| 1. |
- Wilkie, George, 1983, et al.
(författare)
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First principles of modelling the stabilization of microturbulence by fast ions
- 2018
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Ingår i: Nuclear Fusion. - : IOP PUBLISHING LTD. - 0029-5515 .- 1741-4326. ; 58:8
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Tidskriftsartikel (refereegranskat)abstract
- The observation that fast ions stabilize ion-temperature-gradient-driven microturbulence has profound implications for future fusion reactors. It is also important in optimizing the performance of present-day devices. In this work, we examine in detail the phenomenology of fast ion stabilization and present a reduced model which describes this effect. This model is derived from the high-energy limit of the gyrokinetic equation and extends the existing 'dilution' model to account for nontrivial fast ion kinetics. Our model provides a physically-transparent explanation for the observed stabilization and makes several key qualitative predictions. Firstly, that different classes of fast ions, depending on their radial density or temperature variation, have different stabilizing properties. Secondly, that zonal flows are an important ingredient in this effect precisely because the fast ion zonal response is negligible. Finally, that in the limit of highly-energetic fast ions, their response approaches that of the 'dilution' model; in particular, alpha particles are expected to have little, if any, stabilizing effect on plasma turbulence. We support these conclusions through detailed linear and nonlinear gyrokinetic simulations.
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| 2. |
- Wilkie, George, 1983, et al.
(författare)
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Fundamental physics of the fast ion stabilization of electromagnetic ITG turbulence
- 2017
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Ingår i: 44th EPS Conference on Plasma Physics, EPS 2017.
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Konferensbidrag (refereegranskat)abstract
- In recent years, it has been observed that both electromagnetic effects and fast particle populations suppress transport from ITG turbulence. This effect was discovered via detailed numerical simulations of JET discharges. Further work has investigated these effects in the context of experimental scenarios, but the underlying physics remains somewhat unresolved. However, in pursuit of increased performance, experiments will continue to push to ever-higher beta. Similarly, burning plasmas will always have self-generated fast ion populations. Thus, understanding the physics behind this suppression is key to projecting its importance for future devices. Our analysis of the physical mechanisms comprises two parts: a study of the linear physics, and targeted nonlinear simulations. Firstly, an in-depth study of the linear physics is performed to disentangle the competing effects upon the ITG mode. These effects include dilution of the main ions by fast ions, changes to the magnetic equilibrium, and changes to the pressure gradients in the plasma. To clarify these results we derive a simplified dispersion relation for electromagnetic ITG including a fast ion population, and use it to demonstrate which parameters dominate the linear physics. Guided by our linear results, we use nonlinear simulations to examine the structure of the turbulence when stabilized by fast ions. Through this study, we show which effects lead to a reduction of stiffness, and why. We also explore which effects lead to changes in the nonlinear upshift of the critical temperature gradient. We enumerate which of these physical mechanisms contribute to the experimentally-observed reduction in heat flux. Given this physical understanding, we identify which class of fast ions contribute most beneficially to this reduction and the conditions under which the electromagnetic stabilization is most effective. We conclude by extrapolating these results towards ITER and DEMO.
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| 3. |
- Abel, Ian, 1985, et al.
(författare)
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Multiscale modelling for tokamak pedestals
- 2018
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 84:2
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Tidskriftsartikel (refereegranskat)abstract
- Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of edge localised modes (ELMs), the inter-ELM pedestal and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other is covered in detail. This framework is completely self-consistent; it is derived from first principles by means of an asymptotic expansion of the fundamental Vlasov-Landau-Maxwell system in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius and the low plasma beta (the ratio of thermal to magnetic pressures) typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match our systems of equations onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is briefly discussed.
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| 4. |
- Kunz, M. W., et al.
(författare)
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Astrophysical gyrokinetics: turbulence in pressure-anisotropic plasmas at ion scales and beyond
- 2018
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 84:2
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Tidskriftsartikel (refereegranskat)abstract
- We present a theoretical framework for describing electromagnetic kinetic turbulence in a multi-species, magnetized, pressure-anisotropic plasma. The turbulent fluctuations are assumed to be small compared to the mean field, to be spatially anisotropic with respect to it and to have frequencies small compared to the ion cyclotron frequency. At scales above the ion-Larmor radius, the theory reduces to the pressure-anisotropic generalization of kinetic reduced magnetohydrodynamics (KRMHD) formulated by Kunz et al. (J. Plasma Phys., vol. 81, 2015, 325810501). At scales at and below the ion-Larmor radius, three main objectives are achieved. First, we analyse the linear response of the pressure-anisotropic gyrokinetic system, and show it to be a generalization of previously explored limits. The effects of pressure anisotropy on the stability and collisionless damping of Alfvenic and compressive fluctuations are highlighted, with attention paid to the spectral location and width of the frequency jump that occurs as Alfven waves transition into kinetic Alfven waves. Secondly, we derive and discuss a very general gyrokinetic free-energy conservation law, which captures both the KRMHD free-energy conservation at long wavelengths and dual cascades of kinetic Alfven waves and ion entropy at sub-ion-Larmor scales. We show that non-Maxwellian features in the distribution function change the amount of phase mixing and the efficiency of magnetic stresses, and thus influence the partitioning of free energy amongst the cascade channels. Thirdly, a simple model is used to show that pressure anisotropy, even within the bounds imposed on it by firehose and mirror instabilities, can cause order-of-magnitude variations in the ion-to-electron heating ratio due to the dissipation of Alfvenic turbulence. Our theory provides a foundation for determining how pressure anisotropy affects turbulent fluctuation spectra, the differential heating of particle species and the ratio of parallel and perpendicular phase mixing in space and astrophysical plasmas.
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| 5. |
- Paul, Elizabeth J., et al.
(författare)
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An adjoint method for neoclassical stellarator optimization
- 2019
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 85:5
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Tidskriftsartikel (refereegranskat)abstract
- Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often necessitating the use of gradient-based methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring O(N) flux computations, where N is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finite-collisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large (O(10(2))), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjoint-based optimization of the field strength to obtain minimal bootstrap current on a surface. With adjoint-based derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Furthermore, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.
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| 6. |
- Wilkie, George, 1983, et al.
(författare)
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Global anomalous transport of ICRH and NBI-heated fast ions
- 2017
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Ingår i: Plasma Physics and Controlled Fusion. - : IOP Publishing. - 1361-6587 .- 0741-3335. ; 59:4, s. 044007-
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Tidskriftsartikel (refereegranskat)abstract
- By taking advantage of the trace approximation, one can gain an enormous computational advantage when solving for the global turbulent transport of impurities.In particular, this makes feasible the study of non-Maxwellian transport coupled in radius and energy, allowing collisions and transport to be accounted for on similar time scales, as occurs for fast ions. In this work, we study the fully-nonlinear ITG-driven trace turbulent transport of locally heated and injected fast ions. Previousresults indicated the existence of MeV-range minorities heated by cyclotron resonance,and an associated density pinch e ect. Here, we build upon this result using the t3core code to solve for the distribution of these minorities, consistently including the e ects of collisions, gyrokinetic turbulence, and heating. Using the same tool to study the transport of injected fast ions, we contrast the qualitative features of their transport with that of the heated minorities. Furthermore, we move beyond the trace approximation to develop a model which allows one to easily account for the reduction of anomalous transport due to the presence of fast ions in electrostatic turbulence.
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| 7. |
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| 8. |
- Wilkie, George, 1983, et al.
(författare)
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Validating modeling assumptions of alpha particles in electrostatic turbulence
- 2015
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Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 81:3
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Tidskriftsartikel (refereegranskat)abstract
- To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In this work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian, while previously shown to give an adequate order-of-magnitude estimate of the diffusion coefficient, gives incorrect estimates for the radial alpha particle flux, and a method of correcting it in general is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution.
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