CarMa code. The MARS-K calculations for a DIII-D plasma shows that the fast ion contributions, which can give additional drift kinetic stabilization in the perturbative approach, also drive an extra unstable branch of mode in the self-consistent kinetic modelling. The CarMa modelling for the ITER steady state advanced plasmas shows about 20% reduction in the RWM growth rate by the volumetric blanket modules. The multi-mode analysis predicts a weak interaction between the n = 0 and the n = 1 RWMs, due to the 3D ITER walls. The CarMa code is also successfully applied to model the realistic feedback experiments in RFX.
    Plasma Physics and Controlled Fusion 09/2010; 52(10):104002. · 2.42 Impact Factor
  • Article: Modelling resonant field amplification due to low-n peeling modes in JET
    [show abstract] [hide abstract]
    ABSTRACT: The MHD code MARS-F is used to model low-n, low-frequency, large-amplitude resonant field amplification peaks observed in JET low-pressure plasmas. The resonant response of a marginally stable, n = 1 ideal peeling mode is offered as a candidate to explain the experimental observation. It is found that, unlike the response of a stable resistive wall mode, the peeling mode response is not sensitive to the plasma rotation, nor to the kinetic effects.
    Plasma Physics and Controlled Fusion 03/2010; 52(4):045011. · 2.42 Impact Factor
  • Article: An improved method to evaluate the ideal no-wall beta limit from resonant field amplification measurements in JET
    [show abstract] [hide abstract]
    ABSTRACT: Modelling the low-n, low frequency resonant field amplification (RFA) effects for JET plasmas, using the MHD code MARS-F, offers explanations to one of the recent observations made in experiments, namely a mismatch between the measured RFA threshold and the predicted no-wall beta limit according to ideal MHD calculations. The mismatch is minimized by applying a new way of determining the RFA threshold, based on evaluating the logarithmic derivative of the RFA amplitude as a function of the normalized plasma pressure. This improved method is shown, at least in theory, to be robust in predicting the no-wall beta limit for JET plasmas.
    Plasma Physics and Controlled Fusion 10/2009; 51(11):115005. · 2.42 Impact Factor
  • Source
    Article: Progress in physics and control of the resistive wall mode in advanced tokamaks
    [show abstract] [hide abstract]
    ABSTRACT: Self-consistent computations are carried out to study the stability of the resistive wall mode (RWM) in DIII-D [ J. L. Luxon, Nucl. Fusion 42, 614 (2002) ] plasmas with slow plasma rotation, using the hybrid kinetic-magnetohydrodynamic code MARS-K [ Y. Q. Liu et al., Phys. Plasmas 15, 112503 (2008) ]. Based on kinetic resonances between the mode and the thermal particle toroidal precession drifts, the self-consistent modeling predicts less stabilization of the mode compared to perturbative approaches, and with the DIII-D experiments. A simple analytic model is proposed to explain the MARS-K results, which also gives a qualitative interpretation of the recent experimental results observed in JT-60U [ S. Takeji et al., Nucl. Fusion 42, 5 (2002) ]. Our present analysis does not include the kinetic contribution from hot ions, which may give additional damping on the mode. The effect of particle collision is not included either. Using the CARMA code [ R. Albanese et al., IEEE Trans. Magn. 44, 1654 (2008) ], a stability and control analysis is performed for the RWM in ITER [ R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002) ] steady state advanced plasmas, taking into account the influence of three-dimensional conducting structures.
    Physics of Plasmas 04/2009; 16(5):056113-056113-12. · 2.15 Impact Factor
  • Article: Stability of the resistive wall mode in JET
    [show abstract] [hide abstract]
    ABSTRACT: The kinetic effects influencing the stability of the resistive wall mode (RWM) are investigated by applying a drift kinetic code to calculate the change in the potential energy of the mode in the presence of thermal and energetic particles. The analysis is carried out for typical JET high-β plasmas. It is found that the strongest kinetic damping of the RWM arises due to mode resonance with the precession motion of the trapped thermal particles. The stability of the RWM in JET plasmas is also probed by using active MHD spectroscopy. The frequency spectrum of the plasma response to oscillating externally applied fields has been measured and fitted to parameter models in order to infer the stability of the RWM. A new model retaining information about the plasma response is presented to describe the resonant field amplification in the presence of a stable RWM.
    Plasma Physics and Controlled Fusion 03/2009; 51(5):055015. · 2.42 Impact Factor
  • Source
    Article: Modelling resistive wall modes in ITER with self-consistent inclusion of drift kinetic resonances
    [show abstract] [hide abstract]
    ABSTRACT: We investigate drift kinetic effects on the resistive wall mode (RWM) stability in ITER plasmas, due to the mode resonance with magnetic precession drifts and/or bounce motion of bulk plasma thermal particles. A toroidal drift kinetic model is self-consistently incorporated into the MHD formulation. Self-consistent simulations using the hybrid kinetic-MHD code MARS-K (Y.Q. Liu et al 2008 Phys. Plasmas 15 112503) predict a parameter space for ITER steady-state plasmas, where the RWM is fully stabilized by the drift kinetic effects combined with the toroidal plasma flow. A wider stable parameter space is predicted by the perturbative approach based on the ideal kink mode or the fluid RWM eigenfunction. The difference is attributed primarily to the self-consistent determination of the mode eigenvalue in the non-perturbative approach.
    Nuclear Fusion 02/2009; 49(3):035004. · 4.09 Impact Factor
  • Source
    Article: Overview of physics results from MAST
    [show abstract] [hide abstract]
    ABSTRACT: Several improvements to the MAST plant and diagnostics have facilitated new studies advancing the physics basis for ITER and DEMO, as well as for future spherical tokamaks (STs). Using the increased heating capabilities P-NBI <= 3.8 MW H-mode at I-P = 1.2 MA was accessed showing that the energy confinement on MAST scales more weakly with I-P and more strongly with B-t than in the ITER IPB98(y, 2) scaling. Measurements of the fuel retention of shallow pellets extrapolate to an ITER particle throughput of 70% of its original designed total throughput capacity. The anomalous momentum diffusion, chi(phi), is linked to the ion diffusion, chi(i), with a Prandtl number close to P-phi approximate to chi(phi)/chi(i) approximate to 1, although chi(i) approaches neoclassical values. New high spatial resolution measurements of the edge radial electric field, E-r, show that the position of steepest gradients in electron pressure and E-r (i.e. shearing rate) are coincident, but their magnitudes are not linked. The T-e pedestal width on MAST scales with root beta(ped)(pol) rather than rho(pol). The edge localized mode (ELM) frequency for type-IV ELMs, new in MAST, was almost doubled using n = 2 resonant magnetic perturbations from a set of four external coils (n = 1, 2). A new internal 12 coil set (n <= 3) has been commissioned. The filaments in the inter-ELM and L-mode phase are different from ELM filaments, and the characteristics in L-mode agree well with turbulence calculations. A variety of fast particle driven instabilities were studied from 10 kHz saturated fishbone like activity up to 3.8 MHz compressional Alfven eigenmodes. Fast particle instabilities also affect the off-axis NBI current drive, leading to fast ion diffusion of the order of 0.5 m(2) s(-1) and a reduction in the driven current fraction from 40% to 30%. EBW current drive start-up is demonstrated for the first time in a ST generating plasma currents up to 55 kA. Many of these studies contributed to the physics basis of a planned upgrade to MAST.
    Nuclear Fusion. 01/2009; 49(10):104017.
  • Article: Experimental studies of stability and beta limit in JET
    [show abstract] [hide abstract]
    ABSTRACT: The paper presents results on the use of resonant field amplification for experimental probing of stability and β-limits (β is the ratio of the plasma pressure to the magnetic field pressure) in JET. It is found that an externally applied helical magnetic field is strongly enhanced when the plasma exceeds the ideal no-wall stability limit or approaches proximity to other marginally stable (i.e. current-driven) modes. This effect is known as the resonant field amplification (RFA) and was used for the systematic probing of stability in different advanced regimes on JET. The application of this technique on JET is discussed in the paper and the results of the RFA measurements are presented and related to the observed limitations in β.
    Plasma Physics and Controlled Fusion 11/2008; 50(12):124030. · 2.42 Impact Factor
  • Source
    Article: The physics of sawtooth stabilization
    [show abstract] [hide abstract]
    ABSTRACT: Long period sawteeth have been observed to result in low-β triggering of neo-classical tearing modes, which can significantly degrade plasma confinement. Consequently, a detailed physical understanding of sawtooth behaviour is critical, especially for ITER where fusion-born α particles are likely to lead to very long sawtooth periods. Many techniques have been developed to control, and in particular to destabilize the sawteeth. The application of counter-current neutral beam injection (NBI) in JET has resulted in shorter sawtooth periods than in Ohmic plasmas. This result has been explained because, firstly, the counter-passing fast ions give a destabilizing contribution to the n = 1 internal kink mode—which is accepted to be related to sawtooth oscillations—and secondly, the flow shear strongly influences the stabilizing trapped particles. A similar experimental result has been observed in counter-NBI heated plasmas in MAST. However, the strong toroidal flows in spherical tokamaks mean that the sawtooth behaviour is determined by the gyroscopic flow stabilization of the kink mode rather than kinetic effects. In NBI heated plasmas in smaller conventional aspect-ratio tokamaks, such as TEXTOR, the flow and kinetic effects compete to give different sawtooth behaviour. Other techniques applied to destabilize sawteeth are the application of electron cyclotron current drive (ECCD) or ion cyclotron resonance heating (ICRH). In JET, it has been observed that localized ICRH is able to destabilize sawteeth which were otherwise stabilized by a co-existing population of energetic trapped ions in the core. This is explained through the dual rôle of the ICRH in reducing the critical magnetic shear required to trigger a sawtooth crash, and the increase in the local magnetic shear which results from driving current near the q = 1 rational surface. Sawtooth control in ITER could be provided by a combination of ECCD and co-passing off-axis negative-NBI fast ions.
    Plasma Physics and Controlled Fusion 11/2007; 49(12B):B385. · 2.42 Impact Factor