W. M. Nevins

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...

Transport by intermittency in the boundary of the DIII-D tokamak

A271 TRANSPORT BY INTERMITTENCY IN THE BOUNDARY OF THE DIII-D TOKAMAK. Intermittent plasma objectives (IPOs) featuring higher pressure than the surrounding plasma, are responsible for {approx} 50% of the E x B{sub T} radial transport in the scrape off layer (SOL) of the DIII-D tokamak in L- and H-mode discharges. Conditional averaging reveals that the IPOs are positively charged and feature internal poloidal electric fields of up to 4000 V/m. The IPOs move radially with E x B{sub T}/B{sup 2} velocities of {approx} 2600 m/s near the last closed flux surface (LCFS), and {approx} 330 m/s near the wall. The IPOs slow down as they shrink in radial size from 4 cm at the LCFS to 0.5 cm near the wall. The skewness (i.e. asymmetry of fluctuations from the average) of probe and beam emission spectroscopy (BES) data indicate IPO formation at or near the LCFS and the existence of positive and negative IPOs which move in opposite directions. The particle content of the IPOs at the LCFS is linearly dependent on the local density and decays over {approx} 3 cm into the SOL while their temperature decays much faster ({approx} 1 cm).

Can inertial electrostatic confinement work beyond the ion–ion collisional time scale?

Inertial electrostatic confinement (IEC) systems are predicated on a nonequilibrium ion distribution function. Coulomb collisions between ions cause this distribution to relax to a Maxwellian on the ion–ion collisional time scale. The power required to prevent this relaxation and maintain the IEC configuration for times beyond the ion–ion collisional time scale is shown to be greater than the fusion power produced. It is concluded that IEC systems show little promise as a basis for the development of commercial electric power plants.

Validation in fusion research : Towards guidelines and best practices

Because experiment/model comparisons in magnetic confinement fusion have not yet satisfied the requirements for validation as understood broadly, approaches to validating mathematical models and numerical algorithms are recommended as good practices. Previously identified procedures, such as, verification, qualification, and analysis of errors from uncertainties and deficiencies, remain important. However, particular challenges intrinsic to fusion plasmas and physical measurement therein lead to identification of new or less familiar concepts that are also critical in validation. These include the primacy hierarchy, which tracks the integration of measurable quantities, and sensitivity analysis, which assesses how model output is apportioned to different sources of variation. The use of validation metrics for individual measurements is extended to multiple measurements, with provisions for the primacy hierarchy and sensitivity. This composite validation metric is essential for quantitatively evaluating comparisons with experiments. To mount successful and credible validation in magnetic fusion, a new culture of validation is envisaged.

Discrete Particle Noise in Particle-in-Cell Simulations of Plasma Microturbulence

Recent gyrokinetic simulations of electron temperature gradient (ETG) turbulence with flux-tube continuum codes vs. the global particle-in-cell (PIC) code GTC yielded different results despite similar plasma parameters. Differences between the simulations results were attributed to insufficient phase-space resolution and novel physics associated with toroidicity and/or global simulations. We have reproduced the results of the global PIC code using the flux-tube PIC code PG3EQ, thereby eliminating global effects as the cause of the discrepancy. We show that the late-time decay of ETG turbulence and the steady-state heat transport observed in these PIC simulations results from discrete particle noise. Discrete particle noise is a numerical artifact, so both these PG3EQ simulations and the previous GTC simulations have nothing to say about steady-state ETG turbulence and the associated anomalous heat transport. In the course of this work we develop three diagnostics which can help to determine if a particular PIC simulation has become dominated by discrete particle noise.

The thermonuclear fusion rate coefficient for p-11B reactions

Analytic approximations to the p-11B fusion rate coefficient suitable for use at both low (1 keV ≤ T ≤ 70 keV) and high (50 keV ≤ T ≤ 500 keV) temperatures are developed. Comparisons between these analytic approximations and calculations of the p-11B fusion rate coefficient based on numerical integration indicate that the overall error in these approximations is dominated by errors in the experimental measurement of the underlying p-11B fusion cross-sections.

New Stokes’ line in WKB theory

The WKB theory for differential equations of arbitrary order or integral equations in one dimension is investigated. The rules previously stated for the construction of Stokes’ lines for Nth‐order differential equations, N⩾3, or integral equations are found to be incomplete because these rules lead to asymptotic forms of the solutions that depend on path. This paradox is resolved by the demonstration that new Stokes’ lines can arise when previously defined Stokes’ lines cross. A new formulation of the WKB problem is given to justify the new Stokes’ lines. With the new Stokes’ lines, the asymptotic forms can be shown to be independent of path. In addition, the WKB eigenvalue problem is formulated, and the global dispersion relation is shown to be a functional of loop integrals of the action.

Simulation of microtearing turbulence in national spherical torus experimenta)

Thermal energy confinement times in National Spherical Torus Experiment (NSTX) dimensionless parameter scans increase with decreasing collisionality. While ion thermal transport is neoclassical, the source of anomalous electron thermal transport in these discharges remains unclear, leading to considerable uncertainty when extrapolating to future spherical tokamak (ST) devices at much lower collisionality. Linear gyrokinetic simulations find microtearing modes to be unstable in high collisionality discharges. First non-linear gyrokinetic simulations of microtearing turbulence in NSTX show they can yield experimental levels of transport. Magnetic flutter is responsible for almost all the transport (∼98%), perturbed field line trajectories are globally stochastic, and a test particle stochastic transport model agrees to within 25% of the simulated transport. Most significantly, microtearing transport is predicted to increase with electron collisionality, consistent with the observed NSTX confinement scaling....

Electromagnetic Gyrokinetic Simulations

A new electromagnetic kinetic electron δf particle simulation model has been demonstrated to work well at large values of plasma β times the ion-to-electron mass ratio [Y. Chen and S. E. Parker, J. Comput. Phys. 198, 463 (2003)]. The simulation is three-dimensional using toroidal flux-tube geometry and includes electron-ion collisions. The model shows accurate shear Alfven wave damping and microtearing physics. Zonal flows with kinetic electrons are found to be turbulent with the spectrum peaking at zero and having a width in the frequency range of the driving turbulence. This is in contrast with adiabatic electron cases where the zonal flows are near stationary, even though the linear behavior of the zonal flow is not significantly affected by kinetic electrons. Zonal fields are found to be very weak, consistent with theoretical predictions for β below the kinetic ballooning limit. Detailed spectral analysis of the turbulence data is presented in the various limits.

Transitions of turbulence in plasma density limits

A series of BOUT [X. Q. Xu et al., Phys. Plasmas 7, 1951 (2000)] simulations is conducted to investigate the physical processes which limit the density in tokamak plasmas. Simulations of turbulence in tokamak boundary plasmas are presented which show that turbulent fluctuation levels and transport increase with collisionality. At high edge density, the perpendicular turbulent transport dominates the parallel classical transport, leading to substantially reduced contact with divertor plates and the destruction of the edge shear layer, and the region of high transport then extends inside the last closed flux surface. As the density increases these simulations show resistive X-point mode→resistive ballooning modes. The simulations also show that it is easier to reach the density limit as the density increases while holding pressure constant than holding temperature constant. A set of 2D transport simulations with increasingly large radial outboard transport, as indicated by BOUT for increasing density, shows...