Theory Weekly Highlights for January through June 2002
Highlights for June 2002
A semi-implicit operator splitting has been developed to treat collisions in the electromagnetic version of the GYRO code. Recently (as reported at the recent Sherwood Theory Meeting in Rochester), collisionless GYRO simulations of DIII-D L-mode discharges reproduced the experimental rho_star scaling, but overestimated the absolute value of transport by about a factor of 2.7. New collisional simulations reduce this overshoot to only 1.7. This is the first time a comprehensive gyrokinetic simulation has been matched so closely with experimental data. This is a milestone for gyrokinetic research.
Highlights for May 2002
A shared visualization demonstration was performed for the DIII-D Experimental Team using tiled display walls at General Atomics and the Argonne National Laboratory. The demonstration included simultaneous viewing of a simple IDL visualization program (ReviewPlus) and a complex 3D program (SciRUN) based on OpenGL. The shared visualization capability was well received both for use in the DIII-D control room and in smaller working meetings. Work will continue to develop this technology for beta testing deployment with the DIII-D team.
Modifications to the GA ideal MHD stability code GATO were made to enable reading of equilibria from the PPPL inverse equilibrium code JSOLVER. This will now enable the GATO code to directly evaluate the stability of the FIRE and IGNITOR equilibria being analyzed in preparation for SNOWMASS. Previously, this evaluation required recalculation of the equilibria from either the TOQ or EFIT code.
A detailed benchmark of calculated MHD growth rates and mode structures between the GATO ideal MHD stability code and the recently developed ELITE MHD stability code found excellent agreement for two equilibria, one with a high edge pedestal that is strongly unstable to ballooning-like modes over a broad range of n, and one that is unstable to edge localized external peeling modes driven by the edge current density. The agreement in the calculated growth rates is within 3% over the entire region of overlap in toroidal mode numbers n=4,5,6,7,8,9. Also, comparison of the calculated eigenmodes for n=8 finds them to be virtually identical. This benchmark is an important test since the GATO and ELITE codes employ very different formulations. GATO is a well established, global finite element code designed to study low to intermediate n modes, whereas ELITE directly solves the Euler equations for the Fourier mode amplitudes, including an expansion through two orders in 1/n, allowing for efficient study of intermediate to high n (n>~5) modes localized in the outer regions of the plasma.
In the well-known work of Glasser, Green and Johnson, Phys. Fluids 18, 875 (1975), the existence of overstable modes or "modified tearing modes" in tokamak discharges is posed as a possibility, but these modes have not yet been shown to exist in experiments. In recent NIMROD analyses of DIII-D discharge 98549, high-m modes localized near the X-points and edge show a linear growth rate that oscillates in time with a constant frequency - a trademark of overstable modes. A detailed analysis of diamagnetic stabilization effects on these modes is ongoing which is expected to answer why these modes are not observed in the experiment.
The time dependent and time independent finite difference forms of the coupled set of transport equations in Onetwo were recently both rewritten to account for the application of boundary conditions at arbitrary values of the minor radius (normalized flux). In particular, in simulation mode, each equation can now have an independent boundary specified as a function of time. This not only allows studies of the effects of various boundary conditions but it also makes possible the L to H transition modeling with GLF23 and provides for a flexible core/edge coupling methodology.
Highlights for April 2002
Feedback stabilization of the RWM using poloidal and radial field sensors was studied in DIII-D geometry using the normal mode formulation. Poloidal field sensing is found to be much more effective than radial field sensing. The study found that, with poloidal field sensing, a single central band of external feedback coils is sufficient for stabilization of RWMs with growth rates up to 30 times as fast as the rate of flux diffusion through the resistive wall.
Two invited talks were given at the 2002 International Sherwood Theory Meeting in Rochester, NY by Theory Group staff. The talk by Jeff Candy "GYRO Modeling of Anomalous Transport in Tokamaks", described the recent progress with the GYRO code. Jon Kinsey presented the recent work on "Renormalization of the GLF23 Transport Model and Burning Plasma Projections on a Universal Curve of Q versus Tped". In addition, Andrea Garofalo gave an invited talk on theory/experiment comparisons entitled "MHD Stability in a Tokamak Above the Free Boundary Pressure Limit", which described the recent DIII-D wall stabilization results.
One of the most computationally intensive problems in transport analysis is the generation of fully evolved equilibrium states because of the long simulation times required to relax the toroidal electric field to a steady state. A new solution method that allows us to determine the steady state directly has now been added to the ONETWO transport code. Previously, with stiff confinement models (such as GLF23), the standard approach of evolving the system until a steady state is achieved was extremely time consuming since the time steps need to be sufficiently small to avoid artificial bifurcations in the profiles. The new approach uses globally convergent variations of the Newton method to solve the nonlinear finite difference form of the time independent transport equations directly. In favorable circumstances, the required computation time is reduced from about 30 hours to about 15 min. This allows the mapping out of steady state AT modeling scenarios for DIII-D and ITER-FEAT using stiff confinement models to be achieved much more reasonably.
The mapping of the last closed flux surface in GATO was rewritten to eliminate the most common failure mode. The new mapping routine now detects for multiple branches of the flux value being contoured exiting from each grid cell and attempts to choose the correct branch of the flux surface to continue to trace. If the mapping fails to find a branch that leads to a closed surface, the code now automatically repeats the mapping of the boundary, continually increasing the decrement in flux inside the input last closed flux value, until it successfully maps a closed flux surface. The new mapping will be released publicly after complete testing with the standard suite of benchmarks and is expected to greatly enhance the robustness of the GATO code.
Using NIMROD simulations of DIII-D discharge #86166 with accurate kinetic equilibrium fits between sawteeth as initial conditions, 1/1 modes were found to nonlinearly drive an unstable 3/2 mode, in agreement with experimental observations. For this sawtoothing discharge, the axis pressure increases over several neutral beam slowing down times. The NIMROD simulations are also in agreement with PEST-III delta-prime calculations for the same equilibrium sequence, where delta-prime at the 3/2 surface was found to increase during the sequence, and also with experimental observations of a decrease in the decay rates of the earlier 3/2 modes seeded by each sawtooth; according to the modified Rutherford model, the increase in delta-prime reduces the neoclassical threshold for the sawtooth-generated seed islands and decreases the island decay rates below that threshold size. Issues still being addressed are, does the nonlinear saturated island size correlate with the computed linear delta-prime and, is a reduced neoclassical threshold and a reduced decay rate for the 3/2 mode from the larger delta-prime, observed computationally. To answer these, differences in the evolution of the 3/2 mode from an early time between sawteeth, which did not trigger a 3/2 NTM in the experiment, and a later time with slightly higher core pressure and delta-prime, which does trigger a 3/2 NTM, are being analyzed.
Highlights for March 2002
The theory of Greene, Johnson and Weimer for tokamak equilibria has been extended to include equilibria with a central current hole region. The current hole region is shown to be connected with the external region with a regular equilibrium profile through a contact singularity, where the magnetic field is continuous, with the possibility of a discontinuous current density distribution, but no singular currents. However, equilibria with a negative current density region between the current hole and an external positive current region have been shown to not exist in general. These conclusions are consistent with the observation of current holes in tokamaks and the fact that negative currents have never been observed to develop in the current holes.
The GYRO global gyrokinetic code has reached maturity after three years of development. Since December 2001, the code has been used to simulate the transport power flow for specific L-mode DIII-D core plasmas profiles with a high degree of physical reality: ITG and trapped-passing electrons at finite beta in real geometry. The ExB and general profile shear cause significant reduction in transport as expected. The simulated power flows are rather close to the experimental flows in the one case we have studied. We simulate both electron and ion energy as well as plasma diffusivity, and recently we have added simulation of toroidial viscosity and turbulent electron-ion exchange. We have recently released the GYRO code to PPPL for application to NSTX (and C-mod). A full description, recent papers and playable movies of simulations are available at:
http://web/gat.com/comp/parallel/
Also, see the real geometry movie at
http://web.gat.com/comp/parallel/mpeg/shape.n16.mpg
For support of ITPA modeling group activities at DIII-D, the ability to store ONETWO data has been added to MDSplus. This allows a direct graphical comparison between raw data with uncertainties, fitted data with uncertainties, and power balance output from TRANSP and ONETWO.
Recent experiments in various tokamaks observed a "current hole" near the magnetic axis with virtually zero current. A model, in which the hole is sustained by the beam particle source and the resulting outward mass flow, was developed earlier. An alternative model has now been proposed that, while still ensuring a true steady-state equilibrium, removes some of the restrictions of the earlier model. Specifically, the new model is not restricted to unity poloidal beta and includes the neoclassical bootstrap current effect. This results in a Grad Shafranov equation with two prescribed flux-surface functions - the total particle source rate within a flux surface and the parallel bootstrap current distribution. Since the mass flow is ineffective right at the hole boundary where q is infinite, a diffusive-like hyper-resistivity (Boozer) term is included in Ohms law that effectively replaces the loop voltage and allows for true steady state. An expansion analysis near the hole edge finds a Bessel function solution for the fields, without a singular current at the hole boundary; these profiles also satisfy the 1994 Hegna-Callen high m tearing instability criterion, justifying the use of the Boozer term.
Highlights for February 2002
A computational module that accounts for arbitrarily pulsed fast ion neutral beam sources was implemented in the Onetwo transport code. Hybrid Monte Carlo deposition and analytic fast ion slowing results are combined to produce a much faster running module than would be possible if a pure Monte Carlo approach were used. Applied to DIII-D, it is expected that better agreement with time dependent neutron rates, fast ion charge exchange, stored energy densities, thermalization rates, etc. will be obtained.
A utility to convert GYRO simulation data to netCDF format has been developed. The resultant filetype is compatible with the GKV analysis tool developed by W. Nevins (LLNL). A simulation repository has been established at web.gat.com/comp/parallel/sim_data.html and presently includes exhaustive data for the DIII-D Cyclone base case.
In a sawtoothing, Elming H-mode discharge, the linear 3/2 tearing index calculated from kinetic EFITs between sawtooth events, was shown to increase on the approach to the onset of a 3/2 mode. The amplitudes of the magnetic fluctuations from the 3/2 seed islands show a corresponding decrease in their damping rate, in agreement with the Rutherford model and a decreasing neoclassical threshold. Simulations with the nonlinear resistive code NIMROD, using these kinetic EFITs as initial conditions, show initially 1/1 and 2/2 components growing, with a 3/2 mode being driven by coupling. This is promising because these are the same group of modes observed in the experiment. The differences in evolution of the 3/2 islands from each kinetic equilibrium will be compared to the experimental data and linear tearing results. This may explain why this particular sawtooth triggered the 3/2 mode, while the several similar preceding sawteeth did not.
Highlights for January 2002
In an early January WEEKLY HIGHLIGHT we reported on the renorm of the 1996 GLF23 model to bring it into alignment with the best gyrokinetic simulations. This resulted in the ITG transport strength renormed by 0.27 and the ETG by 4.80. The statistical deviation from a 50 H-mode data base improved from 10% to 8.7%. Due a mistaken input file parameter, we erroneously reported that the ITER-FEAT Q increased by 50% compared to the projection from the 1996 model. We have corrected this input file error and now find that the improvement in the Q = 10 range is no more than 10-15%. Even though the renormed model is less "stiff" than the 1996 model, it is still a stiff model, and in fact Q follows the "stiff" normalization, Q=Qnorm x Function (Tped) quite accurately (Qnorm = _ R (I/a)2 (n/nG)2/Paux). At (n/nG) = 0.85 and Paux = 40MW, Q=10 requires Tped = 4.5 keV according to the renormed model.
Recent results from Neutral Beam heated DIII-D, JET and JT-60U discharges, in which equilibria exhibited a "current hole", have generated considerable attention; these discharges appear to have interesting confinement and stability properties. A new model has been developed, in which the current hole is supported by a flux of hot beam ions into the core, and which successfully describes the major features of the JT-60U equlibrium. The new model predicts that, given sufficient ion flux, this configuration could be maintained in steady state, which opens up the possibility of a steady state tokamak.
The GLF23 transport model was renormalized using an H-mode database comprising nearly 50 discharges from the DIII-D, JET, and C-mod tokamaks. This was motivated by recent gyrokinetic simulations with adiabatic electrons indicating that the saturation levels for ITG transport are nearly a factor of four lower than the gyro-fluid results that were used to normalize the original GLF23 model and by work by Jenko, et al suggesting that ETG streamers can result in significantly larger electron heat fluxes compared with simple isomorphic estimates. Carrying out a 2 parameter search whereby the normalization factors for the ITG/TEM and ETG modes (unity in the original model) were varied independently, the minimum RMS error at zero offset was found in the incremental stored energy. The resulting normalization factors are 0.27 and 4.80 for the ITG and ETG modes, respectively. The renormalized GLF23 model is currently being applied to ITER-FEAT, FIRE, and IGNITOR. For ITER-FEAT, the predicted fusion gain Q increases by 50% compared with the original GLF23 simulations.
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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