M. Kotschenreuther

Comparisons and physics basis of tokamak transport models and turbulence simulations

The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient (ITG) instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transport models, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the mo...

Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities

In plasma physics, linear instability calculations can be implemented either as initial value calculations or as eigenvalue calculations. Here, comparisons between comprehensive linear gyrokinetic calculations employing the ballooning formalism for high-n (toroidal mode number) toroidal instabilities are described. One code implements an initial value calculation on a grid using a Lorentz collision operator and the other implements an eigenvalue calculation with basis functions using a Krook collision operator. An electrostatic test case with artificial parameters for the toroidal drift mode destabilized by the combined effects of trapped particles and an ion temperature gradient has been carefully analyzed both in the collisionless limit and with varying collisionality. Good agreement is found. Results from applied studies using parameters from the Tokamak Fusion Test Reactor (TFTR) experiment are also compared.

On the exploration of innovative concepts for fusion chamber technology

Abstract This study, called APEX, is exploring novel concepts for fusion chamber technology that can substantially improve the attractiveness of fusion energy systems. The emphasis of the study is on fundamental understanding and advancing the underlying engineering sciences, integration of the physics and engineering requirements, and enhancing innovation for the chamber technology components surrounding the plasma. The chamber technology goals in APEX include: (1) high power density capability with neutron wall load >10 MW/m 2 and surface heat flux >2 MW/m 2 , (2) high power conversion efficiency (>40%), (3) high availability, and (4) simple technological and material constraints. Two classes of innovative concepts have emerged that offer great promise and deserve further research and development. The first class seeks to eliminate the solid “bare” first wall by flowing liquids facing the plasma. This liquid wall idea evolved during the APEX study into a number of concepts based on: (a) using liquid metals (Li or Sn–Li) or a molten salt (Flibe) as the working liquid, (b) utilizing electromagnetic, inertial and/or other types of forces to restrain the liquid against a backing wall and control the hydrodynamic flow configurations, and (c) employing a thin (∼2 cm) or thick (∼40 cm) liquid layer to remove the surface heat flux and attenuate the neutrons. These liquid wall concepts have some common features but also have widely different issues and merits. Some of the attractive features of liquid walls include the potential for: (1) high power density capability; (2) higher plasma β and stable physics regimes if liquid metals are used; (3) increased disruption survivability; (4) reduced volume of radioactive waste; (5) reduced radiation damage in structural materials; and (6) higher availability. Analyses show that not all of these potential advantages may be realized simultaneously in a single concept. However, the realization of only a subset of these advantages will result in remarkable progress toward attractive fusion energy systems. Of the many scientific and engineering issues for liquid walls, the most important are: (1) plasma–liquid interactions including both plasma–liquid surface and liquid wall–bulk plasma interactions; (2) hydrodynamic flow configuration control in complex geometries including penetrations; and (3) heat transfer at free surface and temperature control. The second class of concepts focuses on ideas for extending the capabilities, particularly the power density and operating temperature limits, of solid first walls. The most promising idea, called EVOLVE, is based on the use of a high-temperature refractory alloy (e.g. W–5% Re) with an innovative cooling scheme based on the use of the heat of vaporization of lithium. Calculations show that an evaporative system with Li at ∼1 200°C can remove the goal heat loads and result in a high power conversion efficiency. The vapor operating pressure is low, resulting in a very low operating stress in the structure. In addition, the lithium flow rate is about a factor of ten lower than that required for traditional self-cooled first wall/blanket concepts. Therefore, insulator coatings are not required. Key issues for EVOLVE include: (1) two-phase heat transfer and transport including MHD effects; (2) feasibility of fabricating entire blanket segments of W alloys; and (3) the effect of neutron irradiation on W.

Quantitative predictions of tokamak energy confinement from first-principles simulations with kinetic effects

A first‐principles model of anomalous thermal transport based on numerical simulations is presented, with stringent comparisons to experimental data from the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. This model is based on nonlinear gyrofluid simulations, which predict the fluctuation and thermal transport characteristics of toroidal ion‐temperature‐gradient‐driven (ITG) turbulence, and on comprehensive linear gyrokinetic ballooning calculations, which provide very accurate growth rates, critical temperature gradients, and a quasilinear estimate of χe/χi. The model is derived solely from the simulation results. More than 70 TFTR low confinement (L‐mode) discharges have been simulated with quantitative success. Typically, the ion and electron temperature profiles are predicted within the error bars, and the global energy confinement time within ±10%. The measured temperatures at r/a≂0.8 are used as a boundary condition to predict the temperature profiles in the main confinement ...

Super-X divertors and high power density fusion devices

The Super-X Divertor (SXD), a robust axisymmetric redesign of the divertor magnetic geometry that can allow a fivefold increase in the core power density of toroidal fusion devices, is presented. With small changes in poloidal coils and currents for standard divertors, the SXD allows the largest divertor plate radius inside toroidal field coils. This increases the plasma-wetted area by 2–3 times over all flux-expansion-only methods (e.g., plate near main X point, plate tilting, X divertor, and snowflake), decreases parallel heat flux and hence plasma temperature at plate, and increases connection length by 2–5 times. Examples of high-power-density fusion devices enabled by SXD are discussed; the most promising near-term device is a 100 MW modular compact fusion neutron source “battery” small enough to fit inside a conventional fission blanket.

On heat loading, novel divertors, and fusion reactors

The limited thermal power handling capacity of the standard divertors (used in current as well as projected tokamaks) is likely to force extremely high (∼90%) radiation fractions frad in tokamak fusion reactors that have heating powers considerably larger than ITER [D. J. Campbell, Phys. Plasmas 8, 2041 (2001)]. Such enormous values of necessary frad could have serious and debilitating consequences on the core confinement, stability, and dependability for a fusion power reactor, especially in reactors with Internal Transport Barriers. A new class of divertors, called X-divertors (XD), which considerably enhance the divertor thermal capacity through a flaring of the field lines only near the divertor plates, may be necessary and sufficient to overcome these problems and lead to a dependable fusion power reactor with acceptable economics. X-divertors will lower the bar on the necessary confinement to bring it in the range of the present experimental results. Its ability to reduce the radiative burden impart...

Electron thermal confinement studies with applied resonant fields on TEXT

Externally applied magnetic fields are used on the Texas Experimental Tokamak (TEXT) to study the possibility of controlling the particle, impurity and heat fluxes at the plasma edge. Fields with toroidal mode number n = 2 or 3 and multiple poloidal mode numbers m (dominantly m = 7) are used, with a poloidally and toroidally averaged ratio of radial to toroidal field components 〈|br/Bo〉 ≅0. 1%. Calculations show that it is possible to produce mixed islands and stochastic regions at the plasma edge (r/a ≥ 0.8) without affecting the interior. The expected magnetic field structure is described and experimental evidence of the existence of this structure is presented. The edge electron temperature decreases with increasing 〈|br/Bo〉, while interior values are not significantly affected. The implied increase in edge electron thermal diffusivity is compared with theoretical expectations and is shown to agree with applicable theories to within a factor of three.

Particle transport studies with applied resonant fields on TEXT

Externally applied resonant magnetic fields have been used on TEXT to modify the particle flux and the radial electric field near the plasma edge. Magnetic fields with primary mode numbers m/n = 7/3 and 7/2, and an average radial field amplitude |br|/B ? 0.1% have been employed. This perturbation produces mixed islands and stochastic regions at the plasma edge (r/a ? 0.8) without affecting the interior. Working particle transport is shown to be increased by typically 30% only in the presence of (computed) magnetic islands. The effect is diminished at high perturbing field strength when the islands become stochastic. A novel transport mechanism due to ? convection is proposed to explain this. Outward impurity transport is increased as well.

Stabilizing impact of high gradient of β on microturbulence

It is shown here that microturbulence can be stabilized in the presence of steep temperature and density profiles. Indeed in high β plasmas, pressure profile gradients are associated with high |β′|=−∂β/∂ρ, where β=P/(B2/2μ0) and ρ the square root of the toroidal flux normalized to its edge value. It is shown here that high values of |β′| have a stabilizing influence on drift modes. This may form the basis for a positive feedback loop in which high core beta values lead to improved confinement, and to further increase in β. A gyrokinetic electromagnetic flux tube code, GS2 [M. Kotschenreuther, G. Rewoldt, and W. M. Tang, Comput. Phys. Commun. 88, 128 (1995)], is used for analyzing the microstability. In high β spherical tokamak plasmas, high |β′| rather than low aspect ratio is a source of stabilization. Therefore, the effect of high |β′| should be stabilizing in the plasmas of the National Spherical Torus Experiment [Y.-K. Peng, M. G. Bell, R. E. Bell et al., Phys. Plasmas 7, 1681 (2000)].

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes.