Theory Weekly Highlights for January through December 2004
Highlights for December 2004
A Monte-Carlo code ORBIT-RF coupled with TORIC full wave solutions along the equatorial plane using a single dominant toroidal and poloidal wave number was applied to compare its results with TORIC calculations, and with DIII-D and C-Mod experimental measurements. TORIC assumes Maxwellian plasma distributions. For a previous DIII-D discharge with 4th harmonic damping on injected deuterium beam ions, the predicted ICRF power absorption from ORBIT-RF falls within a range of TORIC calculations. Experimentally measured enhanced neutron rate is reproduced to within 30% from ORBIT-RF simulations. Preliminary C-Mod results of fundamental harmonic damping on minority H ions indicate that the computed RF absorbed power from ORBIT-RF is within 50% of the power absorption predicted from TORIC. Since ORBIT-RF treats the non-Maxwellian ion distribution self-consistently, the difference with TORIC results appears reasonable. Benchmarking the predicted tail energy spectrum from ORBIT-RF with C-Mod NPA spectrum is underway. For more quantitative comparisons, coupling of TORIC 2D full wave solutions as a function of (R,Z) to ORBIT-RF will be done.
For disruption mitigation using massive gas injection, the rate of delivery of neutrals into the plasma must be sufficiently fast to prevent avalanche runaway growth. The propagation of a neutral gas and cold temperature front into the plasma has been calculated assuming poloidally and toroidally symmetric injection and by solving for the cooling front propagation velocity as an eigenvalue problem. Although the neutral penetration distance into the plasma is small, the radiation cooling of the plasma is exceedingly fast for high Z dense gases. Thus, the plasma can very quickly cool down to a temperature where the neutrals become transparent to the plasma. For ITER-like parameters and with a gas density at the boundary about 100 times the plasma density, the calculations indicate that the neutral gas penetration time is similar in magnitude to the time required to initiate the runaway current, and the avalanche runaway may be avoided.
Previous simulations of nonlinear dynamics of peeling-ballooning modes exhibited explosive bursts of filamentary structures. However, the full energy and particle losses during the ELM crash could not be accounted for solely from loss of the filaments themselves. Two plausible mechanisms have been proposed to explain the increased losses, both of which may be important: 1) The filaments, which remain connected at the ends to the hot core plasma, act as conduits, transporting heat and particles along the filament which is then lost onto open field lines via fast diffusion and/or secondary instabilities. 2) The growth and propagation of the modes strongly damps the sheared rotation in the edge region, collapsing the edge barrier and leading to a temporary return to enhanced L-mode transport. Detailed predictions of these mechanisms are being investigated.
Highlights for November 2004
Dr. Deng Zhou from the Hefei Institiute of Plasma Physics completed his one-year tenure at General Atomics and returned to China this week. During his stay Dr. Zhou contributed to the development of transport analyses by coupling the TOQ inverse equilibrium solver to the ONETWO transport code and initiating coupled transport and stability calculations. He subsequently went on to develop discharge scenarios for the EAST Experimental Advanced Superconducting Tokamak using the tools he developed at GA. He will continue his work on various EAST simulations using ONETWO after he returns to China.
Simulations of nonlinear dynamics of peeling-ballooning modes utilizing the 3D, two-fluid electromagnetic BOUT code show an explosive burst of one or many filamentary structures occurs, transporting heat and particles radially outward into the open field line region. Peeling-ballooning modes are believed to be responsible for edge localized modes (ELMs) in tokamaks. In the early phase of the simulations, the modes exhibit behavior consistent with linear peeling-ballooning studies. In the nonlinear phase, the explosive behavior is qualitatively similar to expectations from nonlinear ballooning theory, though significantly more complex dynamics is seen in the simulations, including a characteristic lull as perturbations approach equilibrium amplitude. Results have been compared to experimental observations of ELMs on DIII-D and MAST, and numerous similarities have been noted, including the poloidal extent and filamentary structure of the modes. This work was highlighted in the invited talk by P. Snyder at the 2004 APS Meeting in Savannah.
Preliminary nonlinear simulations of Edge Localized Modes using the extended MHD NIMROD code (http://nimrodteam.org) show an interesting distribution in the growth rates with toroidal mode number n. When the higher n modes are most unstable linearly, they grow to energies large enough for nonlinear coupling to become important and then nonlinearly drive low n modes. These are driven at much larger growth rates than the high n linear growth rates. This group of low n modes thus forms a "shelf" with increased instantaneous growth rate. The distribution is reversed when the lowest n modes are most unstable linearly and grow to large amplitude first. In this case groups of higher n modes are driven until each group reaches the nonlinear coupling energy and in turn begins driving the next higher group of modes. This causes multiple "shelves" at successively larger growth rate with increasing n. The physical meaning of these "shelves" and how they relate to the final nonlinear state of the system is being investigated.
The GATO ideal MHD stability code is now available as a worldwide computational service on FusionGrid. This Grid computing deployment offers a very easy and convenient facility for running GATO in a secure environment. Presently, the service runs on a 2-CPU server. Data preparation and the invoking of a run are done through an IDL-based PreGATO utility. Both input and output data are written into MDSplus in a tree structure designed to be appropriate for any stability code. Future plans for the GATO service include adding a batch run feature, adding a run queue for efficient use of resources, expanding the server to include many more compute nodes, creating a non-commercial software based PreGATO, and building a set of general MDSplus tools to process and visualize the results. This service is expected to be a prototype for future stability codes. For more information on the National Fusion Collaboratory Project (FusionGrid), see http://www.fusiongrid.org/
Highlights for October 2004
A new analysis has clarified the effects of electron-ion collisions on the linear zonal flow polarization. Previously, GYRO simulations found little or no effect of electron-ion collisions on zonal flows. Though this agreed with the Rosenbluth-Hinton collisionless residual obtained including only the m=0 potential, it was a puzzle because the electron-ion collision frequency is much larger than the ion-ion collision frequency so the effect was expected to be much larger than the effect of ion-ion collisions. By including the m=0, +1, -1 potentials in the gyrokinetic equation for ions and the drift kinetic equation for electrons, a new damped root appears in the "dispersion relation" for the zonal flows at approximately the electron-ion collision frequency. However, when the system of equations is solved to determine all three potentials, the additional m= +1, -1 potentials are found to be smaller than the m=0 potential by two orders in the ion Larmor radius, because the coupling between the m= +1, -1 potentials and the m=0 potential is small in the Larmor radius. The residual in the m=0 potential is therefore only weakly affected by the electron damping from the m= +1, -1 potentials.
A Singular Value Decomposition (SVD) method was developed to calculate surface perturbations from measurements of the magnetic field at the DIII-D vessel wall. Normally, the VACUUM code calculates the magnetic field at or near the surface of the vacuum vessel as a response matrix to the normal component of the perturbed magnetic field at the plasma surface. In inverting this relation, the SVD provides an effective way to deal with the different dimensionalities of the variables as well as the possible singular behavior of the response matrix. For model cases with 256 data points describing the plasma surface, as few as 64 observation points (Mirnov loops), are sufficient to accurately reproduce the plasma surface perturbation in DIII-D. Both the poloidal and toroidal components of the Mirnov loop measurements are now calibrated with respect to the plasma magnetic perturbation.
Simple ITG-adiabatic electron simulations have been to quantify the nonlocal transport mechanism for breaking gyroBohm scaling. The simulations are described by a heuristic formula that has been developed for a nonlocal growth rate corresponding to a localized radial average of local growth rates. The nonlocal growth rate can be used in place of the local growth rate in local gyroBohm transport models like GLF23. This will quantify how turbulence from locally unstable regions drains into locally stable region as ρ* increases and growth rates decrease. GyroBohm transport scaling will be broken toward Bohm in the unstable regions and toward super-gyroBohm scaling in the stable regions.
Modeling of feedback stabilization using the MARS-F stability code has yielded an improved understanding of RWM active stabilization experiments using the internal I-coils in DIII-D. The optimum phasing angle of the upper and the lower I-coils with respect to the sensor signal has been obtained and agrees with the experimentally measured angle. Moderate deviations from this phasing angle lead to a reduced feedback effectiveness. Large deviation of more than 90 degrees leads to a failure of the feedback, as expected from general theoretical expectations. This also correlates with the observation of disruptions in the experiments.
During a visit to GA by Alan Glasser, significant progress was made in understanding the source of the major difficulty in the linear resistive asymptotic matching code TWIST-R, namely that the calculated _' values are clearly unphysical despite solutions that look reasonable. This problem also occurred in the DCON-resistive code; the source of the difficulty turned out to be that the usual equilibrium accuracy for input to ideal codes is insufficient for a linear resistive asymptotic matching code. This is also the likely source of the problems in TWIST-R and is suggested by the observation that the results are sensitive to numerically implementing different analytically equivalent expressions for j and curl(B). A new method is being developed by Glasser to obtain 'refined equilibria' from input equilibrium codes. Several alternative options were discussed but equilibrium refinement may be solution in both approaches.
Highlights for September 2004
The new version of SAV (Signal Analysis and Visualization Code) is ready to be tested. In this version, the user interface is improved so that the user can input or change data parameters and computational parameters interactively, more signal arrays and test signal options are provided, and the visualization functionality is improved with better proper annotations and a resizable plot window. The action log and status message mechanism are also improved. With these and several other enhancements and corrections, this version is expected to be more robust than the previous version. By comparing against similar functionalities in the previous Heat Pulse Analysis code, the results of currently available computational functionalities were validated.
The ONETWO transport code was updated recently with several new NTCC modules. This includes the updated fast ion physics package NUBEAM and it's associated support codes, the PEDESTAL code and the inverse equilibrium code TOQ. Other NTCC modules previously included in the ONETWO code are TORAY, CURRAY, and GLF23. TOQ was recently reworked for submission as an NTCC module and was benchmarked within ONETWO by running a sample current evolution simulation case. The results are in general agreement with those using the inverse equilibrium solver and the direct solver present in ONETWO.
The model developed to explain the variety of tearing mode phenomena observed in DIII-D, in which the instability growth and the equilibrium time development are both taken into account, was shown to reproduce maximum and minimum heating rates for NTM onset. Similar qualitative behavior has been observed in DIII-D experiments; at slow beam power ramp rates NTMs do not appear, at extremely fast rates disruptions occur, and in between NTMs are triggered. Classically destabilized NTM evolution was analyzed in the presence of different heating rates. In the fast heating regime, the change in the linear stability as beta approaches the ideal limit dominates the evolution and the tearing mode grows faster than the rate of current relaxation. Above the maximum rate the integrated tearing mode growth time is longer than the heating time and the ideal mode becomes unstable before the NTM can grow. In the slow heating regime, the enhanced transport losses from the mode modify the current distribution and change the linear stability and this dominates the evolution; the tearing mode grows slowly enough to be affected by the current redistribution. Below the minimum heating rate, the seed island remains saturated and does not evolve into a large NTM. Between the two critical heating rates, classically destabilized NTMs are observed, and the predicted beta value reached as a function of island size agrees with experiment. Nonlinear initial value simulations are being used to test the simple model predictions in the presence of nonlinear mode coupling and so far confirm this picture.
A new, more accurate method for treating the finite Larmor radius (FLR) terms in the gyro-fluid equations has been derived. With this improvement the growth rate for the ITG mode remains accurate for very large temperature gradients, deep into the region of perpendicular wavelength shorter than an ion gyroradius. In previous models the FLR terms fell off too suddenly in this region, resulting in a growth rate that also decayed too rapidly. This improvement is expected to be important for the near separatrix region where the temperature and density gradients can be very steep.
Highlights for August 2004
GYRO simulations were used to study the interaction between the n=0 neoclassical radial transport and high-n ExB transport from ITG turbulence. It was found that the conventional addition of independent neoclassical and turbulent flows is a good approximation. At vanishing rho-star there is no interaction. For finite rho-star global simulations, GYRO now computes the radial neoclassical flows with the addition of the neoclassical n=0 driver, as well as number, energy, and momentum conserving Krook ion-ion collisions. In the presence of turbulence, the neoclassical flows are the local space average of the large orbit neoclassical flows. The n=0 radial modes (zonal flows) induce corrugations in the ambipolar neoclassical flows centered about the null flow. The neoclassical driver combined with a neoclassical n=0 initial value, produces a parallel ion velocity shear which provides the Kelvin-Helmhotz drive to the ITG mode via the nonlinear interaction. The neoclassical drive and neoclassical flows have little effect on the high-n EXB turbulent flows apart from the Kelvin-Helmhotz drive. The ion-ion collisions weakly damp the zonal flows and yield slightly higher ITG transport as expected.
Extensive numerical studies have been performed using the ICRF full wave code TORIC coupled to the ORBIT-RF Monte-Calro code to model DIII-D ICRF discharges, in collaborations with J. Wright and P. Bonoli of MIT. As a first test, a set of converged TORIC ICRF wave solutions for a DIII-D discharge is passed on to ORBIT-RF to compute the wave absorbed power. Initial results indicate that using a single dominant poloidal and toroidal wave number to model the wave spectrum the computed absorbed power from ORBIT-RF is within a factor of two of the power absorption from TORIC. This difference is likely due to the approximation of the poloidal wave spectrum as a delta function, that neglects effects due to other poloidal and toroidal mode numbers. By refining the wave spectrum, we expect further improvement in agreement.
Version one of the ProfileViewer has been made available on the GA Fusion LSF cluster. This new tool allows for plotting of experimental signals versus various radial flux surface labels using EFIT reconstructed equilibria from MDSplus. ProfileViewer fully supports profile overlaying and interactive time slicing, in addition to the full array of features inherited by using the GAPlot Objects.
Recent GYRO nonlinear scans in ExB shear with adiabatic electrons have shown that two different states can exist at low transport levels yielding two different quench points. Without the destabilization effects of parallel velocity shear, simulations with ExB shear on from the beginning yield no transport above a critical shear rate. However, if the simulation is restarted from a previous one with a finite saturation level, then the transport drops to a nonzero saturation level using the same critical shear rate value. This effect has only been observed in simulations without any parallel velocity shear. When the destabilizing effect of parallel velocity shear is included, transport is not quenched by ExB shear. This will be further investigated.
The characteristics of feedback stabilization of the n=1 resistive wall mode in DIII-D geometry are studied systematically using the MARS-F code for a set of equilibria with beta varying from the no wall to the ideal wall limit, and with experimentally measured characteristics of the amplifier and feedback circuit. It is found that the limiting beta value that can be feedback stabilized is related to the inherent phase lag introduced by the amplifier circuit and to a lesser extent introduced by the time delay. The frequency range of the feedback circuit needs to be extended upward before an equilibrium with beta approaching the ideal wall limit can be stabilized. Improvements in performance by using improved feedback circuits are being investigated.
Highlights for July 2004
The Friday Science Meeting has been made available for remote participation. The presentation video is captured with a high-resolution network camera and is broadcast via the camera's web-server. The meeting audio is broadcast using the ESNET Telephone Bridge. Remote DIII-D researchers and collaborators can now conveniently participate in the Friday Science Meetings with their office computers and telephones. The remote participation information is available on the web at Science Meeting Access
and is included in the regular Friday Science Meeting announcements.
A detailed investigation of a spherically symmetric plasma liner from multiple high-velocity plasma jets imploding on a magnetized plasmoid, found that to obtain ignition conditions, extremely supersonic jets (Mjet ~ 60) are required in order to deliver the requisite ram pressure to the target. It had previously been assumed that the merged jets would form a homogeneous plasma liner with the same Mach number as the original N jets. Instead, a supersonic, radially inward flow is created along the contact surface at the edges of the intersecting jets, where the small change in direction at an angle θ ~ 2/N has to be accomplished through a standing shock. The flow is refracted across this shock into a narrow hexagonal boundary layer surrounding each jet and containing the hot shocked material. After the merging is completed, the shocked layer is no longer in stable pressure equilibrium and starts to break up, thus exchanging heat with the cool interior. In the strong shock limit pertaining here, (Mjet*θ)2 >>1, the resultant energy equipartition reduces the liner Mach number to Mliner ~ (1/θ)(3/2) ~ N(3/4) independent of Mjet. For N = 78, Mliner = 9.1. A more refined examination to confirm this result is underway.
In an experiment to investigate the effects of 3D error fields on magnetic surfaces in DIII-D, slowly rotating n = 1 traveling waves at 5 Hz and various amplitudes (~ 0.1 - 0.3% of the poloidal equilibrium field) were applied to perturb the edge magnetic surfaces by pre-programming the I-Coil currents. At 0.1% perturbation, the observed difference in the vertical separatrix location between magnetic reconstructions, which assume toroidal symmetry, and Thomson scattering measurements of electron temperature at a single toroidal location, responds in phase with the applied perturbed field with an oscillation amplitude ~ 2 cm. At 0.3% perturbation, however, the amplitude of the difference in separatrix location grows in time, correlated with an early discharge termination, due to the appearance of a locked mode. The results are consistent with the conjecture that the observed separatrix location differences between magnetic and Thomson scattering measurements in some DIII-D discharges are due to the small toroidal asymmetry of the external shaping coil locations and that the plasma response is important in amplifying the error field and can enhance this difference. This will be investigated in future work.
Convergence tests for the latest version of the TWIST-R linear resistive MHD code have now found near-quadratic convergence in the matching data Delta' and Gamma' with radial mesh, over a range of Mercier index 0.5 < mu < 1.5 values for a Solov'ev equilibrium series. The study also showed the expected pole in the tearing mode matching data Delta'(mu) at mu = 1. In the latest version, numerical bugs were corrected, which resulted in physically reasonable solutions, and a more flexible and more consistent implementation of the poloidal fourier decomposition was provided to minimize the expansion truncation errors. Numerically computed, circular cross section toroidal equilibria were also tested and Delta' and Gamma' were computed, with good convergence properties obtained for these cases as well. For all of these studies, a new tool to study and summarize the convergence of the matching data over a range of cases was also developed; this tool analyzes the convergence rate automatically and finds converged values as a best fit from the computed data. This tool should be extremely useful in future studies.
Lang Lao and Vincent Chan participated in the 2nd US-PRC Magnetic Confinement Workshop in Kunming China, June 23-25, and presented two talks on recent DIII-D results and validation of simulations against experiments. The workshop was hosted by the Southwest Institute of Physics and attended by about 30 scientists, including six US institutions. The purpose of the workshop was to discuss collaboration ideas for the next two years.
Highlights for June 2004
Ideal calculations for a sequence of fully bootstrapped equilibria obtained by scaling the vacuum toroidal field showed instability with no wall but stability with the DIII-D wall and with considerable structure in the growth rates as functions of q_0, q min, and q_edge. Minima and maxima in the growth rates do not correspond to integer values of any of q_0, q_min, and q_edge. The perturbed flux on the outer, low field side boundary is also remarkably insensitive to these parameters over a wide range (5 5 < q_0 < 12.05), including the successive maxima and minima in the growth rate. The outboard mode structure is insensitive to the q_edge value even though the poloidal m = n* q_edge harmonic (n = 1) dominates at the boundary, and is even insensitive to he presence or absence of nearby integer q_edge values where there is a strong peeling component. This result implies that active feedback control of the associated RWM should also be quite insensitive to these parameters, which may simplify feedback schemes.
Based on the assumption that the angular momentum confinement time is the same as the energy confinement time, a formula has been devised for the toroidal rotation frequency expected in ITER. This projects a 2.4 kHz rotation frequency for ITER, given an efficiency of 50% for generating toroidal momentum from a 1 MeV neutral beam. The method also predicts a 21 kHz rotation rate for DIII-D, which is of the order that is generally observed. This should be extremely useful in ITER design work, especially for Resistive Wall Mode stabilization.
Recent modeling has shown that, given sufficient pulse length, a steady state ITER configuration is achievable assuming the GLF23 energy and toroidal rotation transport model and fixed density profiles. The simulations were based on current 9-MA discharge ITER design parameters and used the ONETWO transport code, together with ECH and ECCD calculations from TORAY-GA and fast wave ICH and ICCD from CURRAY. The steady state configuration features a constant E parallel, with essentially 100% non-inductive current drive, and is maintained by a total of 73MW of input power, consisting of 33MW of 1MeV NNBI, 20 MW of fast wave and 20 MW of ECH. Optimization of the non-inductive current fraction and fusion gain assuming the initial ITER hardware capabilities is underway.
Highlights for May 2004
A new gyro-Landau fluid (GLF) system of moment equations that includes both trapped and passing particles, covering both electrons and ions has been completed. This unified model has been a long-sought goal. For each species, the new GLF system has twelve moments for passing and three for trapped particles, but in the absence of trapped particles, reduces to the six-moment Beer and Hammett equations. The system is solved as an eigenmode problem and can resolve subdominant instabilities not found by an initial value calculation; the eigenmode solution is no more expensive near threshold and is faster than existing initial value gyro-kinetic linear stability codes. The model has been tested for wavenumbers from the lowest trapped ion range to the highest electron temperature gradient mode. Benchmark scans over subsets of a large database of gyro-kinetic linear stability calculations find growth rate and frequency standard deviations typically about 10%. The new model has wide application as a data analysis tool and will be incorporated in a successor to the GLF23 transport model.
In an external initiative to test the scalability of the new vector architecture Cray X1 supercomputer, GYRO was run on a temporarily configured X1 with 504 Multi-Streaming Processors (MSPs). Using the full machine, a GYRO benchmark case was run showing very good scalability and a step time of 0.07s. The same case was tested on the IBM Power3 at NERSC using up to 2688 processors, with the best step time of 0.41s at 1792 processors. Thus, the Cray exceeded the peak IBM performance by a factor of 6 using 3.5 times fewer processors. This is very good news for Cray and clearly highlights the effectiveness of their new vector architecture for our compute-intensive simulation problems.
In new work on pellet fueling of tokamak plasmas, it was shown that injection through a guide tube that is bent through 90 degrees can still deliver the pellet largely intact, though strongly deformed into a long pencil-shape. Normally, the tubes used to guide pellets from the low field side to their injection point at the high-field point, as called for in the ITER design, must bend through a considerable angle to achieve the desired trajectories normal to the magnetic surface. It was found that an initial right-cylinder pellet of volume �a3/4, deforms into an object of length (= a(R/a)2/5 and diameter r=a(a/R)1/5 upon executing a 90� guide tube bend. Here R denotes the radius of curvature. This result depends on the validity of the fluid model, which is generally well satisfied, and is independent of pellet velocity. For ITER parameters, ( = 4.8 cm and r = 0.45 cm when a=1cm and R= 50 cm. Future work will focus on the ablation of such pencil-thin pellets from the high field side.
Torkil Jensen died peacefully on May 1 2004 after a long battle with cancer, and ended a long, productive, and uniquely innovative career at General Atomics and DIII-D spanning almost 50 years. His humanity, his wonderfully playful sense of humor, and, of course, his famous Limericks, will be deeply missed. He contributed this highlight:
The Highlightwriter's Plight
Each Friday he turns on his lights
To search for spectacular sights
Of new innovations
And mental gestations
Each week he will aim for new heights
T. Jensen.
Highlights for April 2004
The latest version TORAY-GA1.7 is ready for public release. Dimensions of both equilibrium and radial grid point arrays are now allocated automatically and the different common block files previously needed to run with different resolution are now replaced by a single file. TORAY-GA1.7 was validated to test its robustness and reproducibility across platforms. The test cases include comparisons of the absorbed power and driven current profiles for different launch locations, harmonic, X-mode or O-mode waves, different damping and current drive modules, and varying equilibrium and profile resolution. Within reasonable accuracy, the code gives the same results on both Linux (gemini) and HP (hydra) systems and interacts correctly with other codes, ONETWO, CQL3D, and GAFIT for each test case. This validation work is summarized in a file "Doc_toray1.7.doc" in the CVS directory.
The Linux cluster that performs between-shot EFIT, CER analysis and profile fitting analysis has been upgraded. It now has 12 dual-Xeon 2.66 MHz processors. The cluster can now complete a typical magnetic EFIT calculation in 30 seconds, including data retrieval, which is about half of the time that the previous cluster took. Whereas the old cluster was running at full capacity during operations, with the new cluster, significantly more analyses can be added between shots, such as map_to_rho and spectrometry analysis. Kinetic EFIT and power balance analysis an also potentially be included.
Nonlinear extended MHD simulations of ELMs with NIMROD have shown an energy distribution in the mode structure peaked at low and high mode numbers. Low n modes initially have a lower linear growth rate compared to higher n. Assuming equipartition of energy in the toroidal modes as an initial condition, preliminary results indicate that the higher n modes grow linearly to large amplitude and their beating nonlinearly drives the lower n modes to large amplitude. Intermediate n=5-10 modes are robustly linearly unstable but are not strongly driven by the higher n modes in the early nonlinear phase. The coupled modes form complex structures in flow velocity and temperature; high temperature areas are seen flowing out with vortices clearly evident, in agreement with other models. The temperature and flow structures are antisymmetric above and below the midplane. The simulations cannot yet be continued late into the nonlinear phase due to the need for higher toroidal mode resolution; presently up to n = 21 is included. Although inclusion of higher modes will almost certainly change some results significantly, the bipolar energy distribution is expected to remain in the early nonlinear phase, since it is driven by the nearest-neighbor beating process.
See also http://fusion.gat.com/theory/NIMROD_ELM_simulations for details.
A new, web-based, video conferencing software for audio and video broadcasting, VRVS, has been set up to make DIII-D operations widely available for remote participation. Both DIII-D operations and the 8:05AM pre-operation meeting are being broadcasted via dedicated "DIII-D Virtual Room". Currently, there are three video streams from the control room and one video stream from the building 34 conference room available. The audio is the combination of physics operator audio, session leader audio, and pre-operation meeting room audio. A controllable, web-based, high-resolution camera is also installed in the DIII-D control room. As a result, DIII-D researchers and collaborators can now participate remotely in DIII-D experiments and the pre-operation meetings using their office desktop computer.
Investigations into the ideal MHD stability of tokamaks with a current hole region, lead to the conclusion that their stability can be treated as a plasma with two 'vacuum like' regions. For perturbations with finite toroidal mode number, the current hole region behaves exactly like a vacuum region. This is consistent with standard tokamak external kink analyses where the stability of a vacuum and a current free and pressure gradient free plasma are identical when there are no rational surfaces in the region. For axisymmetric perturbations, however, the analysis is more subtle. In that case, the minimizing perturbation consists of the superposition of three different kinds of independent displacements: a vertical displacement, which does not contribute to the stabilization of the plasma, and two other displacements that compress the plasma and the toroidal magnetic field respectively. These are non-negative definite so cannot provide any destabilization. However, we have not yet been able to prove that these contributions can be made to vanish for the minimizing perturbation.
Highlights for March 2004
A new variation of the model for mass shedding due to magnetic shear induced differential drift of a pellet cloud has been implemented in the Pressure Relaxation Lagrangian (PRL) code. This code calculates the fast inward MHD drift and fuel deposition profile of pellet ablation material following HFS pellet injection. The code has also been coupled with the PELLET code to initialize the cloud parameters along the ablation track. Penetration calculations were done with temperature profiles having a tanh function pedestal, where the pedestal height is defined as the inflection point. The resulting deposition profiles for a 6mm pellet injected into an ITER-like Te profile (To=20kev, Tped = 4 kev and pedestal width = 8.5 cm), are significantly different for pellets with velocities of 300 and 1000 m/s, but there is little difference between pellets with velocities of 1000 and 1500 m/s. The conventional, curved guide tube, ITER injection scheme limits pellet speeds to 300 m/s, but the PELLET code predicts that these pellets will burn out in the pedestal region, and this degrades subsequent MHD penetration of the ablated and ionized material. Parameter scans and sensitivity tests for the temperature and q profile are underway to confirm if this holds universally.
GYRO simulations motivated by SciDAC benchmarking efforts have revealed several encouraging general results. Global GYRO simulations yield transport coefficients that agree in the limit of small gyroradius to system size, with local (flux-tube) turbulence simulations from the GS2 and PG3EQ codes. This firmly establishes the "local hypothesis" which forms the basis of the GLF23 transport modeling code. However, the GTC results, which originally popularized this case, do not satisfy the local hypothesis. In addition, very-long-time GYRO flux-tube simulations (10x the usual simulation time, or about 10ms of a DIII-D discharge) have verified that the turbulence achieves a true statistical steady state; this validates the use of a time-dependent turbulence simulation to determine time-independent transport coefficients.
The algorithm to extract the coefficients of the large and small Frobenius solutions in the TWIST-R linear resistive stability code was successfully adapted from the original 1D version to the 2D toroidal case. The ratio of the leading small and large Frobenius components for the odd and even parity solutions yields the tearing and interchange stability indices Delta' and Gamma'. The 2D case has the additional complication that the solution contains a regular component in addition to the two Frobenius components that must be carefully extracted to reveal the subdominant small solution accurately. In a sample test case, mocking a solution for a 2D Solovev equilibrium, the coefficients of the small solution were extracted to sufficient accuracy on a moderate radial grid. For the more difficult situations that TWIST-R is designed to handle with the Mercier index mu > 1, the small solution is buried below two terms of the large and regular solutions each. However, the same accuracy should be recovered by simply doubling the mesh size.
The ONETWO suite of codes was installed at ORNL on the RANIER computer. This provides additional, badly needed, computing power to analyze Advanced Tokamak current drive scenarios using the computationally demanding GLF23 transport model. Results from these calculations were recently presented at the DIII-D PAC meeting. Of particular value is the ability to model steady state current drive situations using the nonlinear solution methods recently introduced into ONETWO; these increase the efficiency an order of magnitude by solving directly for the steady state solution without having to evolve through intermediate time steps. The RANIER system is presently being used for steady state ITER-FEAT modeling and the combination of the additional computing resources and nonlinear methods reduces meaningful current drive studies using the GLF23 model from the order of days to a more feasible several hours.
Highlights for February 2004
Calculations using the MARS-F code have revealed a synergistic effect between active feedback and rotational stabilization of the resistive wall mode (RWM) with the feedback coil located outside the plasma chamber. This synergistic stabilization is most effective when the growth rate of the RWM, gamma, has been slowed by rotation to a sufficiently low value of gamma*tau_w < 3, where tau_w is the flux diffusion time constant of the resistive wall. At that time the feedback gain required for stabilization is reduced considerably. This synergistic effect may be utilized advantageously in future devices such as ITER where plasma rotation by itself may not be sufficient to stabilize the RWM.
The theory developed for the onset and early evolution of tearing modes in high beta sawtoothing discharges in DIII-D appears to be valid in Alcator C-mod as well. Extensive nonlinear simulations of the seeding mechanism for DIII-D previously established the crucial role of evolving the linear stability in addition to modeling the nonlinear drive in the neoclassical island evolution. Preliminary analyses of equilibrium reconstructions from a similar Alcator C-mod experiment are consistent with the importance of both the classical linear and the nonlinear coupling drive to the tearing mode onset and early evolution, even though the sawtooth physics and neoclassical drive are expected to be different from that in DIII-D. The theory predicts that the details of the sawtooth physics and neoclassical drive are not important in determining the relative amplitude of the nonlinear drive to the early island evolution. This relative amplitude appears to be consistent with the theory in both experiments.
Previous theories of transport barrier formation have put forward the idea that a radial region that contains a minimum-q (zero shear) point is favorable to the formation of an ion transport barrier. However, studies of reversed shear plasmas using the GYRO code show, on the contrary, that there is no transport suppression in such a minimum-q region. These simulations indicate that the appearance of non-resonant ITG modes, which are neglected in the barrier formation theories, ensure that transport remains smooth across the point where shear vanishes. This result implies that theories of ITB formation that invoke special gyrokinetic effects at zero shear can be discounted; one needs to look at non-gyrokinetic explanations.
MDSplus data from 2003 was migrated from the old RAID array to the new Atlas server. The long-term plan is to replace the old RAID array with a new mass storage system, at which time all MDSplus data will be served from the new Atlas server the new Atlas server serves data faster than the old system.
Summary data from DIII-D discharge 70200 to the present were loaded into the DIII-D Relational Database (D3DRDB). These data values include scalars that summarize the characteristics of each discharge. A list of quantities in the summaries table is available at:
Highlights for January 2004
A re-analysis of published simulation predictions for the early MHD bursts in the Beta_N = 2 L-Mode NCS discharge 87009, has shown that many of the predictions are exhibited in more recent, lower Beta_N L-Mode NCS discharges. These were not previously understood or observed in discharge #87009. In both the simulations from the NFTC and FAR codes and the experimental data, the initially localized resistive interchange mode at the inner rational surface broadens until it reaches the magnetic axis. It then reconnects either at or just off-axis, consistent with a double tearing structure in which the innermost island is weaker than the outer island. The inner island then dissipates forming a single tearing mode. In the original simulations, the tearing was partly successful in explaining the Beta limit disruption. In the lower Beta_N experiments, however, the modified profiles lead simply to a loss of high performance, which is more consiste
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
|
.