J. Candy

Kinetic calculation of neoclassical transport including self-consistent electron and impurity dynamics

Numerical studies of neoclassical transport, beginning with the fundamental drift-kinetic equation (DKE), have been extended to include the self-consistent coupling of electrons and multiple ion species. The code, NEO, provides a first-principles based calculation of the neoclassical transport coefficients directly from solution of the distribution function by solving a hierarchy of equations derived by expanding the DKE in powers of ρ*i, the ratio of the ion gyroradius to system size. This includes the calculation of the first-order electrostatic potential via the Poisson equation, although this potential has exactly no effect on the steady-state transport. Systematic calculations of the second-order particle and energy fluxes and first-order plasma flows and bootstrap current and comparisons with existing theories are given for multi-species plasmas. The ambipolar relation ∑azaΓa = 0, which can only be maintained with complete cross-species collisional coupling, is confirmed, and finite mass-ratio corrections due to the collisional coupling are identified. The effects of plasma shaping are also explored, including a discussion of how analytic formulae obtained for circular plasmas (i.e. Chang–Hinton) should be applied to shaped cases. Finite-orbit-width effects are studied via solution of the higher-order DKEs and the implications of non-local transport on the validity of the δf formulation are discussed.

Implementation and application of two synthetic diagnostics for validating simulations of core tokamak turbulence

The deployment of multiple high-resolution, spatially localized fluctuation diagnostics on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] opens the door to a new level of core turbulence model validation. Toward this end, the implementation of synthetic diagnostics that model physical beam emission spectroscopy and correlation electron cyclotron emission diagnostics is presented. Initial results from their applications to local gyrokinetic simulations of two locations in a DIII-D L-mode discharge performed with the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are also discussed. At normalized toroidal flux ρ=0.5, we find very good agreement between experiment and simulation in both the energy flows and fluctuation levels measured by both diagnostics. However, at ρ=0.75, GYRO underpredicts the observed energy flows by roughly a factor of 7, with rms fluctuation levels underpredicted by a factor of 3. Interestingly, at both locations we find good agreement in the sha...

Measurements of core electron temperature and density fluctuations in DIII-D and comparison to nonlinear gyrokinetic simulations

For the first time, profiles (0.3<ρ<0.9) of electron temperature and density fluctuations in a tokamak have been measured simultaneously and the results compared to nonlinear gyrokinetic simulations. Electron temperature and density fluctuations measured in neutral beam-heated, sawtooth-free low confinement mode (L-mode) plasmas in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] are found to be similar in frequency and normalized amplitude, with amplitude increasing with radius. The measured radial profile of two fluctuation fields allows for a new and rigorous comparison with gyrokinetic results. Nonlinear gyrokinetic flux-tube simulations predict that electron temperature and density fluctuations have similar normalized amplitudes in L-mode. At ρ=0.5, simulation results match experimental heat diffusivities and density fluctuation amplitude, but overestimate electron temperature fluctuation amplitude and particle diffusivity. In contrast, simulations at ρ=0.75 do not match either the experimentally de...

Gyrokinetic simulations of ion and impurity transport

A systematic study of turbulent particle and energy transport in both pure and multicomponent plasmas is presented. In this study, gyrokinetic results from the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] are supplemented with those from the GLF23 [R. E. Waltz, G. M. Staebler, W. Dorland et al., Phys. Plasmas 4, 2482 (1997)] transport model, as well as from quasilinear theory. Various results are obtained. The production of a particle pinch driven by temperature gradients (a thermal pinch) is demonstrated, and further shown to be weakened by finite electron collisionality. Helium transport and the effects of helium density gradient and concentration in a deuterium plasma are examined. Interestingly, it is found that the simple D-v (diffusion versus convective velocity) model of impurity flow is consistent with results obtained from nonlinear gyrokinetic simulations. Also studied is the transport in a 50-50 deuterium-tritium plasma, where a symmetry breaking is observed indicating...

Beta scaling of transport in microturbulence simulations

A systematic study of the beta (β) scaling and spatial structure of thermal and particle transport in gyrokinetic turbulence simulations is presented. Here, β is the ratio of the plasma kinetic pressure to the magnetic pressure. Results show that the nonlinear self-consistent temperature profiles exhibit a (statistically) time-stationary flattening in the vicinity of rational surfaces with a concomitant drop in the electrostatic components of the thermal diffusivity. Simultaneously, the increased magnetic fluctuation amplitude at these surfaces enhances the steady-state electromagnetic (flutter) component of the electron thermal diffusivity. The electromagnetic components of the ion transport coefficients remain close to zero, as expected on theoretical grounds. Only a weak dependence of ion energy transport on β is observed, consistent with recent tokamak experiments [C. C. Petty et al., Phys. Plasmas 11, 2514 (2004)].A systematic study of the beta (β) scaling and spatial structure of thermal and particle transport in gyrokinetic turbulence simulations is presented. Here, β is the ratio of the plasma kinetic pressure to the magnetic pressure. Results show that the nonlinear self-consistent temperature profiles exhibit a (statistically) time-stationary flattening in the vicinity of rational surfaces with a concomitant drop in the electrostatic components of the thermal diffusivity. Simultaneously, the increased magnetic fluctuation amplitude at these surfaces enhances the steady-state electromagnetic (flutter) component of the electron thermal diffusivity. The electromagnetic components of the ion transport coefficients remain close to zero, as expected on theoretical grounds. Only a weak dependence of ion energy transport on β is observed, consistent with recent tokamak experiments [C. C. Petty et al., Phys. Plasmas 11, 2514 (2004)].

Coupled ion temperature gradient and trapped electron mode to electron temperature gradient mode gyrokinetic simulations

Electron temperature gradient (ETG) transport is conventionally defined as the electron energy transport at high wave number (high-k) where ions are adiabatic and there can be no ion energy or plasma transport. Previous gyrokinetic simulations have assumed adiabatic ions (ETG-ai) and work on the small electron gyroradius scale. However such ETG-ai simulations with trapped electrons often do not have well behaved nonlinear saturation unless fully kinetic ions (ki) and proper ion scale zonal flow modes are included. Electron energy transport is separated into ETG-ki at high-k and ion temperature gradient-trapped electron mode (ITG/TEM) at low-k. Expensive (more computer-intensive), high-resolution, large-ion-scale flux-tube simulations coupling ITG/TEM and ETG-ki turbulence are presented. These require a high effective Reynolds number R≡[k(max)∕k(min)]2=μ2, where μ=[ρsi∕ρsi] is the ratio of ion to electron gyroradii. Compute times scale faster than μ3. By comparing the coupled expensive simulations with (1)...

ITER predictions using the GYRO verified and experimentally validated trapped gyro-Landau fluid transport model

The trapped gyro-Landau fluid (TGLF) transport model computes the quasilinear particle and energy driftwave fluxes in tokamaks with shaped geometry, finite aspect ratio and collisions. The TGLF particle and energy fluxes have been successfully verified against a large database of collisionless nonlinear gyrokinetic simulations using the GYRO code. Using a new collision model in TGLF, we find remarkable agreement between the TGLF quasilinear fluxes and 64 new GYRO nonlinear simulations with electron–ion collisions. In validating TGLF against DIII-D and JET H-mode and hybrid discharges we find the temperature and density profiles are in excellent agreement with the measured profiles. ITER projections using TGLF show that the fusion gains are somewhat more pessimistic than the previous GLF23 results primarily due to finite aspect ratio effects included only in TGLF. The synergistic effects of density peaking, finite β and E × B shear due to finite toroidal rotation lead to significant increases in fusion power above a reduced physics ITER base case. The TGLF results for ITER are confirmed using nonlinear GYRO simulations in place of TGLF to predict the temperature profiles within the TGYRO transport code. These results represent a snapshot of the ongoing effort to improve the TGLF model, validate it against experimental data, and make predictions for ITER.

L-mode validation studies of gyrokinetic turbulence simulations via multiscale and multifield turbulence measurements on the DIII-D tokamak

A series of carefully designed experiments on DIII-D have taken advantage of a broad set of turbulence and profile diagnostics to rigorously test gyrokinetic turbulence simulations. In this paper the goals, tools and experiments performed in these validation studies are reviewed and specific examples presented. It is found that predictions of transport and fluctuation levels in the mid-core region (0.4 < ρ < 0.75) are in better agreement with experiment than those in the outer region (ρ ≥ 0.75) where edge coupling effects may become increasingly important and multiscale simulations may also be necessary. Validation studies such as these are crucial in developing confidence in a first-principles based predictive capability for ITER.

Gyrokinetic theory and simulation of angular momentum transport

A gyrokinetic theory of turbulent toroidal angular momentum transport as well as modifications to neoclassical poloidal rotation from turbulence is formulated starting from the fundamental six-dimensional kinetic equation. The gyro-Bohm scaled transport is evaluated from toroidal delta-f gyrokinetic simulations using the GYRO code [Candy and Waltz, J. Comput. Phys. 186, 545 (2003)]. The simulations recover two pinch mechanisms in the radial transport of toroidal angular momentum: The slab geometry E×B shear pinch [Dominguez and Staebler, Phys. Fluids B 5, 387 (1993)] and the toroidal geometry “Coriolis” pinch [Peeters, Angioni, and Strintzi, Phys. Rev. Lett. 98, 265003 (2007)]. The pinches allow the steady state null stress (or angular momentum transport flow) condition required to understand intrinsic (or spontaneous) toroidal rotation in heated tokamak without an internal source of torque [Staebler, Kinsey, and Waltz, Bull. Am. Phys. Soc. 46, 221 (2001)]. A predicted turbulent shift in the neoclassical ...

Gyrokinetic turbulence simulation of profile shear stabilization and broken gyroBohm scaling

A newly developed continuum gyrokinetic code GYRO has been formulated on a radial grid to operate at finite relative gyroradius in a noncyclic radial annulus with profile variation. The code is used to simulate ion temperature gradient mode turbulence and to demonstrate that gyroBohm scaling can be obtained well above the instability threshold but sufficiently strong profile shear stabilization can break gyroBohm scaling down to Bohm scaling (or worse) near threshold. An adaptive source technique is used to maintain profiles. Clear evidence for nonlocal transport is also found in which the local diffusivity depends on the plasma gradients at some considerable radial distance.