Structure of Micro-instabilities in Tokamak Plasmas: Stiff Transport or Plasma Eruptions?

Solutions to a model 2D eigenmode equation describing micro-instabilities in tokamak plasmas are presented that demonstrate a sensitivity of the mode structure and stability to plasma profiles. In narrow regions of parameter space, with special plasma profiles, a maximally unstable mode is found that balloons on the outboard side of the tokamak. This corresponds to the conventional picture of a ballooning mode. However, for most profiles this mode cannot exist and instead a more stable mode is found that balloons closer to the top or bottom of the plasma. Good quantitative agreement with a 1D ballooning analysis is found provided the constraints associated with higher order profile effects, often neglected, are taken into account. A sudden transition from this general mode to the more unstable ballooning mode can occur for a critical flow shear, providing a candidate model for why some experiments observe small plasma eruptions (Edge Localised Modes, or ELMs) in place of large Type I ELMs.Comment: 11 pages, 3 figure

Using the local gyrokinetic code, GS2, to investigate global ITG modes in tokamaks. (I) s-α{\alpha} model with profile and flow shear effects

This paper combines results from a local gyrokinetic code with analytical theory to reconstruct the global eigenmode structure of the linearly unstable ion-temperature-gradient (ITG) mode with adiabatic electrons. The simulations presented here employ the s-${\alpha}$ tokamak equilibrium model. Local gyrokinetic calculations, using GS2 have been performed over a range of radial surfaces, x, and for ballooning phase angle, p, in the range -${\pi} {\leq} p {\leq\pi}$, to map out the complex local mode frequency, ${\Omega_0(x, p) = \omega_0(x, p) + i\gamma_0(x, p)}$. Assuming a quadratic radial profile for the drive, namely ${\eta_i = L_n/L_T}$, (holding constant all other equilibrium profiles such as safety factor, magnetic shear etc.), ${\Omega_0(x, p)}$ has a stationary point. The reconstructed global mode then sits on the outboard mid plane of the tokamak plasma, and is known as a conventional or isolated mode, with global growth rate, ${\gamma}$ ~ Max[${\gamma_0(x, p)}$], where ${\gamma_0(x, p)}$ is the local growth rate. Taking the radial variation in other equilibrium profiles (e.g safety factor q(x)) into account, removes the stationary point in ${\Omega_0(x, p)}$ and results in a mode that peaks slightly away from the outboard mid-plane with a reduced global growth rate. Finally, the influence of flow shear has also been investigated through a Doppler shift, ${\omega_0 \rightarrow \omega_0 + n\Omega^{\prime}x}$, where n is the toroidal mode number and ${\Omega^{\prime}}$ incorporates the effect of flow shear. The equilibrium profile variation introduces an asymmetry to the growth rate spectrum with respect to the sign of ${\Omega^{\prime}}$, consistent with recent global gyrokinetic calculations.Comment: 10 pages, 8 figures and 1 tabl

Kinetic instabilities that limit {\beta} in the edge of a tokamak plasma: a picture of an H-mode pedestal

Plasma equilibria reconstructed from the Mega-Amp Spherical Tokamak (MAST) have sufficient resolution to capture plasma evolution during the short period between edge-localized modes (ELMs). Immediately after the ELM steep gradients in pressure, P, and density, ne, form pedestals close to the separatrix, and they then expand into the core. Local gyrokinetic analysis over the ELM cycle reveals the dominant microinstabilities at perpendicular wavelengths of the order of the ion Larmor radius. These are kinetic ballooning modes (KBMs) in the pedestal and microtearing modes (MTMs) in the core close to the pedestal top. The evolving growth rate spectra, supported by gyrokinetic analysis using artificial local equilibrium scans, suggest a new physical picture for the formation and arrest of this pedestal.Comment: Final version as it appeared in PRL (March 2012). Minor improvements include: shortened abstract, and better colour table for figures. 4 pages, 6 figure

The use of hormonal therapy with radiotherapy for prostate cancer: analysis of prospective randomised trials

In 1901, Wilhelm Conrad Röntgen won the Nobel prize in Physics for his discovery of the Röntgen rays or, as he himself called them, X-rays. In 1966, Dr Charles Brenton Higgins won the Nobel Prize in Medicine for his breakthroughs concerning hormonal treatment of prostatic cancer. After 31 years, in 1997, the first prospective randomised trials of the combination of hormonal therapy and radiation therapy were published, showing increased survival when compared to radiation therapy alone for patients with prostate cancer. Since 1997, many investigators have published trials combining hormonal and radiation therapy for prostate cancer. This minireview will address the largest and most influential of these trials, and attempt to guide physicians in selecting the appropriate patients for this combined approach

Stabilisation of short-wavelength instabilities by parallel-to-the-field shear in long-wavelength E×B\mathbf{E} \times \mathbf{B} flows

Magnetised plasma turbulence can have a multiscale character: instabilities driven by mean temperature gradients drive turbulence at the disparate scales of the ion and the electron gyroradii. Simulations of multiscale turbulence, using equations valid in the limit of infinite scale separation, reveal novel cross-scale interaction mechanisms in these plasmas. In the case that both long-wavelength (ion-gyroradius-scale) and short-wavelength (electron-gyroradius-scale) linear instabilities are driven far from marginal stability, we show that the short-wavelength instabilities are suppressed by interactions with long-wavelength turbulence. The observed suppression is a result of two effects: parallel-to-the-field-line shearing by the long wavelength $\mathbf{E} \times \mathbf{B}$ flows, and the modification of the background density gradient by long-wavelength fluctuations. In contrast, simulations of multiscale turbulence where instabilities at both scales are driven near marginal stability demonstrate that when the long-wavelength turbulence is sufficiently collisional and zonally dominated the effect of cross-scale interaction can be parameterised solely in terms of the local modifications to the mean density and temperature gradients. We discuss physical arguments that qualitatively explain how a change in equilibrium drive leads to the observed transition in the impact of the cross-scale interactions.Comment: 20 pages, 28 figure

Comparison of robust optimization and info-gap methods for water resource management under deep uncertainty

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.This paper evaluates two established decision-making methods and analyzes their performance and suitability within a water resources management (WRM) problem. The methods under assessment are info-gap (IG) decision theory and robust optimization (RO). The methods have been selected primarily to investigate a contrasting local versus global method of assessing water system robustness to deep uncertainty, but also to compare a robustness model approach (IG) with a robustness algorithm approach (RO), whereby the former selects and analyzes a set of prespecified strategies and the latter uses optimization algorithms to automatically generate and evaluate solutions. The study presents a novel area-based method for IG robustness modeling and assesses the applicability of utilizing the future flows climate change projections in scenario generation for water resource adaptation planning. The methods were applied to a case study resembling the Sussex North Water Resource Zone in England, assessing their applicability at improving a risk-based WRM problem and highlighting the strengths and weaknesses of each method at selecting suitable adaptation strategies under climate change and future demand uncertainties. Pareto sets of robustness to cost are produced for both methods and highlight RO as producing the lower cost strategies for the full range of varying target robustness levels. IG produced the more expensive Pareto strategies due to its more selective and stringent robustness analysis, resulting from the more complex scenario ordering process.This work was financially supported by the UK Engineering and Physical Sciences Research Council, HR Wallingford and The University of Exeter through the STREAM Industrial Doctorate Centre. The authors are grateful to Dr Steven Wade, now at the Met Office, and Chris Counsell of HR Wallingford for providing data for the Sussex North case study

Microstability analysis of pellet fuelled discharges in MAST

Reactor grade plasmas are likely to be fuelled by pellet injection. This technique transiently perturbs the profiles, driving the density profile hollow and flattening the edge temperature profile. After the pellet perturbation, the density and temperature profiles relax towards their quasi-steady-state shape. Microinstabilities influence plasma confinement and will play a role in determining the evolution of the profiles in pellet fuelled plasmas. In this paper we present the microstability analysis of pellet fuelled H-mode MAST plasmas. Taking advantage of the unique capabilities of the MAST Thomson scattering system and the possibility of synchronizing the eight lasers with the pellet injection, we were able to measure the evolution of the post-pellet electron density and temperature profiles with high temporal and spatial resolution. These profiles, together with ion temperature profiles measured using a charge exchange diagnostic, were used to produce equilibria suitable for microstability analysis of the equilibrium changes induced by pellet injection. This analysis, carried out using the local gyrokinetic code GS2, reveals that the microstability properties are extremely sensitive to the rapid and large transient excursions of the density and temperature profiles, which also change collisionality and beta e significantly in the region most strongly affected by the pellet ablation.Comment: 21 pages, 10 figures. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i