Theory Weekly Highlights for January 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)
Highlights for June 2005
A gyrokinetic entropy diagnostic has been derived and added to GYRO. In particular, the creation of entropy through spatial upwind dissipation (there is zero velocity-space dissipation in GYRO) and the reduction of entropy via the production of fluctuations are monitored in detail. This new diagnostic has yielded several key new confirmations of the validity of the GYRO simulations. First, fluctuations balance dissipation in the ensemble-averaged sense, thus demonstrating that turbulent GYRO simulations achieve a true statistical steady state. Second, at the standard spatial grid size, neither entropy nor flux is changed by a four-fold increase (from 64 to 256 grid points per cell) in velocity-space resolution. Third, the measured flux is invariant to an eight-fold increase in the upwind dissipation coefficients. A notable conclusion is that the lack of change in entropy with grid refinement refutes the familiar but incorrect notion that Eulerian gyrokinetic codes miss important velocity-space structure.
In a more detailed analysis of the simulations using ORBIT-RF with TORIC4 for DIII-D it was found that the ORBIT-RF simulation predicts a much weaker absorption at 8ΩD than expected from the linear theory result. Linear theory predicts non-negligible absorption at 8ΩD due to a large k⊥ ρi at the resonance location. The ORBIT-RF simulations use experimentally reconstructed equilibria and profiles of the wave fields and wave numbers from the 2-D full wave code TORIC4 with Monte-Carlo collision operators for pitch angle scattering and fast particle slowing down. Steady state is modeled by re-injecting thermalized ions. Stochastic RF resonant kicks are then modeled using a quasilinear diffusion operator. By analyzing the finite orbit and pitch angle scattering effects, the weak absorption in the simulations is explained by Coulomb scattering of finite orbit resonant ions, which curtails the resonant interaction.
Joint PPPL-GA Theory Highlight:
The Green's function calculation for the magnetic scalar potential used for the vacuum in most delta-W stability codes currently employs a recursion relation to generate modified elliptic functions at finite toroidal mode number, n. The recursion is initiated from the complete elliptic integrals of the first and second kind, E(ρ) and K(ρ) of the normalized source-observer distance 0 < ρ < 1. At each recursion there is a loss of precision due to subtraction of increasingly large terms scaling like n*((1+ρ)/(1-ρ)n times E(ρ) and K(ρ). For an NSTX or MAST case ρmax ~ a/R ~ 0.7 and approximately 108 precision (the precision of the standard expansions for E(ρ) and K(ρ)) is lost for n ~ 9. In joint work between PPPL and GA, a new method to calculate the Green's function was developed by directly integrating the relevant integral representation. A judicious treatment of the singular behavior of the function, together with a transformation of the independent variable, and an accurate quadrature scheme enable a precision that is much greater than before, even approaching machine accuracy at high n. This should eliminate the limit to calculating stability at high n and low aspect ratios.
GA Theory Highlight:
A videoconference using the Access Grid was held with Korean Basic Science Institute (KBSI) physicists to discuss the GA-KBSI KSTAR Modeling and Analysis Collaboration Plan. The agreed plan consists of 4 collaboration topics: EFIT equilibrium reconstruction, ONETWO transport, GATO ideal stability, and KSTAR scenario development. KBSI physicists will become familiar with ONETWO and GATO through participation in the development of those codes for the Fusion Grid. Dr. K.I. You of KBSI is visiting GA 6/6 - 6/17 under this plan to collaborate on the application of EFIT and GATO to KSTAR, and the installation of EFITTools at KBSI.
In collaboration with Dr. Christian Konz from IPP Garching, a successful three-way benchmark of the ELITE, GATO and MISHKA MHD stability codes was performed for intermediate n peeling-ballooning modes in simple geometry using an equilibrium from the HELENA code. HELENA is a commonly used equilibrium code and is tightly interfaced with the European stability code MISHKA. All three stability codes agree to within 2% accuracy on this benchmark case. In order to perform this study, we have set up both ELITE and GATO to work with HELENA. This will enhance our ability to routinely collaborate on studies of edge stability on JET, ASDEX-U and MAST. Dr. Konz will continue working with the GA theory group this summer, studying the effect of rotation on edge stability.
Highlights for May 2005
Application of the GLF23 transport model to ITER predicts that the toroidal rotation generated in ITER by negative ion neutral beams injected in the direction of the plasma current can significantly increase the fusion power produced compared to heating without torque. The increase in fusion power with beam power is predicted to be steeper for co-injected than for balanced beams. Beam voltages in the range of present technology (300-400kev) produced the highest rotation and fusion power enhancement for fixed beam power. The pedestal pressure needed to reach a target fusion power is also lower for co-injection.
New numerical investigations of edge stability using the NIMROD code have resolved an earlier apparent discrepancy between the NIMROD results and ideal linear stability codes DCON and ELITE. Kinetic equilibrium reconstructions from DIII-D discharges with edge localized modes including accurate edge reconstructions, as well as similar model equilibria, were typically found to be unstable at the edge with ELITE and DCON but unstable to a resistive interchange like mode located at the top of the pedestal with NIMROD. The NIMROD formulation includes resistivity and viscosity. Simulations of edge-localized modes in other cases had generally shown agreement between all three codes in mode structure and, in the case of ELITE and NIMROD, in growth rate. In the new analysis, when the resistivity and viscosity are significantly reduced in the edge region, and the ideal mode is fully converged, the linear eigenfunction transitions to an edge mode with growth rates in agreement with the ideal codes. The interchange-like mode in NIMROD is being investigated for a possible role in the large radial transport observed just inside the pedestal region in the experiments.
An analytic formula for the "effective" number of electrons Zeff to be used in calculating the penetration range of plasma electrons in target gases was derived for the case of target gases with many electron atoms, (e.g. argon). The electron penetration range is an important ingredient in the construction of gas jet penetration models in the low temperature edge of tokamaks (Te < 1 keV) and during the post thermal quench phase. In the many electron Thomas-Fermi model of the atom, the orbital electrons are considered as a completely Fermi-degenerate gas and the Fermi energy Ef and the local charge density distribution of the electron cloud, n ~ Ef3/2, are uniquely related to the radial coordinate. The incident electron can only lose energy on cloud electrons with Fermi energy less than the incident electron energy. This criterion, due to Sugiyama (1985), yields an analytic formula for the "effective" number of electrons Zeff to be used in the Bethe-like stopping power formula providing an important low-energy correction below ~1 keV. For a 400 eV electron incident on argon (atomic number Z = 18), the Zeff = 9.67 (see figure in pdf)
This correction increases the penetration range by a factor of almost two from that predicted by the standard Bethe-like formula.
Between-shot TRANSP simulations using the FusionGrid resource were successfully tested during DIII-D operation. The requests were triggered by the between-shot data analysis event system and submitted to the FusionGrid computer at PPPL. With advanced CPU reservation, the request preempted other processes on the computer to guarantee 100% CPU to the between-shot TRANSP run. The process was monitored by the Data Analysis Monitor (DAM) and the results were written back to the MDSplus server at DIII-D.
Highlights for April 2005
A general drift-kinetic equation has been derived without assuming the flow velocity is small or specializing its form. The drift-kinetic equation is the starting point for calculations of neoclassical transport fluxes and turbulent transport. In tokamak plasmas heated by neutral beam injection, ions and impurities flow in the toroidal direction at speeds that are comparable to the impurity thermal speed. In the new equation, the kinetic energy and magnetic moment of the particles are defined in a frame moving with the flow. As a result of rotation shear effects, these are not constant but change with time due to the fact that energy and magnetic moment are defined with their rotational components subtracted out. The variation depends on details of the flow. The guiding center drifts allow particles to carry some of the rotational kinetic energy radially, causing changes in the velocity distributions and therefore affecting the transport. We are presently attempting to simplify the drift-kinetic equation using a particular form for the flow corresponding to sheared toroidal rotation.
The new cluster computer for fusion applications is now operational. This new system has 116 AMD Opteron processors (64-bit, 2.4 MHz) with both gigabit ethernet and Infiniband interconnects. The network filesystem uses the gigabit backbone, while MPI is implemented over Infiniband. Per-processor, the system is four times as fast as the NERSC IBM Power3 (seaborg), twice as fast as the ORNL IBM Power4 (cheetah) and nearly twice as fast as the ORNL SGI Altix (ram). The GYRO and ORBIT-RF codes have been ported to the new cluster and are running in production mode. Porting of the NIMROD and BOUT codes is underway.
In collaboration with Alex James (UCSD) an option to substitute the GATO disk I/O routines with F90 dynamic allocation to memory was tested successfully. The original I/O system was developed to reduce memory requirements in the eigenvalue solver when memory was expensive. Ultimately, flexibility for trading memory and disk depending on the system load will be provided. The new version, however, presently uses either all memory or all disk and the potential savings are undergoing testing. As anticipated, there is little saving in CPU time but savings in wall clock time are expected to be significant when the system load is high. The remainder of the eigenvalue solver is also being converted to F90 syntax with dynamic allocation. In parallel, options for reducing CPU time in the Cholesky decompositions are being evaluated.
Myunghee Choi delivered an invited talk on the Simulation of Fast Wave Damping on Resonant Ions in Tokamaks at the Topical Conference on Radio Frequency Power in Park City, Utah. Carlos Estrada-Mila and Dylan Brennan respectively gave oral presentations on Gyrokinetic simulations of ion and impurity transport and on Nonlinear Evolution of Edge Localized Modes at the Sherwood Fusion Theory Conference in Stateline, Nevada.
The interaction between resonant plasma ion species and the fast Alfven wave was investigated by coupling fast wave electric fields from the 2D full wave code TORIC4 to the Monte-Carlo code ORBIT-RF and compared to recent measurements from Alcator C-Mod. An experimental C-Mod discharge with 5% hydrogen minority fundamental harmonic heating at 78 MHz and 1.0 MW RF power was used in the study. The wave field solutions from TORIC4 were approximated using a single dominant toroidal and poloidal wave number and input to ORBIT-RF. Results from the coupled ORBIT-RF and TORIC4 simulation agree well with the experimentally measured fast ion distribution from a CNPA diagnostic on C-Mod. Compared to the linear absorption result obtained directly from TORIC4 with an assumed tail temperature of 20 keV, ORBIT-RF produces a much broader power deposition profile. The broadening is due to radial diffusion from the fast ion finite orbits and pitch angle scattering, which are treated properly in ORBIT-RF. More detailed validation work is underway.
A recent GYRO simulation of non-local transport shows how local gyroBohm transport scaling is broken. The study used piecewise flat profiles to distinguish the nonlocal breaking of gyroBohm scaling from local breaking due to profile shearing. The simulations are consistent with the following picture of nonlocal transport: The transport is proportional to a locally averaged growth rate where the averaging length L is proportional to the ion gyroradius ρ*. Turbulence drains from locally unstable regions and spreads into stable (or less unstable) regions. Local gyroBohm scaling is then broken in the direction of Bohm scaling in the locally unstable draining regions and in the direction of super-gyroBohm in the less unstable spreading regions. As ρ*, and therefore L, get very small, local gyroBohm scaling in the locally unstable regions with no transport in locally stable regions is recovered. We have developed a heuristic theory of L/a that shows it to be linear in ρ* and inversely proportional to the square root of the local driving rate, in agreement with the simulations. This model of nonlocality will be built into our new GLF23 model and will allow modeling with some nonlocal transport in locally stabilized regions of ITB's and H-mode pedestals.
Highlights for March 2005
Atlas, the primary MDSplus data server for DIII-D data, was upgraded to most recent Red Hat Enterprise operating system and the disk space was expanded to add capacity. The additional disk space is expected to provide sufficient capacity through the end of operations and into the next fiscal year. The operating system upgrade was needed to keep Atlas up-to-date with the latest security patches, to keep it in synch with our other Linux machines, thus simplifying maintenance, and is a requisite for adopting MDSplus access restrictions. Options for solving the long-term problem of keeping up with increasing storage demands through some sort of mass storage solution are being considered.
A new "momentum model" has been constructed to describe jet penetration in disruption mitigation experiments using massive gas injection from a collimated supersonic argon jet. In the DIII-D experiments, camera images indicate that the jets do not penetrate much past the separatrix. In the model, the jet forms a thin ionized boundary layer as it enters the plasma and the plasma and magnetic field are pushed aside. The net magnetic field inside is slightly less than outside the jet. The net magnetic force opposing the jet motion then balances the neutral pressure piling up as a shock behind the tip of the jet. Force balance yields an equation for the actual jet "tip speed" in terms of the "jet speed" in the absence of the shock. The jet cannot penetrate significantly unless the ratio of tip speed to jet speed, U > Ucrit = 1/4, since otherwise the backward propagating shock wave reaches the rear surface. For DIII-D at B ~ 2 T, the model suggests that U is near Ucrit so that penetration may be possible by lowering the field.
Professor Shaojie Wang completed a three-month visit to GA and returned to the Hefei Institute of Plasma Physics in China. During the visit, Professor Wang completed a series of ideal MHD stability calculations with a double transport barrier (DTB). This work extended a previous study of plasmas with an internal transport barrier (ITB), which suggested that beta limit improves with increasing ITB width or moving the ITB location to the edge. The DTB stability calculations assumed a conducting wall at 1.5 times the minor plasma radius. Model equilibria for the study are computed using the TOQ code with a hyperbolic tangent pressure profile for both the ITB and edge transport barrier (ETB). By varying the ratio of ETB to ITB height with the location and width of the ETB fixed, the study suggests that modest ETBs can improve plasma stability. However, strong ETBs drive ideal MHD instabilities, and there is a window in the pedestal pressure, above which the ETBs drive instabilities with a substantial edge component.
A new certificate-based Secure MDSplus system, developed by MIT researchers as part of the National Fusion Collaboratory, was implemented for DIII-D. Regular MDSplus uses host-based authentication, which requires access through a list of known hosts. The new secure system allows users to be authenticated based on their certificate regardless of their host; this means that scientists can access MDSplus while on travel from anywhere offsite, whether from a DHCP-assigned address from home or another laboratory, or through wireless Internet from a coffee shop, library, or airport. For more information see http://www.fusiongrid.org/
Highlights for February 2005
Nonlinear GYRO simulations with kinetic electrons predict a strong turbulent particle pinch for positive magnetic shear with or without finite alpha (Shafranov shift) stabilization included. These calculations are being performed to create a transport database from GYRO scans over magnetic shear around a standard (STD) test case. The simulations are electrostatic and assume shifted circle geometry in an annulus with flat profiles. The particle diffusivity switches sign with weak positive shear, and is positive (outward flux) for reversed shear. The electron and ion energy diffusivities, however, remain positive for all values of magnetic shear and alpha. The database is part of a larger scan that also includes ExB shear scans for ITG and TEM transport, as well finite beta, safety factor, and alpha scans. The database will be used for benchmarking and to fit and test our new GLF transport model that is currently under development.
Instant Messaging (IM) service has been deployed in the fusion group. A secure jabber.gat.com server and multi-user chat module were installed, configured and tested. With this service, DIII-D researchers and collaborators can exchange text messages and present information in approximately real time. Multiple users can hold text conferencing as well. Two public chat rooms have been created and connected to several DIII-D operations-related software applications. By simply entering these chat rooms, users can monitor the experiment status, electronic logbook entries, and Data Analysis Monitor messages.
In a new calculation of angular momentum flux in the small rotation limit of neoclassical transport theory, a significant correction to a 34-year old result of M.N. Rosenbluth et al. from the 1970 IAEA (Plasma Physics and Controlled Nuclear Fusion Research Vol. 1, p495, 1971) was obtained. This correction involves both a sign and magnitude change, predicting a steady-state rotation in the opposite direction from the earlier theory. The new calculation relies on recent large-aspect-ratio perturbative results on distribution functions and involves a formulation using an equation adjoint to the customary linearized drift kinetic equation, bypassing the need to solve a second-order (in ion poloidal gyroradius over scale length) drift kinetic equation. The result can be used to predict steady-state toroidal rotation profiles for discharges with no momentum source using density, temperature, and q profiles.
The raw compute power of the LSF cluster was doubled and the number of processors increased by 42% with the addition of three new dual Xenon Linux computers. Each new machine is a 3.06 GHz Xeon, supporting hyperthreading, with 4 GB RAM and Gigabit Ethernet and is comparable to or better than the existing machines on the cluster in compute power. The new machines can be accessed directly using the new hostnames Eos, Hestia, and Phoebe. However, since most DAAG applications are automatically load leveled on the cluster, users do not need to change anything to take advantage of the new machines.
Highlights for January 2005
A new Gyro-Landau Fluid (GLF) model was tested against the full database of 1799 Gyro-Kinetic Stability (GKS) runs and found to agree markedly better overall with the GKS results than the GLF23 model. The database is divided into three groups representing three different plasma conditions: STD for the core of L and H-modes, NCS for the internal transport barrier region of negative central shear discharges, and PED for the steep gradient region of the H-mode edge. For only four Hermite basis functions in the ballooning mode wavefunction expansion, the errors for the new GLF growth rates were 12% for the STD and NCS group and 17% for the PED group. The frequency errors were respectively 20%, 23% and 41%.
GYRO simulations of D-T plasmas show that in an initial 50-50 D-T mixture, tritium experiences better confinement than deuterium. This asymmetry will give rise to a small (but likely insignificant) build-up of tritium in the core. This effect is robust, and persists over a wide temperature gradient and collisionality range. In related studies, the D-v (diffusion versus convective velocity) model of impurity flow was shown to be consistent with fully nonlinear gyrokinetic simulations. These results, accepted for publication in Phys. Plasmas, represent the first systematic gyrokinetic study of particle transport in tokamak plasmas.
In collaboration with scientists at NIFS (National Institute for Fusion Science, Japan), a method has been formulated to compute the growth rate of a weakly unstable RWM in 3D configurations using results from ideal stability codes. It is shown that the growth rate of the RWM is given reasonably well by the rate at which the available free energy for the ideal external kink can be dissipated by the resistive wall. The eigenfunction is also approximately that of the external kink mode (the mode rigidity condition). This formulation is demonstrated numerically by coupling the computation of dissipation on the resistive wall to the computation of the ideal MHD stability code KSTEP that computes ideal stability of 3D toroidal systems by transforming them into their 2D equivalent systems.
Disclaimer
These highlights are reports of research work in progress and are accordingly subject to change or modification
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