Theory Weekly Highlights for January through December 2002
Highlights for December 2002
Preliminary experimental measurements presented by G.L Schmidt of PPPL at the 2002 APS meeting, for deuterium pellets injected into the JET tokamak, were found to be in good agreement with scaling predictions from the pellet ablation model developed at GA. In this model, the large-R drift of pellet ablation material depends strongly on the initial pressure of the ionized portion of the cloud where the ablation flow is predominately parallel to the magnetic field, while moving as a whole along with the pellet. The higher the pressure the larger the drift distance in the large-R direction. Measurements of the cloud density using Stark broadening techniques for deuterium pellets injected into JET from the high-field-side show that the cloud density, and thus distance that the pellet penetrated into the plasma, increases with time. The measured densities fit quite well with the theoretical predictions for the initial cloud pressure and density n0 as a function of local plasma temperature T, density n and pellet radius, confirming the scaling n0 ~ n*T1.5. The agreement can be seen at JET Pellet Cloud Comparison
A new two-dimensional linear ideal stability code, SCOTS, capable of handling the entire plasma, including open flux lines, was developed previously in collaboration with the University of Manchester Institute of Science and Technology and the Royal Observatory of Belgium. This code is now being used to study the eigenfunctions and map the ideal stability boundaries by varying the open flux and closed flux currents for helicity injected spheromaks and spherical tokamaks. For a given coaxial helicity drive, which drives the closed flux current, the stability boundary for the n=1 open flux kink mode determines the maximum closed flux current attainable in helicity injected experiments, since the instability is typically low amplitude and weakly nonlinear, and helicity injected discharges have previously been shown to remain in the vicinity of the n=1 linear stability boundary. The calculated n=1 stability boundary then determines the total toroidal current from coaxial helicity injection as a function of injected current. This provides an extremely useful tool for predicting the performance of helicity injection in experiments such as HIT-II, NSTX and SSPX. In particular, recent work to include open flux currents in reconstructed NSTX discharge equilibria will provide a good comparison to experiment. The code can also answer questions about the effect of open flux or divertor currents on stability in conventional tokamaks such as DIII-D and JET.
Highlights for November 2002
As part of a collaboration with the Hefei Institute of Plasma Physics in China, the EFIT and the ONETWO equilibrium reconstruction and transport codes were applied to analyze long pulse enhanced confinement discharges in the HT-7 superconducting tokamak. Long pulse, limited H-mode discharges with ITB were produced in HT-7 by combining LHCD and IBW. Transport analyses using ONETWO show that ion transport approaches the neoclassical level inside the ITB region. Analyses using the GKS gyro kinetic stability code indicate that ITG modes are unstable inside the ITB region. The results suggest that the enhanced ion confinement may be due the stabilization of the ITB turbulence by the pondermotive force from IBW.
Dylan Brennan and Jeff Candy gave invited presentations at the 44th Division of Plasma Physics APS Meeting in Orlando. Brennan discussed the new model for resistive tearing stability, based on increasing delta-prime as a discharge approaches an ideal stability limit. Candy presented the recent continuum global gyrokinetic GYRO code developments and comparisons with DIII-D experiments obtained using the code.
In addition to accurately predicting the onset conditions, island evolution modeling for DIII-D Tearing Mode experiments has qualitatively reproduced a previously puzzling, but routinely observed, feature in the evolution of spontaneous NTMs, namely a lull in the growth of the island. Initially, the linearly unstable island saturates at a size determined by the polarization cutoff. However, as _ increases and the ideal limit is approached, _' increases sharply and the island begins to grow rapidly. Subsequently, finite island effects slow the growth. This is the "lull" phase. Once the island has grown sufficiently large, however, the island undergoes the transition to the usual NTM state and the growth rate increases rapidly again. Several features in the modeling are critical to reproducing this behavior. For the early phase, the parameters in the island evolution equation need to be accurately calculated from the equilibrium reconstruction, _ needs to be ramped at the same rate as is observed in the experiment to obtain the correct time dependent behavior of _'. Also crucial is the use of a polarization model that removes the unphysically large polarization of the usual theory for vanishingly small islands. Otherwise, the onset and lull cannot be reproduced.
The renormalized GLF23 and Multi-Mode (MM95) core transport models have been used together with scalings for the H-mode pedestal height to predict the profiles in H-mode discharges. Using a recently developed power dependent pedestal scaling along with the GLF23 model, an RMS error of 20% in the core stored energy is obtained for 47 H-mode discharges from DIII-D, JET, and C-Mod. In combined core and pedestal modeling of ITER, FIRE, and IGNITOR the power dependence of the pedestal height is found to be a critical issue. Results obtained using the GLF23 and MM95 core models, along with the power dependent pedestal model, are more optimistic than the results obtained using MHD limit (power independent) pedestal scalings. These results were recently presented at the IAEA Fusion Energy conference in Lyon, France.
Highlights for October 2002
Good agreement was found between the dependence of the observed pedestal height on pedestal width and other control parameters such as plasma shape and density, in discharges from the DIII-D pedestal database, with the predicted trends of the stability boundaries calculated with ELITE for a series of model equilibria. This agreement suggests that the DIII-D pedestal is limited by peeling-ballooning stability. It also shows that the model equilibria are sufficiently accurate that this technique can be used to estimate trends in pedestal height as a function of pedestal width and control parameters in both present and future experiments.
Vincent Chan, Ron Waltz, Jon Kinsey, Philip Snyder, Lang Lao, Ming Chu, and Rip Perkins represented our group at the IAEA meeting in Lyon, France. Snyder gave an oral presentation on "ELMs and Constraints on the H-Mode Pedestal: A Model Based on Peeling-Ballooning Modes". Waltz, Kinsey, Lao, Chu, and Perkins had poster presentations describing the GYRO gyrokinetic turbulence simulations, GLF23 simulations for ITER, FIRE, and IGNITOR, our ITER modeling work, resistive wall and feedback modeling, and Current Hole theory. Snyder and Lao also attended the ITPA pedestal meeting in Garching, Germany and highlighted our edge modeling work.
The ECCD module developed by Y.R. Lin Liu has been implemented in the TORAY-GA ray tracing code. The previous version of TORAY-GA, used R. Cohen's original implementation of the ECCD model and the user needed to manually replace this by the Lin Liu ECCD module in order to use it. In principle, the Lin Liu model is both simpler and superior to the original Cohen model, though in practice, the differences are typically of the order of 10%. The user can now choose either model for the ECCD calculations in the input file "toray.in", with the new Lin Liu model as the default if none is specified. The new model also has the capability to include collisionality corrections. These are still to be implemented but in the meantime, the new version of TORAY is expected to be released publicly soon.
The US Fusion Grid is now being used to perform scientific data analysis at DIII-D. Developed under the auspices of the National Fusion Collaboratory Project , the Fusion Grid presently consists of MDSplus and SQL data servers at C-Mod and DIII-D, and the TRANSP code located on a linux cluster at PPPL. This computational grid is now being used by scientists at DIII-D for the TRANSP analysis that is being presented at the IAEA and APS/DPP meetings. To tie into the Fusion Grid, new tools were created at DIII-D to allow for preparation of TRANSP input data as well as invoking the TRANSP computation. The advantages to this mode of operation are a greatly improved data analysis throughput rate combined with instant access to the latest version of TRANSP.
A theoretical framework is being developed to solve the coupled, steady-state heat diffusion and Grad - Shafranov equilibrium equations simultaneously, in order to find self-consistent pressure and safety factor profiles for what may be considered as an ultimate vision of a steady-state tokamak reactor. In this framework, the plasma current arises almost entirely from the pressure gradient via the bootstrap mechanism, and the pressure gradient, in turn, is determined by heat conduction with a thermal diffusivity that depends on the poloidal field associated with the plasma current. Under circumstances where the confinement improves with increasing negative shear, a solvability condition for the self-consistent profiles can arise. This may call into question the feasibility of such a fully steady state, tokamak fusion reactor.
Highlights for September 2002
In a new analysis of pellet cloud drift dynamics, it was found that the effect of toroidicity becomes increasingly important as the cloudlet elongates with time. With toroidicity, different segments of the cloudlet start drifting on different flux tubes and the differential slippage causes the cloudlet to fragmentize in a rather orderly fashion; beginning with the outermost fluid cells, the cells are sequentially shed, one by one. The remaining cells, being fairly well aligned within a common magnetic flux tube at any given moment, continue to drift coherently in the large-R direction until the next end cell is shed. The mass shedding model was incorporated into our PRL code (Pressure Relaxation Lagrangian), which obtains the mass deposition profile in the plasma. This can then serve as the source profile in any tokamak transport code. A preliminary comparison was made to the experimental profile from DIII-D shot *98796 and good agreement was found. The comparison can be seen at Comparison.pdf
NIMROD simulations of DIII-D discharges, completed in collaboration with SAIC, and which capture the nonlinear extended MHD dynamics of the NTM seeding by sawteeth and spontaneous NTM generation have been made publicly available via MDS+. These results are now being analyzed with advanced 3D visualization tools using the SCIRun package developed in collaboration with the University of Utah.
Full-physics simulations on the global gyrokinetic code GYRO have been speeded up enormously. Previously, full-physics runs (which are 20 times more expensive than state-of-the-art ITG runs) with trapped and passing electrons, finite-beta, real geometry, profile variation and ExB shear, etc., required five 24hr restarts on 128 processors of SEABORG at NERSC. This resulted in a formidable 7 to 10 day job turn-around. The recent computational advances enable scaling well beyond 128 processors so that these jobs can now be done in a single 24hr run on 512 processors. This is close to the same job turn-around time obtained for the reduced-physics ITG runs of a year ago. The new full physics GYRO runs can now be done in production mode but this will require a large increase in the MPP time available to us; otherwise, a full production schedule will exhaust our upcoming yearly NERSC allocation in as little as three months.
A complete set of transport equations for the plasma and the electromagnetic field have been obtained in the cylindrical limit that is appropriate for large aspect ratio flux surfaces of arbitrary shapes. Novel algorithms are proposed for solving the problem of plasma transport with concurrent change of flux surface geometry. Besides presenting a most comprehensive model of tokamak plasma transport, these results are also useful for studying how long-duration discharges are maintained by bootstrap current. Extension of the theory to include angular momentum transport and implementation of the algorithms will be attempted in future work.
Highlights for August 2002
A new facility was added to the ONETWO transport code to limit the growth rate of the safety factor q near the magnetic axis. This is done by dynamically adjusting a seed current to flatten the toroidal electric field when the current density is decreasing. This option prevents the formation of multiple magnetic axes, which would otherwise cause the transport calculations to break down.
A new working version of IDL 5.5 for OSF V5.1 was implemented by the Data Analysis Group. This eliminates the problems with the previous unpatched version of IDL, which locked up under certain circumstances. Several LSF hosts have already been upgraded and are using the patched version of IDL; other hosts will be upgraded in the next few weeks.
The GA Theory group successfully hosted the Magnetofluid Modeling Workshop on August 19 and 20. This was followed by several satellite workshops August 21 through 23, devoted to detailed discussions for the major national extended MHD modeling efforts: the Center for Magnetic Reconnection Studies (Amitava Bhattacharjee, U Iowa); the Center for Extended MHD Modeling (Steve Jardin, PPPL); and the NIMROD Project (Dalton Schnack, SAIC).
See http://web.gat.com/workshops/mmw02 for details.
Analytic solutions for "doublet FRC" equilibria with double magnetic axes and two teardrop-shaped private flux regions, have verified an earlier speculation that these configurations possess more favorable stability properties than standard FRCs. General expressions for the interchange functions V( and V(( at the O-point - the least interchange stable point - were derived, and the stability criteria compared, for the standard and doublet FRCs; this also revealed a correction to the published expression for V in L. Sparks, R. Sudan, Phys Fluids 27, 626 (1984). For the proposed Swarthmore SSX-FRC experiment (elongation ~ 1.5), stability requires a minimum ratio of edge separatrix-to-O-point pressure of 0.4, compared to 0.58 for a conventional FRC with the same pressure profile. However, more oblate doublet FRCs, or increased indentation at the waist, can lower the edge pressure required for interchange stability, making doublet FRCs a more viable fusion configuration.
Several DIII-D discharges have in the past exhibited apparent phase reversals or 'phase folding' in the Mirnov signals on the inboard side; that is, a signal that superficially appeared to be a simple m = 3 structure but with a region along the inboard side where the mode seemed to be m = -1. These apparent phase reversals were a long-standing puzzle that had prompted a number of somewhat complicated and non-standard explanations. In collaboration with the FARtech group, a re-analysis of the comparison of the Mirnov prediction from the ideal mode computed by the GATO code with the measured signal for DIII-D discharge #87009, however, revealed that there is, in fact, no mystery and no non-ideal processes need be invoked. The phase reversal is only apparent, and is due to the rich poloidal spectrum of the unstable ideal mode, coupled with the noncircular discharge geometry and relative placement of the Mirnov loops.
Highlights for July 2002
In previous analyses of a DIII-D discharge where successive decaying, and ultimately destabilized, 3/2 modes are triggered by a series of saweeth, the decay/growth rates of each 3/2 island qualitatively correlated with changes in delta_prime calculated from PEST-III. New detailed analyses have made this correlation quantitative in both the decay rates of the 3/2 islands and the onset time of the final unstable island. Taking the computed linear delta_prime values from reconstructed equilibria at eight time slices, plus the calculated neoclassical terms and the measured island widths w at the same time slices, the dw/dt values were calculated from the Modified Rutherford Equation (MRE). These were compared directly to the dw/dt values inferred from the measured island decay rates. The resulting growth and decay rates agree very well, including the change in sign from a decaying to a growing mode. A single free parameter was retained in the polarization term. This was assumed to be constant throughout the discharge and adjusted to obtain the best fit. The best fit value is stabilizing, and also agrees well with the most commonly used theoretical polarization model. This is strong confirmation that the MRE, including the often-disputed polarization model, and linear delta_prime, is a valid quantitative model for island evolution.
The renormalized GLF23 confinement model was installed in the ONETWO code and benchmarked against the XPTOR code for several experimental DIII-D discharges as well as several proposed burning plasma experiments (BPX) currently under consideration. Several of the BPX simulations included sawtooth modeling in combination with GLF23. The results indicate that agreement between the codes is satisfactory and the (small) differences that are observed can be explained in terms of understood differences in t
Oral talks were presented at the recent European Physical Society (EPS) meeting in Montreux, Switzerland by J. Candy and A. Turnbull describing the Theory Group's work on the development of the GYRO code and the MHD stability analysis for DIII-D. Both were well received. L. Lao and A. Turnbull also made presentations at the IEA Workshop on ELMs at JET following the EPS meeting. These covered our work on developing the model for Type I ELMs based on ideal stability of intermediate n modes and complemented experimental talks by T. Osborne and A. Leonard.
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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