Theory Weekly Highlights for July through December 2005
Highlights for December 2005
Dr. Klaus Hallatschek has joined the GA theory group for a one-year visit as the 2005 Rosenbluth Award recipient. Dr. Hallatschek received his doctoral degree form the Technical University-Munchen in 1998 and subsequently took a position as a research scientist at the Max-Planck Institute of Plasma Physics in Garching, Germany. At GA he will be working closely with GA scientists in furthering his research in core and edge plasma turbulence studies.
Dr. S. Guo from the RFP Group in Frascati has completed a four week visit at GA during which she worked with Dr. Ming Chu on the physics aspects of resistive wall modes common to RFPs and Tokamaks and on related MHD phenomena.
The MHD and two fluid growth rates of a low beta m=2/n=1 tearing mode in the presence of well-separated central sawtooth oscillations were examined using reconstructions of experimental DIII-D equilibria. The outer ideal MHD solutions between the rational q=1, 2, and 3 surfaces were determined using the PEST3 code for a low beta equilibrium and the outer region solution was matched asymptotically to the Glasser, Greene and Johnson resistive MHD inner layer solutions. This yields a dispersion relation for the linear growth rate in the form of a matrix equation for the matching conditions. The most important effects in the dispersion relation are found to be the resistive interchange parameter D_R and the coupling to the 1/1 surface, both of which were stabilizing in the case considered. Two-fluid diamagnetic effects reduce the growth rates significantly, while inducing a mode rotation near the electron diamagnetic frequency. It is expected that this will be important for large diamagnetic frequencies since the rotation shear between surfaces will then significantly affect the coupling between them through the ideal matching data. This will be studied in future work.
It has been shown that the implementation of the nonconforming and conforming Finite Hybrid element approximations in GATO are equivalent if evaluated at the half node points. The Finite Elements represent the small Frobenius MHD solutions. This implies that the traditional procedure implemented in the code, of reconstructing the final small solution from the conforming (and therefore continuous) elements is valid, despite the discontinuity of the basis (nonconforming) finite elements used to describe the actual displacements. This reconstruction scheme had previously been chosen only heuristically. The nonconforming elements also then provide a straightforward way to allow displacement jumps at rational surfaces generated by the presence of a large Frobenius solution component. This allows a relatively easy extension of the code to treat limiting marginal, but otherwise physically valid, eigenmodes manifested as tearing modes.
Several key results were obtained in the theoretical formalism of the plasma response to external nonaxisymmetric perturbations. For the linearized response, the conditions for completeness of the 2D eigenfunctions of the ideal MHD operator, as a basis for the plasma response, were obtained. Completeness can be lost following projection on the plasma boundary and then inversion back to the full plasma domain. In addition to the obvious case where internal modes exist, the conditions can be violated in certain well-defined situations that can be easily monitored and possibly avoided. In addition, the Nuhrenberg-Boozer application for determining the resonant displacement jumps and associated island sizes was generalized to any (including nonresonant) response feature. The generalization can then be applied to determine the specific externally applied perturbations needed to induce nonresonant perturbations, for independent control of MHD modes and plasma rotation.
Highlights for November 2005
The Linux installation of SCOPE, which is a plotting program appropriate for rapid 2D plots, has been updated to use the new distributed MDSplus infrastructure, and the PAD tool, which is often used in conjunction with SCOPE, has also been installed. PAD is a "scratch pad" for sharing data references between SCOPE, the MDSplus TRAVERSER and with other users. The upgrade improves the performance of SCOPE and provides a chance to test out distributed MDSplus. Instructions and demonstrations are available at: http://web.gat.com/comp/analysis/mdsplus/scope/
The theoretical basis for an exotic new pellet acceleration technology using microwave power from MW gyrotron sources has been developed that could pave the way for high-speed > 3 km/s inner-wall pellet injection on ITER. This technology represents a ten-fold increase in pellet velocity from the present ITER design. The method uses a composite pusher-pellet module that absorbs microwave power and converts it to a high-pressure, high-temperature (un-ionized) gas by means of eddy current dissipation inside small conducting particles embedded homogeneously behind the pellet in the D2 ice pusher. The microwave power is delivered to the pellet-pusher module along a waveguide, which also functions as the pellet guide tube; the power is transmitted through a transparent (diamond/sapphire) window/plug, which also absorbs the pellet recoil momentum during acceleration. A US patent application "Microwave-Powered Pellet Accelerator," No. 11/256,662, was filed on October 21, 2005 by P.B. Parks and F. W. Perkins, and a paper to Nuclear Fusion is being submitted.
Equilibrium radial profile corrugations at low order singular surfaces were first discovered in the GYRO simulations for Fred Hinton's APS 2003 invited talk. The corrugations on the scale of several ion gyroradii are most pronounced in the electron temperature gradient. As predicted, the corrugations are largest for the 2/1 surfaces as the qmin = 2 surface enters the DIII-D tokamak at a mid-radius. Max Austin's APS 2005 invited talk presented DIII-D electron temperature gradient time traces from the ECE diagnostic which have the same size/location and signature (q=2/1 & bump-dip-bump) corrugations as the "full physics" GYRO qmin = 2 simulations. While the corrugations have a signature similar to a 2/1 MHD island, the GYRO simulations show quite clearly that the corrugations are quasi-equilibrium components of the zonal flows and not magnetic islands. This is confirmed by magnetic diagnostics. The DIII-D data suggests that the qmin = 2 corrugations are the trigger for the ITB that follows.
The Second post APS Error Magnetic Field Workshop organized by Lang Lao of General Atomics was successfully held at the Adam's Mark Hotel in Denver, CO on October 28, 2005 with more than 40 participants. The PDF files of the Workshop presentations can be found at http://web.gat.com/~lao/ef/efws2005/
Highlights for October 2005
Kinetic analyses of the m/n = 3/2 tearing mode observed in DIII-D hybrid discharges suggest that counter current driven by the kinetic Alfven wave (KAW) induced by the 2/2 sideband displacement may provide a novel mechanism to regulate the q profile and prevent the sawtooth crash in these discharges. In a previous highlight (see highlight for July 22 2005 ) the ideal 2/2 sideband was suggested as a mechanism to drive the needed current. However, further calculations indicated the driven current is too small to maintain q0 against the diffusion of current density into the core. In contrast, the new KAW scenario does predict sufficient current drive. When the central q value evolves to a value close to 1, the electromagnetic 2/2 sideband induced by the rotating 3/2 tearing mode can be converted into propagating KAWs. These waves drive current counter to the direction of rotation of the 3/2 island more efficiently than the Alfven wave proposed earlier.
A new theoretical study of the stability of the edge region in Quiescent H-Mode (QH mode) employing the ELITE, DCON and GATO codes, has found that QH discharges operate in the vicinity of the low-n kink/peeling stability limit. Previously, the mechanism that drives the "edge harmonic oscillation" (EHO) and allows steady state QH operation has been a puzzle, and this provides a possible candidate for the EHO. The combination of low density, which leads to high bootstrap current in the edge, and strong rotation shear, causes the limiting instability in the edge to be a rotationally-destabilized low-n kink/peeling mode, rather than the intermediate to high-n peeling/ballooning modes which generally limit the pedestal in ELMing discharges. The stability calculations find a QH density limit that increases with stronger discharge shaping, and agrees with observations on DIII-D. Calculations also suggest that the ITER pedestal should be in the allowed QH range for low pedestal densities. These results will be highlighted by P.B. Snyder at the APS/DPP meeting in Denver.
A new Quad Xeon server was purchased and installed to replace Zephyr, a very old Tru64 machine, and the old Atlas RAID array. The new server will be configured to serve MDSplus data. The new server has double the storage capacity of the old RAID array and orders of magnitude more server load capacity than Zephyr.
A prototype FusionGrid service along with a beta-version client PreONETWO for launching the ONETWO code is now available for testing. This limited-functionality prototype can be used to reserve a run ID and enter other metadata about the ONETWO run and upload inputs to the database. The facility can then launch a ONETWO run on FusionGrid and enables the user to view the output when the run is done. Access requires only a grid ID and authorization through ROAM, which can be provided on request, and a small number of environment variables set up correctly. The service can then be accessed by typing "preonetwo" on the command line from any of the Linux hosts in the LSF cluster. More information is available at: http://web.gat.com/comp/analysis/grid/onetwo.html
Several instructional demos are also provided at the following URLs:
http://web.gat.com/comp/analysis/grid/onetwo/preonetwo-demo.html
http://web.gat.com/comp/analysis/grid/onetwo/preonetwo-demo-2.html
http://web.gat.com/comp/analysis/grid/onetwo/onetwo-code-run.html
http://web.gat.com/comp/analysis/grid/onetwo/preonetwo-inputs-demo.html
The TORAY-GA ray tracing code for modeling electron cyclotron heating and current drive has been improved to calculate more accurately the driven parallel current density and the toroidal current density for ONETWO. The new version, TORAY-GA 1.8, runs only with ONETWO versions 3.91 and later. Previously, the driven toroidal current density in TORAY-GA was calculated using approximations to the flux-surface average of the magnetic field and the major radius. This has been corrected in the new version. Self-consistent calculations using TORAY-GA V 1.8 and ONETWO 3.91 are expected to result in corrections to the driven current density of approximately 5-10% in the outer part of the plasma for most DIII-D and ITER cases.
Highlights for September 2005
A globally convergent Newton method based module, GCNM, for solution of stiff transport equations typically encountered in the analysis and modeling of DIII-D and other tokamaks was developed. This module will be part of the NTCC "Predictive Transp" project and is also included in the SWIM project. The module demonstrates the setup of some of the transport equations required to use the solver, analytic and numerical test cases and use of GLF23. It was created to allow easy addition of MPI and OpenMP parallel methods in the near future. The methods developed are suitable for "small scale" problems where direct (as opposed to iterative) solvers are suitable. However, extension to large sparse systems can be done if, for example, it is found that a more direct coupling between core and edge models is appropriate.
In a collaboration to calculate kinetic corrections to the resistive wall mode (RWM) stability, three DIII-D wall stabilized cases were provided to Bo Hu and Riccardo Betti of the University of Rochester for analysis. This is intended to evaluate the importance of kinetic effects in the stabilization of RWM. All three cases were predicted from GATO convergence studies to be wall stabilized. As part of the exchange, the GATO results are being benchmarked against PEST and DCON in detail to further confirm the ideal stability predictions. One case is the near current hole discharge reported previously (see September 9 2005 highlight) and the benchmarking will provide a stringent test of the convergence properties of all the ideal codes in the new interesting strongly reversed central shear regime.
Dr. Christian Konz from Max-Planck Institute of Plasma Physics in Garching has concluded a three month visit collaborating on studies of tokamak edge stability and edge localized modes. During his visit, Dr. Konz has become familiar with the ELITE stability code, and also employed the MISHKA and CASTOR codes for extensive successful benchmarks. In collaboration with Dr. Philip Snyder of GA, Dr Konz has employed the recently added toroidal rotation capabilities of ELITE, and developed a formulation for efficiently including toroidal rotation in MISHKA and CASTOR. ELITE has now been employed in extensive studies of flow shear effects on modes with intermediate to high toroidal mode number n, finding strong stabilization at high n which weakens at intermediate n. Ballooning modes are generally found to be more strongly stabilized than kink modes.
The mesh packing algorithm in the ideal MHD stability code GATO was significantly improved to be more flexible for equilibria with strongly inverted q profiles where a large number of rational surfaces pile up in the core and now works extremely well even for equilibria approaching a current hole. Additional packing can be directed separately to either the innermost or outermost specified q surface if q is inverted and to negative, low, and positive shear, or to the edge or core regions, as desired. The modifications allowed consistent converged results to be obtained for recent high performance (normalized β = 4.1) strongly inverted DIII-D discharges with minimum q > 2. Variation of the packing confirmed that the unstable mode for these discharges with no wall is global, with a large m=2 and m = 3 component across the low shear region but that the mode is wall stabilized. There is little activity in the inner negative shear region where up to 30 rational surfaces were resolved (q on axis ~ 33). Near the marginal wall position (1.05 times the DIII-D wall), the m = 2 is strongly narrowed but the m = 3 component remains broadly extended.
A new GATO manual describing the overall structure and the use of the most important input options can be found on the web at: http://web.gat.com/comp/analysis/grid/gato/gato-manual.pdf
Thomas Johnson from JET visited GA between July 5 and July 29, 2005 to initiate a collaboration between GA and JET on ICRH modeling. During his visit, he became familiar with the ORBIT-RF code. In addition, modifications were made to improve the efficiency and performance of ORBIT-RF simulations. Equilibrium mapping codes that were previously run on different computers (SEABORG at NERSC and STELLA at GA) were ported to the new cluster DROP at GA and a script file was written to run all codes sequentially on the same platform. To improve the performance of the RF operator, the changes in perpendicular magnetic moment due to wave-particle interactions are now calculated over several steps. ORBIT-RF and the related codes were also ported to and successfully tested on the JEC computer at JET. Comparison scenarios for DIII-D and JET experiments between ORBIT-RF and SELFO at JET were discussed and planned.
Highlights for August 2005
A new analytical model was developed for the interaction of an expanding plasma fireball with a cusp magnetic field used to protect an IFE target chamber wall from the energetic ions, and safely divert the charged particle debris out of the target chamber. The lifetime and survivability of the wall is a serious concern for IFE power plants since high-yield targets release bursts of neutrons, X-rays and energetic ions with instantaneous heat loading on the wall a thousand times larger than wall loadings in an MFE power reactor. The physics-based model describes the braking of a quasi-spherical plasma expansion against the magnetic "cushion" and calculates the equilibrium/stopping radius of the plasma cavity. The model indicates that magnetic wall protection, an idea that emerged from the High-Average-Power-Laser (HAPL) program, looks promising and deserves further study. The conventional approach of filling the target chamber with a Xe buffer gas to absorb the ion energy faces the problem of target heating by hot buffer gas which can potentially ruin the frozen DT fuel layer.
Professor Jaiqi Dong from the SWIP in China completed a successful three-week visit to GA to learn how to use several of the GA MHD tools, notably the EFIT, TOQ, GATO, and BALOO codes. An equilibrium for the HL-2A tokamak was successfully constructed and tested for stability with and without the HL-2A vacuum vessel, which was modeled by a suitably smoothed harmonic expansion in poloidal angle.
Recent nonlinear GYRO simulations including kinetic electrons show that the ion and electron energy transport follows a linear q scaling for q values ranging from 1 to 4. The simulations were performed around several reference cases in an annulus with flat profiles and assuming shifted circle geometry. The results are equally valid for positive and negative shear and for cases where the spectrum is dominated by either ITG or TEM modes. The particle transport also follows a linear scaling if the diffusivity is positive (outward). If a particle pinch is predicted, then the passing electron contribution can change sign as q is varied within a scan, resulting in little or no observed q dependence over the entire range of interest. The passing electron contribution to the diffusivity is relatively small compared to the trapped electron contribution, but it is large enough to impact the scaling with q.
A general expression was derived, valid in an arbitrary coordinate system for the existence of magnetic surfaces in 3D. The expression is coordinate independent, which is important when axisymmetry is violated. Applied to a torus, the fact surfaces are guaranteed to exist with any special symmetry, drops out trivially from this formulation. In the general case, surfaces exist if and only if a certain simple equation has solutions. An analogous expression is also obtained for the existence of current surfaces. An effort is underway to derive simplified conditions to yield useful criteria for existence of proper nested flux surfaces.
The NIMROD code has been successfully ported to the GA Opteron/Infiniband cluster DROP (see Highlight for April 22 2005). So far, performance on most NIMROD routines is up to a factor of four faster than on the NERSC SEABORG machine. Production studies of edge-localized modes with flow shear and current drive from resistive instabilities in DIII-D have begun on the machine. However, the NIMROD iteration stage is currently a bottleneck, limiting overall performance to about twice that of SEABORG. The port to the DROP cluster required a special build of the MVAPICH library to prevent communication lock-up on parallel computations, where an offending optimization was removed and this may be responsible for the performance lag. Curiously, this lock-up problem has also been observed in attempts to port NIMROD to the new NERSC Opteron/Infiniband cluster, JACQUARD. We are working with the MVAPICH team to identify the root cause of the problem.
Highlights for July 2005
Joint GA PPPL Highlight:
In joint work with PPPL, further improvements to the 2D Green's function calculation for the vacuum energy in &delta-W stability codes were made to avoid the Riemann-Lebesgue like cancellation due to the oscillatory behavior of the integrand for large toroidal mode number n. This was accomplished by deforming the integration contour into the complex plane so that the integrand now decays exponentially. An accurate evaluation is then obtained by using Gaussian quadratures over a finite range. An analytic result obtained by expanding the integrand in a power series to fifth order agrees well with the new algorithm. The recursion and direct quadrature methods described previously (see Highlight for June 10 2005) works well for small values of the normalized distance between source and observer points, ρ, but the cancellation destroys the precision for moderately large values ρ ~ 1. There is considerable overlap in the applicability of all these techniques so that the Green's function can now be accurately calculated for any practical values of n and &rho.
A plausible theoretical scenario for explaining a key feature of the hybrid scenario discharges in DIII-D has been developed. In these discharges the central plasma evolves to a quasi-steady state without sawteeth. The central safety factor, q0, is pegged close to 1 and this correlates with the development of a rotating 3/2 magnetic island. Equilibria modeling these discharges with different central q were analyzed using the PEST-III stability code. The linearly unstable 3/2 island develops a 2/2 side-band with increasing amplitude as q0 approaches 1. This near-resonant Alfven wave propagates with enhanced phase speed relative to the background plasma. With sufficient phase speed, the 2/2 sideband could drive currents which impede the decrease in q, causing q0 to remain just above 1 as observed.
The conference room in building 15 is now equipped with a QuickTime broadcaster and a streaming server. Currently, the presenter video and meeting audio are configured for broadcasting in real time to participants from remotely located fusion sites. The plan is to improve remote participation capability of fusion meetings held at General Atomics by adding the web browser-based broadcasting interface. This capability will be ready and used during the 2004-2005 DIII-D Year-End Review.
An incompressible fluid model for pellet breakup has shown that high velocity pellets are incompatible with the curved waveguides currently envisaged for ITER pellet fuelling. It is anticipated that in ITER, guide tubes will carry pellets of frozen DT accelerated by gas guns to a velocity of V ~ 1 km/s to a launch position along the high field side of the separatrix. These tubes have one or more 90o. bends. The new analysis predicts that the centrifugal force in the waveguide bends fractures pellets when V > 500m/s. This is in agreement with recent ORNL experiments. For V > 1 km/s, successive fractures turn the pellet into a DT dust cloud. The fluid model finds that the cloud diameter decreases to preserve volume so that the dust cloud will extend a length L = 2(Δφ (Rd)1/2 along the guide tube, where Δφ denotes the angle the waveguide bends through, R ≈ 1m denotes the curvature radius, and d ≈ 0.005m is the pellet diameter. Interestingly, the pellet elongation is independent of pellet velocity. The pellet velocity limitations are avoided by pellet launch from the transformer core.
Justin Burruss gave an invited talk entitled "Grid Performance and Fusion Science" at the Grid Performance Workshop in Edinburgh, Scotland.
A detailed justification has been obtained for the approach of calculating the neoclassical angular momentum flux in the banana and Pfirsch-Schluter regimes using the drift-kinetic-equation theory. The justification is restricted to the case of up-down symmetric flux surfaces and small values for the ratio of poloidal to toroidal fields. The use of the drift-kinetic-equation approach in general geometry has been questioned because second order terms in gyro-radius over the plasma scale length are not included. It turns out that the drift-kinetic approach does incorporate the leading part of the second-order terms in a subsidiary expansion in the ratio of poloidal to toroidal fields. Revisiting the Pfirsch-Schluter regime calculation has revealed substantial errors, which are now being corrected using the adjoint equation approach that was successfully used recently for the banana regime. (See February 11 2005 highlight)
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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