Princeton Plasma Physics Laboratory And Alcator C-Mod Collaboration. Five Year Plan

Transcription

1 Princeton Plasma Physics Laboratory And Alcator C-Mod Collaboration Five Year Plan PPPL Staff May, 2003 Plasma Physics Laboratory Princeton University Princeton, NJ, USA

2 Contents 1. Introduction Advanced Tokamak Highlights of Recent Research Lower Hybrid Launcher MSE Diagnostic Startup and Improvements Proposed Research Lower Hybrid Current Drive MSE Current Distribution Measurements Burning Plasma Experiments Highlights of Recent Research Initial Single-null/Double-null Studies Proposed Research Compare Single-null/Double-null Diverted Discharges ICRF Heating at High Power Levels D( 3 He) Minority Heating Transport Divertor and Plasma Boundary RF (ICRF and LHCD) Global Stability Advanced Tokamak Integrated Scenarios Transport Highlights of Recent Research Marginal Stability and Turbulence ITB Modeling Proposed Research Marginal Stability and Turbulence Electron Transport ITB Modeling Divertor and Plasma Boundary Highlights of Recent Research GPI Edge Turbulence Visualization Edge Neutrals Modeling Reflectometer Upgrade Proposed Research Edge Turbulence Visualization Extended Comparison with Theoretical Simulations Edge Turbulence Control Experiments Edge Modeling Extended RF Physics and Wave-particle Interactions Highlights of Recent Research D(H) Minority Heating Experiments Mode Conversion Experiments ICRF Modeling LH Modeling Proposed Research D( 3 He) Minority Heating Experiments

3 FWCD experiments MCCD experiments Flow drive studies LH wave physics LHCD physics RF Modeling Theory and Computation of Macroscopic Stability Overview Model Development Ideal MHD Two-fluid Extended-MHD Kinetic Extended-MHD Beta limiting MHD modes Sawtooth Phenomena Neoclassical Tearing Modes Energetic Particle Modes Edge MHD Stability and the behavior of ELMs Linear Analysis Nonlinear Physics of ELMs & Evolution of Free Boundary Modes Prediction of the Cause and Effect of Disruptions Physics of the Disruption Disruption Forces Control Issues Profile and Shape Control The Physics of Pellet Fueling Internal Mode Control Appendix: Macrostability Codes Supported by PPPL Theory Department Facility Highlights of Recent Research Rework of 4 ICRF transmitters Fabrication, installation, upgrading of 4-strap ICRF antenna Ongoing ICRF engineering support Completion of LHCD launcher Proposed Research LHCD launcher #1 installation and commissioning Fabrication of LHCD launcher # Participate in 4-strap ICRF antenna # Participate in tunable cavities for ICRF transmitters 1 and Budget Manpower Contributors

4 1. Introduction The purpose of the PPPL C-Mod collaboration is to conduct and enable forefront scientific research on the Alcator C-Mod tokamak and to perform engineering/technical support for the joint MIT/PPPL team. Research aims include: Research on the effectiveness of off-axis current drive via Lower Hybrid current drive and its effect on plasma performance. This program includes design and fabrication of the launcher and participation in the associated research; Experimental study of basic ICRF plasma-wave interaction processes and their comparison with theory in order to gain predictive capability for heating and current drive in reactorgrade experiments; Creation and understanding of internal transport barriers, off-axis current drive for PEP/ITB mode studies, and low frequency (ω<ωci) current drive for reactor application via ICRF heating and mode conversion current drive; and Core confinement, and H-mode behavior including pedestal characteristics and fluctuations. Recent and proposed hardware upgrades include both plasma control and diagnostic components: ICRF antennas for plasma heating and current drive; LHCD launchers and coupling hardware for control of the plasma current profile; Current profile diagnostics to increase understanding of current drive and plasma behavior (in conjunction with a C-Mod-provided diagnostic neutral beam); Edge diagnostics (edge fluctuation measurements at the plasma periphery with reflectometry and 2-D imaging of edge turbulence) to increase understanding of turbulence and transport. Engineering and technical support for RF power systems include: Engineering assistance in tuning and maintaining the ICRF transmitters; Technical assistance in modifying the new 4-strap ICRF antenna following its initial operation in FY2000 through FY2002; and Engineering participation in the design, fabrication, and installation of the Lower Hybrid current drive system as part of the Lower Hybrid project. In all these areas PPPL provides assistance in areas where PPPL has competence and capabilities needed by the C-Mod program while enhancing research opportunities for PPPL scientists

5 2. Advanced Tokamak 2.1. Highlights of Recent Research Lower Hybrid Launcher Based on our experience with Lower Hybrid current drive on both the PLT and PBX tokamaks, PPPL proposed the design and fabrication of a Lower Hybrid launcher for C-Mod. This will be used to launch directed waves and drive an off-axis current, which together with ICRF heating will result in current and pressure distribution profile modifications producing the Advance Tokamak discharge configuration MSE Diagnostic Startup and Improvements A key objective of the Alcator C-Mod experimental program for next five years is improved understanding of Advanced Tokamak (AT) physics in plasma regimes relevant to long-pulse burning plasma experiments and fusion reactors. Broadly speaking, AT plasma regimes are characterized by a degree of control of temperature, density, transport, current and flow profiles - 5 -

6 that yield significant improvements in energy confinement and beta limits. Historically, AT regimes were developed on a number of tokamaks using modified plasma growth and early plasma heating to create hollow q(r) profiles, coupled with beam-driven current and plasma flows. Concurrently, development of the Motional Stark Effect (MSE) diagnostic throughout the 1990's provided local measurements of q(r) that were crucial to understanding the improved confinement and beta and to empirical optimization of AT performance. The inductive plasma startup and beam-driven flows give the experimenter considerable flexibility to alter the magnetic shear and flow-shear profiles which has proven very useful in unraveling their role in controlling confinement and stability. Unfortunately, these techniques have limited applicability to high density, long-pulse tokamaks including fusion reactors. To complement the ongoing AT research at NSTX, DIII-D and elsewhere, the Alcator program will exploit its unique capabilities -- especially LHCD and high density -- to study AT physics issues crucial to establishing the feasibility of AT plasma scenarios in reactors and long-pulse burning plasma experiments. As elsewhere, measurements of the q-profile on C-Mod will be essential to study the physics of noninductive current drive (LHCD, MCCD) and the influence of magnetic shear on transport. Working closely with C-Mod staff, PPPL has developed and installed a 10-channel MSE diagnostic which will be the cornerstone diagnostic for measuring the q-profile in AT physics studies. The C-Mod environment is hostile to MSE diagnostics: limited access mandates the use of invessel optical components which are subject to large accelerations (hundreds of g's) during disruptions. Prior to the 2003 run period, the mechanical support structure for two large in-vessel glass mirrors was redesigned to reduce the disruptive forces and to provide resilience against accelerations up to 500g. In parallel, PPPL has designed silver-coated replacement Inconel mirrors which will be available for installation, if needed, in FY Proposed Research Lower Hybrid Current Drive The Advanced Tokamak scenario requires all the plasma current to be driven by non inductive methods. Since it is not practical to drive the all current with exterior methods such as LHCD and NBI the bootstrap current has to be optimized. This is obtained by actively controlling transport barriers and current profiles. The LHCD system is equipped with the maximum flexibility possible for power deposition and includes the possibility of changing the spectrum (therefore the driven current) in real time. Figure 2.1 shows the extent of the power spectrum vs. the refractive index in the toroidal direction

7 6 P (a.u.) 4 POWER SPECTRUM 24 waveguides cm opening 0.15 cm septum P (a.u.) 60º 90º 120º 4 150º 180º n Fig 2.1. Power spectrum of the PPPL/C-Mod Lower-Hybrid launcher. As seen in the figure, the maximum directivity is obtained for very fast waves which damp on fast electrons: the addition of the second coupler will allow us to use one coupler (one spectrum) to generate a fast electron tail in the desired radial position. This might require high n, therefore the efficiency might be low. The other coupler will then launch waves with faster phase velocities, thereby increasing the efficiency. 6 P (a.u.) Φ= n Figure 2 n spectrum for various progressive phase differences (line), compared to the spectra obtained by keeping the the high power phase shifter at Φ=90 while changing the phase in the low power phase shifter (gray)

8 The phase relation between the two adjacent waveguide columns fed by the same Klystron is set by a mechanical phase shifter that can be changed only between pulses. It is possible to obtain a slightly less directional power spectrum but in real time - using the low power phase shifter before the Klystron. An example of this spectrum is shown as the shaded areas in Figure MSE Current Distribution Measurements Improved Spatial Resolution - Additional Spatial Channels The number of MSE radial measurement locations will be doubled by installing 10 additional detector systems (PMT's, filters, electronics) and rearranging the present fiber bundles (FY04). Improved Spatial Resolution - Beam Collimation The present short-pulse Diagnostic Neutral Beam (DNB) which is on loan to C-Mod until mid-fy04 has a circular footprint with a 1/e diameter of approximately 8 cm that limits the radial resolution to about 4 cm ( r/a = 0.18) at r = a/2. The permanent, long-pulse replacement DNB to be installed in FY05 has improved divergence corresponding to a 6- cm diameter. Further improvements in the radial resolution will require beam collimation; initial design calculations indicate that a beam as small as 2-3 cm could be realized at the cost of a factor 2-3 reduction in signal strength. PPPL will design a variable aperture system capable of varying the beam diameter from the 2-3 cm range desired for some MSE studies up to the present beam size to accommodate the needs of other beam-based diagnostics (BES, CXRS) that prefer maximum signal strength (FY05). Edge Electric Field Measurement A second optical system will be added to view the plasma from a different angle to discriminate between the usual MSE electric field (v B) and radial electric fields at the plasma edge (FY05). Measurement and Analysis Improvements Hardware upgrades in combination with ongoing maturation of the MSE analysis and its integration into equilibrium codes (EFIT) will provide increasingly detailed and accurate q-profile and shear-profile measurements over the campaign. While various stages of the MSE development will certainly overlap, a representative progression of steps is presented below. The steps are characterized by an ever-increasing requirement for accuracy of the measured q-profile, e.g. merely demonstrating that LH drives currents requires only modest accuracy, while detailed comparisons of transport barrier behavior with microturbulence codes involves the radial derivative of the q-profile and hence needs highly accurate MSE measurements. These improvements will allow us to: Confirm existence of LH-driven currents (FY04)

9 Parameterize the LH current drive efficiency and radial localization of LH-driven currents. Compare with ACCOME code calculations and TRANSP using the LSC code as the LH package (FY04-05). Characterize the effect of modified magnetic shear by LHCD on transport barriers, e.g. correlate radial position of transport barriers with ρ min, q min (FY05-06). Extend magnetic shear studies to plasmas having high bootstrap current fraction in addition to LHCD (FY06-07). Compare transport barrier behavior (location, magnitude, parametric scaling) and microturbulence model calculations that include the measured magnetic-shear and flow-shear profiles (FY05-7). Extensive code calculations by the C-Mod staff have identified plasma regimes in which LHCD can drive sufficient current to reverse the q-profile and thereby access improved confinement. LHCD is most effective at high electron temperature and with density relatively low for C-Mod, though still high compared to most other LH experiments. Central temperatures of over 5 kev have been demonstrated in experiments with n e (0) = 1.5 x m -3 with ICRH applied during current ramp-up. Modeling based on such a target scenario with increased ICRH predicts that LH will drive a current of 390 ka and generate reversed shear over a broad region, with (r/a) qmin ~ We expect adequate signal-tonoise ratios for the MSE measurement over this density range with the present DNB and its proposed long-pulse replacement. Truly reactor-relevant AT regimes require a high bootstrap fraction in addition to noninductive magnetic-shear profile control. To achieve a high bootstrap fraction, it is necessary to operate at higher plasma density and confinement. Modeling based on target plasmas with edge and/or core transport barriers have identified regimes with bootstrap fractions of 65-75%, reduced LH driven current (270 ka), but maintaining a strongly reversed current profile. These plasmas have central densities in the range 3 x m -3 which, based on prior experience, is expected to produce inadequate signal-to-noise for core q-profile measurements. In these high-density regimes MSE may be supplemented by a proposed 20-channel polarimeter that views the across the plasma from a horizontal port. The MSE diagnostic will contribute important q-profile measurements to a number of other research topics in the Alcator C-mod program, including: Stabilizing NTM Both LHCD and Mode Conversion Current Drive have been proposed as a tool for stabilizing Neoclassical Tearing Modes in burning plasma experiments. Under the RF physics program, MSE will measure the current drive efficiency and radial localization of both techniques for comparison with theory and code predictions. Then under the auspices of the C-Mod MHD Stability program, MSE will provide measurements to document the magnitude and radial localization of driven currents that are needed to stabilize NTM's in open-loop. The understanding gained from these programs will form the basis for development of a feedback algorithm and control scheme to demonstrate feedback stabilization in a high-performance H-mode plasma

10 Sawtooth Stabilization C-Mod's Burning Plasma program proposes to include a study of the feasibility of using fast wave current drive to control the amplitude, extent and frequency of sawtooth activity. A purely empirical evaluation of FWCD on sawtooth activity can be carried out without a detailed knowledge of the q-profile, but MSE will contribute information pertaining to the efficiency and radial localization of FWCD which may prove useful in guiding the experiments. Low Frequency FWCD Fast wave current drive with ω < ω ci for all species is potentially attractive for burning plasmas because it avoids the possibility of parasitic absorption on the α-particles. MSE will document the current drive efficiency and radial localization as part of the Burning Plasma program. 3. Burning Plasma Experiments Alcator C-Mod is well suited to addressing a broad range of physics R&D issues of interest to next step burning plasma experiments such as ITER or FIRE. Alcator C-Mod is roughly a 1/3 scale model of FIRE with all metal plasma facing components and the flexibility to operate with double null poloidal divertors. Plasma control capabilities for plasma heating (ICRF), current drive (LHCD) and pellet fueling are very similar to the capabilities envisioned for FIRE. Alcator C-Mod has the capability of operating in the H-Mode; in the Enhanced D-Alpha mode; and in the RF controlled Internal Transport Barrier modes and has just completed the LHCD Project which will allow the exploration of reversed shear advanced tokamak regimes. Therefore, C-Mod is a valuable facility for addressing specific physics issues as well as integrated tests of several potential operating scenarios for burning plasma experiments. If fully implemented, the burning plasma support program and capabilities proposed (C-Mod 5 Year Proposal Section 4) by the Alcator C-Mod group would address many critical issues for ITER and FIRE. This section highlights the areas of particular interest to ITER and FIRE within PPPL. The PPPL burning plasma study group has begun active participation in the C-Mod collaboration only recently, and so our specific proposed collaborative efforts in this area are less well defined than for the Advanced Tokamak, RF, and Transport research thrusts. Broadly speaking, PPPL proposes to develop and carry out Miniproposals that will exploit C-Mod s unique parametric and diagnostic capabilities to address critical burning-plasmas issues Highlights of Recent Research Initial Single-null/Double-null Studies A number of C-Mod research results described in Section 4 of the C-Mod 5 Year proposal are important for ITER and FIRE experiments. Of particular interest are the studies just beginning on comparison of single-null diverted discharges with double-null diverted discharges. The type of divertor configuration single null or double null and pumping capability single pump or

11 double pump has a significant effect on plasma performance and engineering for burning plasma experiments. These studies involving H-modes will seek to quantify the effect of SN/DN and plasma cross-section triangularity on confinement (pedestal), ELMs and divertor detachment. Also of interest is the determination of disruption characteristics for DN plasmas with a neutral stability region Proposed Research Compare Single-null/Double-null Diverted Discharges The studies described in section will not be completed in the present 5-year plan, and will be carried over into the proposed 5-year program. The scope of the experiments will be extended to include the effect of divertor pumping as that capability is added to C-Mod ICRF Heating at High Power Levels C- Mod has the capability for high power density ICRF and this is of interest to both ITER and FIRE. The practical experience gained on C-Mod will be invaluable in finalizing launcher design for ITER and for optimizing the choice of launcher and coupling physics for FIRE D( 3 He) Minority Heating Minority heating using 3 He will be used as a primary heating method on ITER and FIRE for heating in H, He, D and T plasmas. Extending these studies to power levels and parameters approaching those in ITER and FIRE will be an important contribution to the burning plasma program. See section 6.2 for specific RF physics issues Transport Confinement Scaling of H-Mode with SN/DN and High Triangularity Results from ASDEX Upgrade, JET and JT-60U all show an increase in the ITER H-mode scaling multiplier H98(y,2) as the triangularity is increased for densities in the range 0.7 < n/n G < 1. Data from C-Mod in this area would help fill out the ITPA Confinement and Modeling Data Base and the ITPA Pedestal Data Base and would strengthen the physics basis for ITER and FIRE. Similarity Discharge Studies Similarity H-Mode discharges with the same ν* and β as ITER and FIRE will be investigated as another technique for understanding and projecting ITER and FIRE H- mode performance. Of particular interest is to also extend the range of similar parameters to the pedestal region, and to the SOL/divertor region. Transport Scaling in ITBs

12 The internal transport barriers (ITB) that are induced by off-axis ICRF and then controlled by on-axis ICRF heating are of particular importance to an ICRF heated burning plasma. An important question is whether strong central alpha heating will deplete the transport barrier in the same manner as on-axis ICRF heating appears to do on Alcator C-Mod. Rotation with RF Only and Impact on Confinement Flow shear associated with beam-induced rotation has been exploited in several tokamaks to study the physics of transport barriers and to substantially improve both local transport and global performance. It may become progressively more difficult to use beams to provide such control as plasmas become larger and denser in burning plasma experiments. Therefore, understanding the mechanism for plasma rotation without externally injected momentum that has been observed on C-Mod is very important for future reactor plasmas. Continued experiments and modeling in this area will be carried out in close cooperation with the C-Mod scientific staff. Particle Transport (Peaked Density Profiles-Fuel Mix Optimization) Increased attention is needed on particle transport for burning plasmas since controlling the fueling mixture and profile has very high leverage for a burning plasma experiment like ITER or FIRE. Pellet injection from the high field side is a potentially powerful technique for fueling the core of a burning plasma. A key question is whether confinement modes with improved energy confinement will also have improved particle confinement that leads to unacceptable impurity accumulation in long pulse discharges. Studies of particle (fuel and impurities) transport in conjunction with H-Mode, EDA, ITB and AT plasma regimes will be carried out to address this issue Divertor and Plasma Boundary The divertor and plasma boundary issues are very important for a burning plasma experiment and the follow-on reactor plasma. In the ARIES advanced tokamak power plant plasmas, a radiative divertor with metal plasma facing components was proposed to handle the large plasma power exhausts of P heat /R ~ 80 MW/m while maintaining a low tritium inventory. This will require significant radiation in the SOL and in the divertor to achieve reasonable power deposition densities on the first wall and divertor. In addition, the capability to exhaust the helium ash must be maintained. C-Mod has all metal PFCs and has shown that the tritium retention is in the acceptable range of ~0.2%. THE C-Mod exhaust power densities are P heat /R ~ 10 MW/m are significant and will provide data relevant to both ITER (P heat /R ~ 20 MW/m) and more compact burning experiments such as FIRE (also P heat /R ~ 20 MW/m). Tests of a Tungsten Bush Module The studies of power deposition, tritium retention and effects of ELMs will be extended to tests of a FIRE-like tungsten brush module as part of the proposed C-Mod program. This will be of interest to ITER as well. Impact of SN/DN Configuration on ELMs

13 Type I ELMs are projected to severely damage the divertor target plates in burning plasma experiments and even more so in an ARIES scale reactor. ASDEX-U, JT-60U and DIII-D have observed a transition to smaller Type II Elms which would be acceptable in FIRE and possibly in ARIES-RS. A set of experiments is proposed to investigate ELM behavior as the plasma configuration is changed from SN to DN and as the triangularity is increased. This will also be done for radiative divertor conditions. This is of great interest to both ITER and FIRE. Optimum Pumping Divertor Configuration A major issue for burning plasma and reactor design is to determine the optimum particle pumping configuration. In the present C-Mod configuration that divertor pumping is not sufficient to prevent significant particle recycling from the first wall. The baseline C-Mod plan is to investigate a configuration where the lower divertor takes the plasma exhaust heat load and the upper divertor chamber takes the particle exhaust load. Another set of experiments is proposed to investigate the effectiveness of a full double null configuration with both divertor chambers pumping that would be compared to partial pumping configurations. Integrated Detached Divertor Operation with All Metal Walls and Advanced Tokamak This is a crucial need for the future of an advanced burning plasma experiment and would be one of the major accomplishments of the US Base program. The proposed C-Mod program would have the capability to carryout this task RF (ICRF and LHCD) Coupling Physics of ICRF and LHCD The proposed experimental program will be of great importance in providing experience on the coupling of ICRF in various RF heating scenarios of interest to FIRE. It will be important to resolve the LHCD efficiency issue that was raised at Snowmass so that uncertainties in the ITER and FIRE LHCD current drive calculations can be reduced. ICRF and LHCD Launcher Development The experience gained on the operational characteristics of the high power launchers will be valuable for the design of launchers for both FIRE and ITER-FEAT Global Stability NTM Stabilization by LHCD FIRE proposes to use LHCD as one of the techniques for stabilizing the neoclassical tearing mode in 10 Tesla H-mode operation. Initial experiments on Compass-D have shown promise for stabilizing the NTM mainly by modification. Experiments on C- Mod would extend these results toward FIRE-like parameters

14 Disruption mitigation with a neutral stability point due to DN Disruption mitigation and prevention are very important for burning plasma experiments and are essential for a tokamak reactor. A neutral stability point has been observed to slow the onset of vertical disruptions in JT-60U. A balanced DN configuration has a neutral stability point that may allow implementation of a fast vertical feedback system to control and possibly eliminate vertical disruptions. If the C-Mod configuration evolves to a balanced DN configuration then this area of research could be expanded to include ultra fast feedback coils imbedded in the vacuum vessel wall to control disruptions Advanced Tokamak Simulation of AT Regimes The C-mod advanced tokamak regime using LHCD with the capability to produce strongly reversed shear resulting in f bs ~ 65% and β N 3 without a conducting wall are of great interest to ITER and FIRE. PPPL has significant modeling capability in the Tokamak Simulation Code (TSC) and current drive (LSX) that would be useful in refining the AT scenarios and in analyzing the experimental results. PPPL and FIRE would propose to have significant collaboration in this area Integrated Scenarios Conventional Edge Barriers (H-Mode, EDA) with Radiative All-metal Divertor The integration of confinement, MHD stability, divertor and plasma boundary for SN/DN plasmas with radiative divertors would be an important contribution to the physics basics for both FIRE and ITER. C-Mod offers the unique features of all metal PFCs and reactor level magnetic fields in these experiments. Advanced Tokamak with Radiative, All-Metal Divertor This is a critical item for burning plasma R&D leading directly along the path to an attractive tokamak reactor concept, and C-Mod is uniquely positioned to carryout an extensive R&D program in this area. This is the mode of operation for ARIES-RS/AT and for advanced tokamak modes in FIRE and ITER. ITER would be more interested in the SN configuration while FIRE would be most interested in the full integration of a DN divertor with double pumping. The flexibility to investigate a range of scenarios with from weakly reversed central shear to strongly reversed central shear in essentially steadystate discharges with ~ 5 current redistribution times will provide a strong basis for AT modes with parameters up to f bs ~ 65% and β N 3. Of particular interest will be the energy and particle confinement within the q min surface and its scaling with respect to dimensional parameters (I p, P, B, etc.) as well as dimensionless scaling. If the confinement barrier is effective then perhaps higher β N could be explored with resistive wall mode stabilization as a future upgrade. TRANSP analysis of transport properties and TSC/LSX simulation of the overall discharge are capabilities that PPPL can contribute to this collaboration

15 4. Transport 4.1. Highlights of Recent Research Marginal Stability and Turbulence The measured temperature gradients exceeded - by 50% or more - the best estimates available in the late 90s of the theoretical critical gradient for ion-temperature-gradient (ITG) modes. The theoretical effort was strengthened with more complete simulations undertaken by PPPL researchers, and linear micro-stability theory continued to be at odds with the available measurements. This motivated nonlinear turbulence simulations using the gyrokinetic code GS2 [1,2], which showed that the discrepancy could be understood as a substantial nonlinear upshift (the so-called Dimits shift ) in the effective critical gradient due to stabilization of ITG modes by zonal flows. This upshift had been previously predicted theoretically, but no experimental evidence for it had been put forward. These results are illustrated in Fig. 5.1 where the power conducted by the computed turbulence is plotted against the normalized ion temperature gradient. The experimental gradient likely to be 50% higher than the linear critical gradient at R/L Ti =4.5. Conducted power (MW) Nonlinear GS2 simulations Kinetic electrons and ions C-Mod EDA H-mode r mid =0.56a IFS-PPPL model Lower ν e & ν i Standard collisionality Lower ν i P heat Measured R/L Te R/L T Fig Conducted power as a function of R/L T as computed by the IFS-PPPL model and the GS2 code

16 This work led to a further discovery with potentially great importance because it highlighted the importance of a kinetic treatment of the electron dynamics [3], which had been ignored in previous theoretical predictions of the Dimits shift. It appears from the current work that the Dimits shift may be much smaller than previously thought in lower-collisionality tokamaks such as JET, DIII-D, and ITER (see the lower ν e & ν i curve in the Figure). The shift appears to be large in C-Mod because its highly collisional plasma largely erases the non-adiabatic features of the electron dynamics that can weaken the Dimits shift. References 1. M. Kotschenreuther, G. Rewoldt, W.M. Tang, Computer Phys. Comm, 88, 128, W. Dorland, F. Jenko, M. Kotschenreuther, B.N., Phys. Rev. Lett. 85, 5579, D. Mikkelsen, et al., "Nonlinear Simulations of Drift-Wave Turbulence in Alcator C- Mod", in Proceedings of the 19th IAEA Fusion Energy Conference", Lyon, IAEA-CN- 94/EX/P5-03, ITB Modeling Linear and nonlinear calculations of gyrokinetic microturbulence have been carried out with the GS2 flux tube code at the trigger time for formation of an internal transport barrier in the offaxis RF H-mode. It is found that ITG modes are unstable outside the core plasma, that only weak instabilities are present in the plasma core and that in the barrier region the plasma instabilities are quiescent at the trigger time. Sensitivity studies indicate that the normalized electron temperature gradient drives the suppression of instability most strongly in the region where the ITB will form, consistent with experimental measurements. References 1. Alcator C-Mod H-modes", APS conference, April 5-9, 2003, Philadelphia, PA. 2. "Gyrokinetic Microturbulence and Transport Calculations for NSTX and Alcator C- Mod", Transport Task Force Conference, April 2-5, 2003, Madison, WI. 3. "Gyrokinetic Calculations of Microturbulence and Transport for NSTX and Alcator- CMOD H-modes", to be presented at the 30th EPS Conference on Plasma Physics and Controlled Fusion, July 7-11, 2003, St. Petersburg, RU Proposed Research Marginal Stability and Turbulence It has become clear that nonlinear processes are crucial in determining both the saturated level of turbulence and its associated transport and the effective critical gradient (which was previously thought to be more easily calculable via simple linear stability). In order to truly understand transport, one must measure the turbulence directly and understand the nonlinear saturation processes. C-Mod provides plasmas that are complementary to those of other tokamaks, and thus helps to complete our understanding

17 PPPL will contribute to this understanding by providing and operating a reflectometer which will measure turbulent fluctuations. We will carry out detailed comparisons of data from all the C-Mod fluctuation diagnostics with nonlinear gyrokinetic turbulence simulations using the GS2 and GYRO codes. As data from these diagnostics becomes available we will help to plan experiments that should optimize the overlap between diagnostic capability and theoretically expected fluctuation characteristics. Key parameters will be identified in simulations, and experiments will be designed to test the importance of those parameters in real plasmas. This work will also benefit from the experience gained by PPPL researchers active in complementary studies at other sites Electron Transport As the fusion program progresses toward reactor-grade plasmas, with predominantly electron heating and strongly coupled electron and ion temperatures, the importance of electron transport necessarily grows. Experimental opportunities for electron fluctuation measurements are described in the C-Mod 5-year plan, and relevant turbulence simulations will be carried out at PPPL. An experiment proposed by PPPL personnel and carried out in C-Mod with MIT has demonstrated that it is possible to measure the electron temperature gradient scale length to high precision (5-10%) when sawtooth heat pulses can be minimized. We plan to search for a way to exploit this capability by designing experiments that will be in a regime with a critical gradient dependence on electron temperature, but with a weak dependence on the ion temperature gradient (which is more difficult to determine). We would then compare the experimental and theoretical dependences of the electron temperature gradient as an important parameter such as the q profile is varied ITB Modeling The nonlinear ITG calculations will be processed with the Nevin s GKV post-processor and heat and particle fluxes will be compared with transport analysis for the off-axis RF experiment. The existence of a Geodesic Acoustic Mode in the plasma core at the trigger time will be explored. Initial GYRO code simulations of CMOD will be extended and compared with those from GS2. The Ohmic H-mode ITB (Fiore, Phys. Plas. 2001) has many similarities to the offaxis RF H-mode ITB, but does not appear to be triggered by reduced electron temperature gradient, so a parallel study of gyrokinetic microstability will be interesting and can be used to plan for future experimental tests. Nonlinear calculations of ETG turbulence for CMOD will give some insight into the role of ETG on electron thermal transport on this ITER-relevant tokamak. 5. Divertor and Plasma Boundary 5.1. Highlights of Recent Research GPI Edge Turbulence Visualization

18 The PPPL/MIT gas puff imaging (GPI) diagnostic of edge turbulence was proposed in 1998, designed in 1999, and installed on Alcator C-Mod in early The first 2-D images were reported at the APS meeting in 2000, and initial results were presented in invited talks at the APS meetings in 2001 [1] and 2002 [2]. This project is a close collaboration between PPPL researchers and Jim Terry, Brian LaBombard, and others at MIT, in addition to people from several other institutions (LANL, Garching, Dartmouth, and Princeton Scientific Instruments, Inc.). The first GPI results were obtained with a 60 Hz Xybion intensified camera gated at 2 µsec/frame, as shown in Fig. 5.1 [1]. The strongly turbulent structure was evident, but the motion of the turbulence could not be seen due to the low framing rate. The frequency spectrum and fluctuation level were checked to be similar to those seen by a Langmuir probe at the same radial position. Initial comparisons were made with the 3-D fluid simulations of Hallatschek and Rogers based on a local model, i.e. using the gradients at a representative point in the edge. The GPI diagnostic was significantly improved in 2001 by the addition of an ultra-fast CCD camera obtained through an SBIR with Princeton Scientific Instruments, Inc. With this PSI-3 camera the motion of the turbulent blobs could be seen for the first time, as illustrated in Fig. 5.2 [2-3]. This allowed us to visualize the rapid outward motion of the turbulent blobs, which had been predicted theoretically [4]. An upgraded 28 frame PSI-4 camera was operated on C-Mod in 2002 and many additional movies of the turbulence have been created under various conditions

19 Fig D images of edge turbulence in C-Mod taken with the GPI diagnostic near the outer midplane at 60 frames/sec with an exposure time of 2 µsec per frame. The diamond-shaped region is 6 cm x 6 cm, with the radially outward direction toward the left, and the separatrix is the black line through the center of the images. Fig D images of edge turbulence in C-Mod taken with the Princeton Scientific Instruments PSI-3 camera at 250,000 frames/sec with the same field of view as in Fig. 1. The rapid radial motion of the turbulent blobs can be seen with reference to the fixed arrows

20 Theoretical simulations of C-Mod edge turbulence were improved by Hallatschek in 2002 to include nonlocal effects, i.e. the radial profile of the edge parameters. A direct comparison of the k-poloidal spectrum between GPI and simulation is shown in Fig. 5.3 [2]. The spectral range and shape agree fairly well in the SOL, but the simulation underestimates the turbulence in the limiter shadow (right hand side). Nevertheless, this is among the most successful of the few direct comparisons to date between tokamak turbulence measurements and numerical simulations of turbulence. Fig Direct comparison between the GPI results and the NLET simulations of edge turbulence in C-Mod. On the left is the measured k-poloidal spectrum of turbulence vs. minor radius, and on the right is the simulated k-poloidal spectrum from NLET. The NLET simulations have been post-processed to calculate the actual spectrum of D α light as measured by GPI. The agreement is fairly good in the SOL, but the simulation underestimates the turbulence in the limiter shadow (right hand side). Also in 2002 the GPI diagnostic was further improved by the addition of a second Xybion camera, which allowed two-time and two-color imaging of the edge turbulence. Initial results were reported at the APS 2002 meeting [5]. This work will be continued in 2003 with the aim of measuring the motion of the turbulence during the entire discharge and the ratio of electron density to temperature fluctuations. Modeling of the atomic and neutral physics of the GPI diagnostic was also done using the DEGAS-2 code. Simulations of GPI experiments on Alcator C-Mod demonstrated that the connection between the emission patterns and plasma parameters is sufficiently complicated to prohibit a direct inversion of the camera images into separate density and temperature fluctuation images [6]. However, it was also shown that the same spatial structure was apparent in the density and/or temperature patterns and the GPI line emission patterns, suggesting that a wavenumber analysis would yield the same spectrum in both cases. References 1. S.J. Zweben, D.P. Stotler, J.L. Terry, B. LaBombard, M. Greenwald et al, Phys. Plasmas 9, p (2002)

21 2. J.L. Terry, S.J. Zweben et al, Observations of the Turbulence in the SOL of Alcator C- Mod and NSTX and Comparison with Simulation, to be published in Phys. Plasmas (2003). 3. J.L. Terry, S.J. Zweben et al, Fusion Energy Conference IAEA S. Krasheninnikov, Phys. Lett. A 283, 368 (2001); D.A. D Ippolito et al, Phys. Plasmas 9, 222 (2002). 5. B. Bai, J.L. Terry et al, Bull. Am. Phys. Soc. 47, 9 p. 236 (APS DPP meeting 02). 6. D.P. Stotler, B. LaBombard, J. Terry, S. Zweben, J. Nucl. Mat , 1066 (2003) Edge Neutrals Modeling The behavior of neutral gas in the periphery of magnetic fusion devices plays a crucial role in controlling the core density and in establishing the boundary conditions for the core. The plasma density at the last closed flux surface determines the relationship between limits on the edge and scrape-off layer density and the core density. Furthermore, transport theories based on critical gradients suggest that the plasma temperature just inside the last closed flux surface will strongly affect the core temperature. The core parameters in burning plasma experiments then in turn set the fusion power. The hypothesis of and growing evidence for the dominance of main chamber recycling over that of the divertor must be examined and understood in order for scenarios for power and particle control to be developed in future devices. That understanding can be deduced from an examination of detailed computer models of the plasma and neutral transport that reproduce the available measurements in the edge and divertor of present machines. Neutral pressure measurements and imaging of visible light emissions (e.g. the Balmer- α or D α line) are the most useful diagnostics signals for comparison with neutral gas transport models. However, these models require a specification of the plasma parameters everywhere in the machine as well as the location and strength of neutral gas sources. The extensive diagnostics available on Alcator C-Mod have permitted the development of simple models of the plasma variation in the scrape-off layer and divertor that are largely determined by diagnostic data. As a result, the neutral gas behavior can be examined by a stand-alone code such as the DEGAS-2 Monte Carlo neutral transport code. A first attempt along these lines yielded neutral pressures and D α signals much smaller than the measured values [1]; the discrepancy was blamed on the omission of ion-neutral and neutralneutral elastic scattering from the model. The subsequent addition of these processes to DEGAS- 2 coincided with the execution of experiments dedicated to the study of neutral gas transport in the Alcator C-Mod divertor and sub-divertor [2]. In spite of the model improvements, the discrepancies persisted. Potential explanations for the discrepancy were then evaluated by determining the sensitivity of the simulated values to changes in the assumptions underlying the simulations [3]. Models of the plasma-surface interaction processes (such as reflection and absorption) and of the interpolation of plasma parameters between probe locations were highlighted as potentially viable explanations. References 1. DEGAS 2 Neutral Transport Modeling of High Density, Low Temperature Plasmas, D. P. Stotler, et al., PPPL Report PPPL-3221 (January 1997). Proceedings of the

22 Sixteenth International Conference on Plasma Physics and Controlled Nuclear Fusion Research, (Montreal, Canada, September 1996), Vol. 2, p Modeling of Alcator C-Mod Divertor Baffling Experiments, D. P. Stotler, et al., Proceedings of the Fourteenth International Conference on Plasma Surface Interactions in Controlled Fusion Devices, (Rosenheim, Germany, May 22 26, 2000). PPPL Report, PPPL-3523 (November 2000). J. Nucl. Mater , (April 2001). 3. Understanding of Neutral Gas Transport in the Alcator C-Mod Tokamak Divertor, D. P. Stotler, et al., PPPL Report PPPL-3690 (May 2002). Atomic Processes in Plasmas, 13th APS Topical Conference on Atomic Processes in Plasmas, (Gatlinburg, Tennessee, April 22 25, 2002), p Reflectometer Upgrade Two new, higher frequency, channels have been added to the C-Mod microwave reflectometer, which will allow us to measure plasma fluctuation farther up the edge pedestal, and possibly to the ITB region at low density. The hardware for these new 130 and 140 GHz channels has been installed and checked out. Analysis codes have been ported from JT-60U, where they were developed and first used by G. Kramer, to the PPPL Petrel cluster for use with the C-Mod measurements Proposed Research Edge Turbulence Visualization Extended In FY 03 and FY 04 the GPI diagnostic on C-Mod will be used to explore the edge turbulence behavior under a wide variety of edge conditions. This will be greatly helped by the anticipated use of a 312 frame PSI-5 camera instead of the present 28 frame PSI-4 camera, since over 10 times more data can be obtained per shot. The main goal will be to make detailed quantitative comparisons between the turbulence measurements and theoretical simulations. A secondary goal is to determine the empirical correlations between the edge turbulence and edge transport; for example, during the EDA and ELM-free H-modes vs. L-mode, and near the Greenwald density limit. In each of these cases there is reason to believe that the turbulence plays a major role in determining the edge transport state, but so far no clear causal relationship has been established. In FY we would like to significantly increase the capabilities of the edge turbulence imaging system on C-Mod. Several options listed below, one or more of which could be implemented during this period. In FY 07 and 08 we will use the upgraded GPI system to further explore the physics of edge turbulence, and compare the results with other C-Mod diagnostics and with theoretical simulations. Note that each of these potential upgrades could be done independently of the existing GPI system and each other, so that more than one can be done at the same time or over several years D imaging of edge turbulence near the inner SOL D imaging of edge turbulence near the X-point D imaging with two wavelengths for ne/te measurements

23 4. Supersonic gas injector for increased radial coverage. 5. High resolution 2-D imaging of small-scale edge turbulence. 6. Wide angle 2-D imaging for large-scale edge turbulence. Some details about these diagnostic upgrades are discussed below: 1. The added capability of 2-D imaging at the inner SOL would be important for testing theory, which generally predicts that inner wall turbulence is stabilized by favorable magnetic curvature. A first step has already been taken in this direction on C-Mod by measuring the gas puff emission on discrete chords near the inner limiter [1], which showed that the fluctuation level there was about ten times lower than on the same flux surface at the outer limiter, in qualitative agreement with simulations. Three-dimensional simulations such as BOUT have already been used to calculate the poloidal distribution of edge turbulence in tokamaks [2], and strong changes in the poloidal distribution have been predicted near the density limit and during L-H transitions, but little or no connection with the measured poloidal distribution of turbulence has yet been made. 2. The X-point of a diverted tokamak is important for edge studies since the local magnetic shear and small poloidal field can strongly change the edge stability and transport. A new class of modes called resistive x-point modes (RX) was recently discovered and a connection between these modes and the H-mode transition and density limit has been proposed [2]. However, very few measurements have been made of edge turbulence near the X-point, and so a 2-D imaging system focused on the X-point would be quite interesting for comparing with theory. For example, BOUT simulations predict that as the density limit is approached, the dominant modes shift from the resistive X-point mode localized near the X-point to the resistive ballooning mode localized near the outer midplane. 3. The present GPI system uses one spectral line at a time to image the turbulence, so both electron density and electron temperature fluctuations can contribute to the observed turbulent structure. In theory, these fluctuations are closely linked; nevertheless, it would be interesting to measure them separately. A technique to do this involving the use of two cameras viewing the same GPI image in two different spectral lines has already been proposed and tested on C-Mod [3], but further development is needed to increase our confidence in the results. This would mainly involve data taking and analysis, rather than new hardware. 4. The present GPI system is limited to the region where neutrals can penetrate into the edge, which extends to just barely inside the separatrix at the outer midplane. The addition of a supersonic neutral gas injector inside the vessel could increase the radial viewing range of the GPI images, thus making it possible to view the H-mode barrier and pedestal region using GPI. This nozzle might also be useful to change the fueling location and increase the fueling efficiency in C-Mod. A nozzle design compatible with the required fueling rate and in-vessel constraints would need to be designed and tested before installation on C-Mod. 5. The spatial resolution of the present 2-D GPI imaging system is limited to 0.3 cm by the in-vessel optics, but might be significantly improved in order to look for the smallscale turbulence with k pol ρ s > 0.5, i.e. λ 0.4 cm. This may be in the wavelength range of the nonlinear inverse-cascade spectrum of ETG modes (which have linear growth near k pol ρ s 50, which is too small to see with GPI). This upgrade would probably require a

24 new magnifying telescope inside the vessel, and perhaps a smaller neutral gas injector and a higher resolution coherent fiber bundle. A detailed study of the limiting spatial resolution of the entire GPI system would have to be completed before this was implemented. 6. At the other end of the size-scale spectrum, the present GPI system is limited to k pol ρ s > 0.03, i.e. λ 4 cm, due to the limited size of the injected gas cloud, the limited field of view of the in-vessel optics, and (to some extent) the curvature of the magnetic field. Since the amplitude of the observed turbulence is still high at the low-k end of the spectrum (Fig. 5.3), it would be very interesting to image a larger poloidal length to determine where the k-spectrum begins to fall, and whether there is any coherent structure at these larger scales. This could potentially be done by using multiple and overlapping GPI systems similar to the present one, or by designing an in-vessel fisheye view, or by imaging a large gas cloud in the toroidal vs. poloidal plane from the side. A detailed study of the limiting spatial resolution of the entire GPI system would have to be completed before this was implemented. References 1. S.J. Zweben, D.P. Stotler, J.L. Terry, B. LaBombard, M. Greenwald et al, Phys. Plasmas 9, p (2002) 2. S.J. Zweben, D.P. Stotler, J.L. Terry, B. LaBombard, M. Greenwald et al, Phys. Plasmas 9, p (2002) 3. B. Bai, J.L. Terry et al, Bull. Am. Phys. Soc. 47, 9 p. 236 (APS DPP meeting 02) Comparison with Theoretical Simulations It is crucial to compare the results of these measurements with the best available models and theoretical simulations in order to understand what we are seeing. In FY 03 and FY 04 we will continue to analyze the existing GPI data and work with theorists to compare the GPI results with edge turbulence simulations and models. This process will continue throughout the 5-year plan period, or until a good understanding of the physics of edge turbulence has been obtained. In order to compare experiment and theory it will be important to calculate the expected GPI light emission patterns from the theoretical simulations of the spatial structure of the plasma turbulence. This modeling was begun using DEGAS 2 in Ref. [1] and will be extended so that the full atomic physics and response of the neutral density can be examined. For example, a more detailed atomic physics model allowing the metastable states of HeI to be treated accurately will be added to DEGAS 2, and their impact on the effective density and temperature dependence of the emission rates will be examined (FY-2003). In addition, a toroidally resolved (i.e., 3-D) simulation of the GPI experiment will be developed, including a 3-D representation of the gas puff and the camera field of view. DEGAS 2 modeling of the various proposed hardware upgrades will also be quire useful, e.g. for the two-color imaging, the supersonic gas nozzle, and the extension of the k-spectral resolution of GPI. There are several distinct areas for comparison with theory: 1. 2-D spatial structure and k-spectrum. 2. Presence of zonal flow or streamers. 3. Dynamics of coherent structures (blobs)

25 4. Scaling with dimensionless parameters. 5. Influence of neutral density and/or atomic physics. 6. Effect of boundary conditions, e.g. separatrix and/or limiters. Some details about these theoretical connections are below: 1. The 2-D spatial structure of edge turbulence has already been measured with GPI in C- Mod. The measured k pol wavenumber spectrum agreed fairly well with the 3-D nonlocal fluid simulations of Hallatschek s NLET edge turbulence simulation code, as shown in Fig Further cases with different edge conditions will be examined using the existing system, and the radial wavenumber spectra will also be compared wherever possible. In particular, the behavior near the density limit and will be studied in detail using He puffing into D discharges (or vice versa) to reduce the background from natural plasma light emission, and the results will be compared with the NLET and BOUT codes. 2. Recent turbulence simulations have pointed out the importance of poloidally directed zonal flows and radially directed streamers for the regulation of turbulence and possibly the origin of the H-mode [2]. Although a related coherent poloidal zonal flow called a geodesic acoustic mode (GAM) has been measured in DIII-D using BES edge turbulence data and in TEXT with the HIBP [3], the more interesting broadband, nearzero frequency zonal flows and streamers discussed in most theoretical papers have not yet been identified in experiment. The high-speed 2-D images from GPI in C-Mod should be an ideal way to identify these structures, although it is likely that the larger data sets such as those from the 312 frame PSI-5 camera will be needed. Direct comparison with theoretical simulation of C-Mod will be made where possible. 3. The presence of coherent structures called blobs is obvious from the existing C-Mod GPI data (Figs. 5.1 and 5.2), and simple models for blob motion have been discussed theoretically [4]. A first attempt at comparison of the GPI data with the blob model will be started in FY 03-04, but most likely the model and database will have to be extended in order to obtain a good quantitative comparison. For example, it is not yet clear from either the model or the data where and how blobs are formed or why the observed blobs move poloidally in addition to the usual radially outward blob motion. Hopefully a clear connection between the simplified blob model and the detailed turbulence simulations will also be established over time. 4. Probably the best check of a theoretical model comes from establishing the scaling of the data with the main parameters in the theory. The main local scaling variables of interest are the collisionality, ion gyroradius, beta, and magnetic shear. At present there is relatively little information about the scaling of edge turbulence in general, although there are experimental and theoretical indications that the density limit [5] and the L-H transition [6] are associated with higher and lower levels of turbulence, respectively. A B-field scaling study using GPI data was started on C-Mod in FY 02, and similar studies will be continued in FY and beyond. 5. The potentially important effect of neutrals and atomic physics on edge plasma turbulence and transport has been noted frequently but seldom quantified either experimentally or theoretically. For example, it is clear that edge temperatures and global confinement can be higher with clean and low recycling walls, but it is not understood why. The present or upgraded GPI system can be used to explore these

26 dependences in C-Mod, e.g. by measuring the observed turbulence with various types of deuterium or impurity gas puffs. This type of study is difficult due to incomplete knowledge and control of the edge neutral and impurity profiles, so it will extend over several years. 6. The plasma magnetic and/or limiter boundary conditions are also well known to affect both the edge and global plasma confinement, but few systematic measurements of edge turbulence have been made to clarify these dependences and compare them with theory. For example, the electrostatic potential and spatial distribution of the limiters in the SOL should affect the radial electric field and parallel flow, thus influencing the edge turbulence and transport. Thus it might be possible to introduce biased limiters or electrodes in C-Mod to study to SOL, similar to experiments done on limited machines [7] and planned for MAST. Alternately, a study of the effect of varying gaps between the diverted plasma separatrix and the wall would be interesting and could be compared with simulations. References 1. D.P. Stotler, B. LaBombard, J. Terry, S. Zweben, J. Nucl. Mat , 1066 (2003) 2. P.H. Diamond et al., Nucl. Fusion 41, 0167 (2001); X. Garbet, Plas. Phys. Cont. Fusion F43, A251 (2001), Z. Lin et al, Phys. Rev. Lett. 88, (2002). 3. M. Jakubowski et al, Phys. Rev. Lett 89, (2002); P.M. Schoch et al., Rev. Sci. Inst.74, 1846 (2003). 4. S. Krasheninnikov, Phys. Lett. A 283, 368 (2001); D.A. D Ippolito et al., Phys. Plasmas 9, 222 (2002). 5. M. Greenwald, Plasma Phys. Cont. Fusion F44, R27 (2002); B. LaBombard et al., Phys. Plasmas 8, 2107 (2001). 6. K.H. Burrell et al., Phys. Plasmas 4, 1499 (1997). 7. J. Boedo et al., Nucl. Fusion 40, 1397 (2000) Edge Turbulence Control Experiments Experiments to control edge turbulence have both a practical and an intellectual value. On the practical side, it would be quite useful to be able to change the edge conditions of an advanced tokamak in an externally controllable way; for example, to increase the width of the edge pedestal during an H-mode. On the intellectual side, a well designed control experiment can be an excellent test of the underlying physics; for example, when the control is based on a specific model of edge turbulence. There are several possible edge turbulence control experiments in C-Mod: 1. Edge minority heating for H-mode control. 2. RF sheath effects for edge turbulence control. 3. Edge fueling control (pellets and strong puffs). 4. Lower hybrid current drive for edge control. 5. Localized limiter or electrode biasing. Some details about these edge turbulence control experiments are discussed below:

27 1. In FY 03 and FY 04 we plan to start edge turbulence control experiments with an edge minority heating experiment, which aim to change the edge radial electric field through controlled generation and loss of minority tail ions. An initial calculation by C.S. Chang has indicated that the edge radial electric field can be significantly changed in C-Mod with 1 MW of RF coupling to the minority tail ions. If this method works, it may be possible to externally trigger an H-mode or to increase the pedestal width of an existing H-mode. Even if this technique does not succeed in C-Mod, it would be interesting to study the local effect of RF tail ions on the edge turbulence through GPI measurements. 2. It is well known, and previously seen on C-Mod [1], that DC electric field sheaths can be generated by rectification of the RF-driven currents to the RF antenna structures. Usually these sheaths are considered a nuisance, since they can lead to edge ion acceleration and impurity generation at the antenna. However, some theoretical work [2] has suggested that these sheaths can be used to modify edge turbulence through the flows generated by the resulting convective cells in the SOL. If so, the RF system might be used to control heat and particle transport across the SOL. Initial experiments might be done using the existing RF antennas, and future control experiments could potentially be designed through modeling and simulation. 3. It was recently shown on DIII-D that edge pellet injection can be used to trigger an H- mode below the conventional power threshold [3]. This discovery has already inspired a new model of edge turbulence which emphasizes the role of the local density gradient on the H-mode threshold [4]. We should be able to check and extend these results using the lithium pellet injector on C-Mod, which can inject Li pellets into the edge. If successful, this can lead to an external control for the onset on H-modes in advanced tokamaks. Alternatively, a strong localized deuterium or low-z impurity gas puff may be used, perhaps with the same supersonic nozzle mentioned in Sec Lower hybrid current drive might be a powerful tool for edge turbulence and transport control, since the LH waves can generate localized edge current and possibly fast electrons at the edge. A first step would be to investigate the theoretical dependence of edge turbulence on the local current density. A second step would be to evaluate whether LH waves can create fast electron loss to the wall, which could change the edge electric field similarly to fast ion loss. After the LH system is installed on C-Mod it would be interesting to observe the effect on edge turbulence, and vice versa. 5. Limiter or electrode biasing has been used previously on tokamaks to change the radial electric field profile and, for example, to induce an H-mode [5]. Although this technique is unlikely to be relevant to a burning plasma experiment, it might be used to control the edge on C-Mod and explore the effects of E r on the edge transport, the L-H transition, and the density limit. Initial experiments could be started with a biased probe or small plate inserted into the SOL, and its effect can be monitored using GPI and other edge diagnostics. References: 1. B. LaBombard, private communication. 2. D.A. D Ippolito et al, Nucl. Fusion 42, 1357 (2002). 3. P. Gohil et al, Phys. Rev. Lett 86, 644 (2001). 4. P.N. Guzdar et al, Phys. Rev. Lett. 89, (2002). 5. J. Boedo et al, Nucl. Fusion 40, 1397 (2000)

28 Edge Modeling Extended The toroidally axisymmetric simulations of Ref. [3] of Section incorporate values for the neutral gas conductances between the various parts of the C-Mod divertor and sub-divertor that are necessarily approximate. By definition, these conductances determine the relationship between the neutral pressure near the target plate (set mostly by the plasma parameters) and that at the location of the experimental diagnostics. In reality, the sub-divertor hardware in C-Mod is three-dimensional. The only way to calibrate the assumed axisymmetric conductances is to analyze that three-dimensional structure. A series of neutral pressure measurements with calibrated gas puffs has provided experimental values for these conductances. Because the impact of the plasma on these measurements is either nonexistent (some experiments were done without a plasma present) or modest, they are ideal for use in calibrating a neutral gas transport model. The Alcator C-Mod vacuum vessel and sub-divertor can be represented by an axisymmetric object with localized asymmetries. DEGAS 2 currently utilizes a very flexible code for setting up axisymmetric geometries. Modest extensions of this code allow the required asymmetric objects to be straightforwardly specified. This is all that is required for the simulation of these experiments since the core of the DEGAS 2 code is naturally three-dimensional. A successful benchmarking of DEGAS 2 against these conductance measurements would lay the groundwork for subsequent investigations of the interaction of neutral atoms and molecules with the plasma. For example, simulations of the impact of the divertor bypass on plasma conditions could be revisited. Or, by combining this neutral transport model with more sophisticated plasma transport models such as UEDGE or OSM, the issue of main chamber recycling could be addressed in a quantitative way. Monte Carlo neutral transport calculations are essential to the design of new particle control hardware. In the event that the Alcator C-Mod team opts to install a cryopump on the tokamak, the calibrated DEGAS 2 model could be used to evaluate and optimize the design. The neutral densities routinely achieved in Alcator C-Mod are high enough that reabsorption of photons emitted by excited atoms can alter the neutral atom excited state distribution. M. Adams has previously used the CRETIN code to simulate radiation transport in the C-Mod divertor. However, CRETIN is not currently capable of treating details of the transport of neutral species. Although a coupling between CRETIN and DEGAS 2 is potentially complex and computationally demanding, the prospect of obtaining a self-consistent solution is sufficiently attractive to make the effort worthwhile Reflectometer Extensions The possibility exists for adding additional reflectometer channels at frequencies above 140 GHz. These would allow the measurement of plasma turbulence even closer to the core, and help to gain insight into the behavior and possibly influence of turbulence on internal transport barriers

29 6. RF Physics and Wave-particle Interactions 6.1. Highlights of Recent Research D(H) Minority Heating Experiments The D(H) minority regime has been used extensively for plasma heating in a wide variety of C- Mod experiments for many years. It will continue to provide heating for many of the physics initiatives even after the installation of LH heating hardware in FY03. PPPL scientists have participated in many C-Mod experiments that rely on D(H) minority heating, and we expect to continue active participation throughout the upcoming five year program Mode Conversion Experiments As the minority ion concentration is raised, or as a third ion species is introduced, the launched Fast Wave may mode convert to either an Ion Bernstein Wave or an Ion Cyclotron Wave (first proposed by R. Perkins, PPPL). C-Mod s high RF power level and its new and unique wave propagation diagnostic have allowed a careful investigation of these processes to take place ICRF Modeling A significant part of the PPPL collaborations program on C-Mod has been focused on the development of quantitatively accurate RF simulations packages to support the experimental program objectives and to advance the understanding of the dynamics of electromagnetic wave interactions in inhomogeneous magnetized plasmas. The METS 1D all-orders kinetic wave solver has been used to explore minority heating and mode conversion scenarios in C-Mod, while the TRANSP time-dependent transport analysis code has been used to analyze ICRF heating experiments and to simulate lower-hybrid driven AT scenarios. These simulations studies have been conducted in close collaboration with Dr. Paul Bonoli (PSFC). The transition from the minority heating regime to the mode conversion regime was analyzed with the 1D METS code and compared to the 2D simulations provided by the TORIC 2D FLR kinetic wave code. Though the simulations from both codes agreed moderately well in the low concentration minority heating regime, there was a pronounced disagreement as the minority concentration was raised and mode conversion processes became significant [1,2]. The studies indicated that TORIC was over-predicting the amount of minority ion absorption, probably due to inaccurate solutions for the RF wave fields. Subsequent work by Dr. Bonoli indicated that an insufficient number of poloidal modes were retained in the simulations, leading to poorly converged solutions. By parallelizing the TORIC code and increasing the number of poloidal modes, the first 2D simulations of mode conversion in C-Mod were obtained [3]. Time-dependent simulations of RF heated discharges provide a critical tool for understanding transport and stability of C-Mod plasmas. Towards this end, the TORIC code was implemented in the TRANSP code to provide the capability to model mode conversion as well as minority heating experiments for the C-Mod program [4]. Because the previous ICRF package in TRANSP, SPRUCE, was based on a reduced order algorithm, it was not capable of analyzing experiments in which mode conversion processes are significant. The TORIC code retains both the fast wave and the mode converted waves in the field and power deposition solutions, though

30 its range of validity is restricted to plasmas in which the Larmor radii of the various plasma species is small compared to the perpendicular wavelength of the modes. The upgraded TRANSP/TORIC package was benchmarked successfully against the TRANSP/SPRUCE package in the minority heating regimes. It was subsequently used to study the RF-induced ITB discharges in C-Mod [3]. References 1. C.K. Phillips et al, Modeling of ICRF Experiments in C-Mod, Bull. Am. Phys. Soc. Vol. 44, No. 7 (1999) pg 206, abstract KP P.T. Bonoli et al, Phys. Plasmas 7 (2000) P.T. Bonoli et al., Numerical Modeling of ICRF Physics Experiments in the Alcator C- Mod Tokamak, Proc. 18 th IAEA Fusion Energy Conf. (Sorrento) EXP4/01(2000). 4. C.K. Phillips et al., US-Japan Workshop on Radio Frequency Physics, March 14-16, 2000 (Plasma Physics Laboratory, Princeton, NJ) LH Modeling The TRANSP package mentioned above also includes a lower hybrid package, LSC, which has been used to explore the potential for maintaining AT discharges in C-Mod using lower hybrid current drive Proposed Research The C-Mod ICRF program allows PPPL to participate in a variety of experiments that follow on from our previous work on PLT and TFTR and that complement on-going experiments on NSTX. The advances in wave diagnostics such as the PCI allow more detailed measurements of wave propagation and absorption. This coupled with our improved modeling capability can lead to a much fully understanding of the multi-ion species ICRF application. Mode Conversion Current Drive (MCCD) and flow shear drive were topics just demonstrated but not fully explored or exploited on TFTR. The C-Mod program presents an opportunity to evaluate these regimes for their Advanced Tokamak application. Fast Wave Current Drive is being utilized on the NSTX experiment at high harmonics of the cyclotron frequency. The C-Mod experiment will allow us to explore the same physics in a different parameter regime and to explore the technical issues involved in controlling an effective antenna spectrum for current drive with different plasma edge and antenna geometry. Both NSTX and C-Mod have observed transport barriers in the presence of RF heating. Exploiting these barriers, as C-Mod has already begun to do with their density control experiments, will be important for achieving the potential of the Advanced Tokamak D( 3 He) Minority Heating Experiments These experiments were initiated on PPPL s PLT tokamak. C-Mod allows a valuable extension into its unique parameter space, with additional and new diagnostics for increased experimental information. These measurements will then allow detailed comparisons with the D(H) minority heating scenario to be performed

31 FWCD experiments FWCD is useful in AT discharges to provide on-axis current drive and q(0) control. The FWCD experiments on C-Mod will be complimentary to those on NSTX since on-axis current drive minimizes the reduction in current drive efficiency due to electron trapping and the required antenna spectral control is different since combined radial position control and high efficiency are not simultaneous constraints. On the other hand, the issues of edge plasma interaction with asymmetric antenna phasing will be important on both machines while other edge parasitic effects may or may not be similar MCCD experiments MCCD can be utilized for on or off-axis supplemental current drive. On TFTR efficient current drive was seen under both conditions. On C-Mod, the PCI diagnostic will allow a better measurement of the correlation between the wave damping and the driven current. The mode conversion scenario also naturally leads into flow drive studies Flow drive studies RF-driven poloidal flow offers the possibility of stabilizing turbulence locally and generating Internal Transport Barriers. These experiments were initially attempted on TFTR in its last months of operation with the just-installed poloidal rotation diagnostic, with incomplete success. In fact, data analysis took place after the end of TFTR experiments. Subsequent theory and modeling work has increased interest in this type of rotation control. C-Mod s higher RF power density and the added and new diagnostics will increase our information yield considerably LH wave physics These experiments will study Lower Hybrid wave launching, propagation, and damping and power deposition. Launcher-plasma separation and phasing will be varied systematically until the optimum directed wave is achieved LHCD physics The purpose of the installation of the LH system is to provide a capability to drive the right amount of current at a selected radial position to modify the current profile as desired. This phase of the experiment will require a considerable experimental time as many parameters will have to be adjusted to obtain the control of the driven current. Throughout the LHCD physics experiments, an X-ray diagnostic will provide some information about the power deposition profile and possible radial diffusion of energetic electrons, but the most essential diagnostic is Motional Stark Effect to measure the radial location of driven currents and changes in the q-profile RF Modeling

32 The C-Mod program will be embarking on a campaign to study the dynamics of long pulse AT plasmas, supported by high bootstrap current fractions, ICRF heating and current drive, and lower hybrid current profile control. The TRANSP / TORIC / LSC package, which provides the ability to analyze the transport properties of these long pulse AT discharges, will be utilized to support the AT experimental program on C-Mod. A new version of the TORIC code, which corrects difficulties encountered in previous version with spurious edge modes, is being tested and installed in TRANSP collaboratively by PPPL [Douglas McCune, C.K. Phillips, B. LeBlanc and the PPPL-CPPG group], the IPP-Garching group [M. Brambilla] and the C-Mod team [Paul Bonoli and John Wright]. Depending on guidance provided by more sophisticated but timeindependent modeling studies with the ACCOME, TORIC and CQL3D packages as well as with comparison to experimental observations, the LSC package may be upgraded or replaced with a more complete model. These simulation studies will be conducted in close collaboration with the C-Mod team. A potentially important aspect of both the lower hybrid and the ICRF studies will be the inclusion of non-maxwellian electron and ion particle velocity distributions in the wave field and absorption calculations. As part of the RF SciDAC collaborative project [1] both the METS 1D and the TORIC 2D full wave modeling codes are being modified to incorporate the effects of non-maxwellian species on both the wave propagation and absorption. This work will continue after the completion of the SciDAC project in July In the lower hybrid regime, previous numerical and theoretical studies have indicated the lower hybrid wave-induced non-maxwellian electron distribution function can play a key role in filling in the spectral gap and in improving the overall current drive efficiency [2]. On C-Mod, fast electron distributions will be measured in the core plasma using imaging hard x-ray spectrometry. These measurements, along with current density measurements from MSE, will be used to benchmark and verify the physics contained in the generalized METS1D and TORIC-LH simulation codes. In minority ICRF heating regimes, nearly 30 years of experimental and theoretical studies have demonstrated that an energetic, non-maxwellian ion tail distribution can be driven by the RF waves. Similarly, fusion-born alpha particles, which are highly energetic and non-maxwellian, will be a significant component in burning plasmas. These energetic ion populations may alter the wave absorption, propagation and mode conversion properties of these discharges. Detailed experimental studies of the dependence of ICRF mode conversion processes on the plasma composition, the plasma density, and the spatial location of the resonance, mode conversion and cutoff surfaces will be compared to simulations from the METS and TORIC codes. These studies will provide the basis for understanding the relative importance of these processes in AT scenarios and in future burning plasmas. References 1. SciDAC research program Numerical Computation of Wave-Plasma Interactions in Multi-dimensional Systems D.B. Batchelor, L.A. Berry, M.D. Carter, E. F. Jaeger, E. D'Azevedo (ORNL); C.K. Phillips, A. Pletzer (PPPL); P.T. Bonoli, J. C. Wright (MIT); D.N. Smithe (Mission Research Corporation); R.W. Harvey (CompX Corporation); and D.A. D'Ippolito, J.R. Myra (Lodestar Research Corporation). 2. S. Bernabei et al., Phys. Plasmas 4 (1997)

33 7. Theory and Computation of Macroscopic Stability 7.1. Overview Macroscopic stability is central to the theory of magnetically confined plasmas. A configuration that violated the ideal-mhd stability criteria would rearrange itself in a time comparable to the Alfven-wave transit time, which is sub-microsecond in modern devices. Configurations that are stable to ideal-mhd must also be examined for stability to dissipative and kinetically-driven modes that can destroy magnetic surfaces, shed energetic particles, and/or lead to discharge termination. The dominant theme in the near term tokamak research is to strengthen the physics basis for the International Thermonuclear Engineering Reactor (ITER). The critical topics as listed by the International Toroidal Physics Activity (ITPA) topical physics group on MHD, Disruption and Control are listed here and described more in the following sections: Beta limiting MHD modes and their active control [including neoclassical tearing modes (NTM), kink modes, and resistive wall modes (RWM)] Edge MHD stability and the behavior of Edge Localized Modes (ELMs) The prediction, avoidance, and mitigation of disruptions in tokamak plasmas with edge safety factor q 95 ~ 3. This includes calculating forces due to halo currents during disruptions, and the prediction, avoidance, and mitigation of large runaway populations during disruptions Control issues in standard and advanced scenarios: shape and position, performance including profile control with emphasis on integrated scenarios for burning plasma experiments. Formally, the PPPL / Alcator C-Mod collaboration does not include direct financial support for theory and computation of macroscopic stability physics issues. However, Alcator C-Mod can access regions of parameter space that are not obtainable in other tokamak facilities, and as such it provides a very useful benchmark for comparison against macroscopic stability theory and various codes. In some cases the Alcator C-Mod parameters are closer to those expected in burning plasma experiments. There is continuing interest within the PPPL macroscopic theory and computation groups to work closely with the Alcator C-Mod scientific staff over the program period for theory/experiment tests Model Development Ideal MHD Ideal MHD theory and computations are now quite mature. The PEST I/II codes have been the community standard for evaluating linear ideal MHD stability in axisymmetric devices for some years. We continue to support these codes, to improve them, to support the use of these codes to benchmark and validate newer codes, and to apply them to new applications. Applications include continuing efforts to understand and optimize the current and pressure limits of toroidal devices, and their sensitivity to plasma shaping and profiles

34 An active emphasis area for tokamaks is to better understand the role of ideal MHD in the transport barrier in reversed shear discharges, and the role of current on the open field lines (halo currents) in providing stability to diverted discharges, and the role of moderate-n ideal MHD Modes in ELMs Two-fluid Extended-MHD Two-fluid Extended-MHD models utilize fluid-like equations for the electrons and the ions where the difference in their relative velocity and the anisotropy of the pressure tensor are accounted for. There is not presently a universally agreed-upon unique form for the two-fluid equations in a fusion plasma. The theoretical challenge is to define the ion and electron stress tensors and heat fluxes in a way to include finite (ion) Larmor radius (FLR) effects (which lead to gyroviscosity) and the effect of long collision lengths parallel to the magnetic field, including magnetic particle trapping (important in neoclassical effects). Defining appropriate closure relations and testing their regions of validity is an important and long-term activity. The M3D code now has the capability for including the ion-gyroviscous contributions to the ion stress tensor, and for taking into account the difference in the ion and electron fluid velocities. These extensions account for several important physical effects, including the omega-star stabilization of ideal and resistive MHD modes, and the Hall term in Ohm s law, which can greatly speed-up magnetic reconnection. This capability has enabled a whole new class of simulations where we should be able to explain many new experimental phenomena that cannot be explained by resistive MHD alone. For example, without these terms, resistive ballooning modes are seen to go unstable in the simulations where they are not observed in the experiments. These terms are also essential to get the trigger and the crash time for the sawtooth. We note here that an in-depth study of these important phenomena will take many years because of the need to perform many cross-checks, including analytic, cross-code, and experimental comparisons. Numerical resolution and stability requirements also need to be clarified. (2004/7) Simulate the effect of the two-fluid terms on tokamak sawteeth and axisymmetric reconnection events (current hole). Benchmark with experimental results as available Kinetic Extended-MHD To model the nonlinear interaction of ions with MHD waves and to include large gyro-orbit and neoclassical effects more self-consistently, we have developed several hybrid methods, where either an energetic ion component or the whole ion population are modeled using the gyrokinetic or drift kinetic equations. In the methods implemented so far, the ion fluid velocity is calculated by solving the momentum equation, and the calculated ion fluid velocity is used in the Ohm s law, assuming quasineutrality. The ion pressure tensor is taken to be in the CLG form and the gyroviscous part of the stress tensor is calculated from the particles. Hot particle populations, for example fusion-produced α-particles or injected neutral beam ions, can be simulated by combining a gyrokinetic hot particle population with a fluid model for the background We have linear codes that calculate the self-consistent interaction of energetic-ion populations with MHD modes: NOVA-K (and NOVA-KN is the nonperturbative version) for modes with low to medium toroidal mode numbers (n), and HINST for high-n modes. We have now

35 completed the project of incorporating a high-energy particle component in the massively parallel unstructured mesh nonlinear MHD code M3D. This represents a unique capability for studying the nonlinear development of energetic particle modes in shaped geometry, of arbitrary aspect ratio fusion devices. It is thus applicable to interpret results from NSTX and present day tokamak and stellarator experiments, and is also a unique tool for assessing the effects of energetic particle modes in a burning plasma. New exploratory applications of this code are being carried out even as it is being benchmarked against theory, the linear-codes, and other non-linear codes. (2005/6) Use NOVA codes to predict the nonlinear mode saturation as well as the alpha particle induced transport in burning plasmas. (2004/6) Model experiments in CMOD with NOVA and HINST codes for better understanding the TAE and energetic particle resonant mode in conditions of the multiple mode excitation. (2004/5) Extend the M3D capability to allow kinetic representation of majority ions in a nonlinear calculation. Benchmark with experimental results as available (2004/8) Simulate the effect of the kinetic terms on tokamak sawteeth with M3D. Benchmark with experimental results as available. 7.3 Beta limiting MHD modes Sawtooth Phenomena The sawtooth instability, present when the current in the tokamak peaks sufficiently so that the central safety-factor is below the stability criteria, is a concern for the next generation of inductively driven burning plasma experiments: including ITER, FIRE, and IGNITOR. These modes introduce an intrinsic non-axisymmetric nonlinearity into the device that can interact with other modes to degrade confinement, shed energetic particles, or induce a disruption. Previous work on the onset conditions for the sawtooth instability needs to be revived and extended to the burning plasma regime. Excellent agreement has been obtained between a theoretically motivated criteria and TFTR data for the occurrence of sawtoothing. The relevant physical effects need to be incorporated into the 3D Extended-MHD code to develop a fully predictive model for when sawteeth occur, what their period is, and how they interact with other modes. There is also interest in modifying the linear stability codes to more effectively deal with the q 0 <1 problem. (2004/5) Perform a systematic study of the sawtooth in the CDX-U tokamak using realistic values of parameters. (2006/8) Compute sawtooth behavior in CMOD plasmas with strong RF heating and compare with experimental results as available. (2008) Study n=1 sawtooth in a burning plasma Neoclassical Tearing Modes The Neoclassical Tearing Mode (NTM) is observed to set the pressure limits in many long pulse discharges. One of the major thrusts of the non-linear MHD effort is to include sufficient physics to simulate the NTM and to differentiate between the competing mechanisms, for which an anisotropic thermal conduction model and a neoclassical closure for the ion and electron viscous stress tensors are essential. The goal of this work is to extend the scaling of the NTM

36 threshold to large devices and investigate relative changes in the importance of the different threshold mechanisms. Another issue is whether the plasma can generate a seed island of sufficient width to exceed the NTM threshold. A wide range of mechanisms have been observed as precursors to NTMs, including the sudden onset of the internal kink, coupling to magnetic field errors, coupling to the magnetic perturbation of an Edge Localized Mode (ELM), and transition from resistive tearing to neoclassical tearing. Another issue is to better explain the cause and effects of island rotation. The M3D two-fluid model should contain the relevant physics needed to realistically simulate the growth of this mode, but the problem is challenging because of the very slow growth rates, necessitating long running times. The PIES code provides a complementary approach to NTMs. Because the mode grows on a resistive time scale, radial force balance is maintained, and the dynamical nonlinear evolution is described by Faraday s law, a three-dimensional equilibrium code with the correct constraints can be used to calculate the evolution. In collaboration with the stellarator group at NIFS in Japan, a three-dimensional bootstrap code has been coupled to PIES, allowing the calculation of the perturbed bootstrap current that drives the NTM. The predictions of the bootstrap code have been benchmarked against Monte Carlo calculations with the ORBIT code, and this has led to an improvement in the bootstrap model near resonant surfaces. At present, PIES maintains a flat current profile in the islands, appropriate to saturated modes. A future upgrade of the code will introduce gridding in the island interiors, allowing the code to follow the island evolution. The M3D and PIES efforts are complimented by several other activities in this area. One is to evaluate the semi-analytic formulas of Hegna, et al, using the PEST-III code to calculate delta-prime. (2006/8) Develop a predictive model of neoclassical tearing modes in tokamaks Energetic Particle Modes We plan to further investigate resonant destabilization of discrete and continuum Alfven modes by energetic particles such as fusion alphas or beam-injected ions. This effort includes toroidal Alfven eigenmodes (TAE), "fishbones", high beta modes (BAE) and energetic particle modes. Current emphasis is on including more realistic models that take into account realistic geometry, non-maxwellian background distribution functions, and self-consistent mode structure so that the energetic particles are included non-perturbatively. Our interest is in both conventional and reversed-shear plasmas. Long term goal is to provide quantitative reliable prediction of the amplitude saturation of collective modes and consequences for ITER, such as alpha particle transport and its effect on plasma burning. (2004/5) Carry out a systematic comparison of energetic particle effects in M3D with other linear and non-linear codes, as available. (2004/5) Perform a study of nonlinear effects of alpha particle modes in burning plasma including excitation of the TAE and fishbone modes and stabilization of the sawtooth 7.4 Edge MHD Stability and the behavior of ELMs

37 The long term goal of this work is to understand the origin and dynamics of the edge localized modes, to make contact with the theory to the experimental characterization of (Type I, II, III and quiescent), and to understand under what conditions a burning plasma can access small ELM regimes Linear Analysis Detailed comparison of the results of linear ideal MHD analysis and experimental results show a good correlation between the stability criteria for intermediate-n ideal peeling/ballooning MHD mode stability and Edge Localized Mode (ELM) activity in experiments. These calculations can provide indications of what the critical gradients are, as a function of edge current density, for edge-localized MHD modes, and what the height of the H-mode pedestal is. What remains to be determined is the width of the region over which the plasma pressure profile can assume the critical value, and the nature of the trigger mechanism for the ELM Nonlinear Physics of ELMs & Evolution of Free Boundary Modes The M3D code is being extended to allow for real free-boundary modes, where a vacuum region surrounds the plasma, which is in turn surrounded by a conducting wall. This requires substantial code development and optimization. The primary application of this extension will be to ELMs, although it will also be useful in the calculation of resistive wall modes (RWMs), as well as for a more realistic description of primarily internal modes, and the onset of plasma disruptions. The goal is to make closer contact with the ELM cycles observed in experiments, and to identify under what conditions the different ELM types will occur: i.e., Type-I, Type-II, etc. (2006/7) Begin the nonlinear study of free boundary modes in tokamaks and stellarators. 7.5 Prediction of the Cause and Effect of Disruptions For tokamaks, the highest performance discharges are often terminated by a major disruption. This event causes rapid loss of thermal energy during the thermal quench phase and then loss of current during the current quench phase. The current quench phase also produces large electric fields that can accelerate substantial populations of electrons to the runaway regime by way of the avalanche process. In reactor scale devices, structural, divertor tile, and first wall damage caused by disruptions is a major concern Physics of the Disruption For the tokamak to succeed as the embodiment of a Fusion Power Plant, we will need a much better understanding of the mechanisms that lead to major disruptions. MHD simulations have been used to identify the mechanism of a particular type of high-ß disruption in the Tokamak Fusion Test Reactor (TFTR): a localized moderate-n ballooning mode nonlinearly destabilized by an internal kink. Further studies with more resolution and improved physics models will be done to produce accurate criterion for such instabilities, which may shed light on ways to control or avoid them. Other disruption mechanisms need to be studied, such as the overlap of islands, and the coupling of sawteeth modes with NTMs and ELMs. These studies will necessitate many different nonlinear code runs with a credible physics model to build up a better understanding of

38 the different sequences of events that lead to disruptions, their statistics, and their dependence on tokamak operating parameters. Another, related, thrust, is to understand the difference in disruption mechanisms between tokamaks, current-carrying stellarators, and spherical tori. Of particular interest is to understand how externally generated transform provides some level of disruption protection. (2004/8) Identify mechanisms for disruptions in tokamaks and operational regimes that are free from these mechanisms Disruption Forces We have developed a detailed axisymmetric model of disrupting tokamaks with the TSC code. This included a model of the thermal quench, current quench, halo currents, runaway electron generation, and the surrounding coils and structure. We have used this to study disruption prevention and mitigation techniques in tokamaks. There is continuing need to apply these tools to ITER in order to evaluate specific mitigation techniques, such as massive impurity injection and massive gas injection by way of supersonic gas jets, extending previous killer pellet injection simulations. There is also a need to calculate the vessel forces due to the non-axisymmetric nature of the disrupting plasma. These non-axisymmetric halo currents have been identified by the ITPA as a critical item affecting the design of ITER. The vacuum and resistive wall additions to the nonlinear code M3D have enabled it to address these issues. (2004/2005) Calculate the range of expected non-axisymmetric halo currents in ITER. Benchmark these calculations with CMOD data as available. 7.6 Control Issues Profile and Shape Control The Tokamak Simulation Code (TSC) is a widely used tool for predicting the axisymmetric evolution of tokamaks and spherical torii. It solves for the transport-timescale evolution of the plasma parameters as well as the poloidal field coil currents and their associated control systems and vessel currents. It was chosen by the ITER project as the standard code for projecting Voltsecond requirements, plasma evolution, plasma shape control and several other functions. We plan to keep developing TSC as the premier code of its type, and to continue to perform new calibrations as available, and to use it to design new experiments and to help optimize existing experiments as required. Recent applications of TSC include the study of tokamak startup by bootstrap overdrive, and a study of methods to prevent the production of runaway electrons in disrupting tokamaks. Future development will concentrate on incorporating better current-drive modules, a better neutral beam package, and incorporation of a more modern graphics package The Physics of Pellet Fueling

39 Injecting small pellets of frozen hydrogen into a tokamak is known to be a viable method of fueling. Early work by Parks, et al. gives a fairly accurate expression for the ablation rate for such pellets once they contact the high temperature plasma in the tokamak. However, it is known from many experiments that the resulting density profile measured after the pellet has ablated is not consistent with what one would infer by assuming the ablated material remained on the flux surfaces where the ablation occurred. The subsequent anomalous redistribution of mass is believed to be due to MHD processes. This mass redistribution is most dramatic in experiments that compare density profiles resulting from outside launch and inside launch, referring to if the pellet is injected from the exterior, low field side of the torus or the interior, high field side. It has been clearly demonstrated that pellets injected from the inside are more effective in fueling the center of the plasma. Near vertical launch is also an attractive option for next-generation experiments. In an initial attempt to model this mass redistribution, the M3D code has been used to model the evolution of a localized density blob in a tokamak, and has verified that MHD effects cause the localized density perturbation to displace towards the low-field side of the plasma. However, this simulation did not have a pellet ablation model, did not follow the pellet trajectory, used single-fluid resistive MHD, and the resolution was fairly coarse. We are extending this modeling in several ways with a new Adaptive Mesh Refinement (AMR) MHD code AMRMHD, developed in conjunction with an applied math group at Lawrence Berkeley Laboratory (LBL). The model being developed has two-fluid physics, the Parks pellet ablation model, anisotropic heat conduction, and adaptive zoning to allow accurate modeling of the expected range of space scales. (2004/2005) Develop a realistic 3D model of pellet injection into a CDX sized plasma (2006/2007) Extend this model, benchmarking as available on CMOD Internal Mode Control It has been demonstrated experimentally that both the sawtooth and the NTM can be controlled by the application of RF heating and current drive. Our goal is to develop theoretical models of this stabilization and to use these models and simulations to interpret and extend the region of applicability of the experiments. It has been demonstrated on JET and other tokamaks that application of ICRH near the q=1 resonant surface can delay or completely stabilize the sawtooth. We propose to study this phenomena from a fundamental level. There are now RF absorption codes that can accurately calculate the absorption of RF waves in fully 3D geometry and the resulting modification of the distribution function. We plan to couple these with the nonlinear 3D Hybrid/MHD code to assess the relative importance of current drive, plasma pressure modification, and energetic particles in controlling this mode. This modeling should be of direct benefit to ITER, as they would like to have the flexibility to control the sawtooth if it becomes necessary. Where NTMs cannot be avoided, active stabilization is required. Both lower hybrid wave and electron-cyclotron emission current drive have been proposed and tested experimentally as mechanisms for stabilizing tearing modes through the generation of current and heat in the vicinity of an unstable island. We propose implementing existing fluid-like models of RF driven current in M3D to investigate the feedback stabilization of NTMs

40 (2006/7) Simulate RF stabilization of a MHD mode through integrated modeling using a coupled RF and 3D MHD code 7.7 Appendix: Macrostability Codes Supported by PPPL Theory Department Free Boundary Evolving Axisymmetric Equilibrium TSC is the Tokamak Simulation Code developed at PPPL and used extensively at Princeton and throughout the world. It can model the evolution of a free-boundary axisymmetric tokamak plasma on several different time scales. The plasma equilibrium and field evolution equations are solved on a two-dimensional Cartesian grid, while the surfaceaveraged transport equations for the pressures and densities are solved in magnetic flux coordinates. An arbitrary transport model can be used, but the Coppi-Tang model is used most frequently. Neoclassical-resistivity, bootstrap-current, auxiliary-heating, currentdrive, alpha-heating, radiation, pellet-injection, sawtooth, and ballooning-mode transport models are all included. As an option, circuit equations are solved for all the poloidal field coil systems with the effects of induced currents in passive conductors included. Realistic feedback systems can be defined to control the time evolution of the plasma current, position, and shape. Required voltages for each coil system can be output as part of a calculation. Vertical stability and control can be studied, and a disrupting plasma can be modeled. TSC can also be run in a "data comparison" mode, in which it reads specially prepared data files for the PBX-M, TFTR, or DIII-D experiments. For each of these, a special postprocessor is available to directly compare TSC predictions with both magnetics and kinetics data for particular shots from these experiments. In all modes, TSC calculates the ballooning-mode stability criteria internally, and it also writes files that are read by the PEST code to calculate ideal and resistive stability for low-n mode. Inverse Equilibrium The JSOLVER code uses the iterative metric method to simultaneously solve for plasma equilibrium and the magnetic flux coordinates. During each iteration, it solves an ordinary differential equation for the toroidal field function g so that the surface averaged parallel current density take on a prescribed form. It has an automatic zone doubling feature to allow efficient generation of high accuracy equilibrium. The ESC Code uses a second-order generalized Newton s method to solve the nonlinear Grad-Shafranov equation. For solving the intermediate linearized Grad-Shafranov equation, it uses either the gridless (sweeping) technique (which guarantees a prescribed accuracy) or the Runge-Kutta (faster) method. 3D Nonlinear MHD Equilibrium The PIES code solves for 3D MHD equilibria without making any assumptions about the form of the magnetic field. It is therefore capable of handling equilibria with islands and stochastic regions, and with a divertor. For tearing unstable plasmas, the code can solve directly for the nonlinearly saturated state of the island, and can be used to track the island

41 as plasma profiles are varied. The code has been used to study error field effects, locked modes, and tearing modes in tokamaks, stellarator equilibria, and 3D tokamak equilibria with ripple. 3D Nonlinear Time-Dependent MHD The code M3D is a nonlinear resistive compressible 3D MHD code. It is a fully toroidal code with no expansion approximation being used. It is an initial value code, and is run analogous to running an actual experiment. As in the experiment, the initial conditions, such as initial density, temperature, and q profiles are first determined. Then, again as in the experiment, the boundary conditions, such as the voltage at the wall, determine the time evolution of the plasma discharge. The code can be run either using a finite difference structured mesh or a finite element unstructured mesh. The code uses a stream function/potential representation for the magnetic vector potential and velocity that has been designed to minimize spectral pollution. The basic solution algorithm is quasi-implicit in that only certain terms in the fluid part that are the most time-step limiting are solved for implicitly, with explicit differencing being used for the remaining terms. M3D, the twofluid version M3D-T, and the particle/mhd hybrid version M3D-K are components of M3D project. The AMRMHD code was developed in conjunction with the APDEC center at LBL, making use of their CHAMBO general adaptive mesh refinement software package. The code solves the MHD equation using a second-order in time generalized 8-wave upwind scheme for solving the MHD equations. The code is fully parallel, and has the feature that zones use timesteps proportional to their linear dimension, resulting in a very efficient method for resolving problems with multiple space scales. Linear Ideal low-n Linearized stability analysis code based on a minimization of the Lagrangian. Uses a finite element technique, PEST-I solves for all three vector components of the displacement and returns a physical growth-time. PEST-II is a linearized stability analysis code. Variational code which minimizes a scalar form of the Euler- Lagrange Eqns. obtained, using a model kinetic energy. Linear Ideal high-n The BALLOON code integrates the 2nd order ODE to find ballooning stability limits and the critical-n from a WKB approximation. The Mercier criterion is calculated and a choice of K.E. norm is available. Output includes contours of local magnetic shear, curvature, and dw contributions from the various driving terms. The CAMINO code constructs the s-a stability curves generalized to arbitrary 2-D tokamak equilibria. The curves from all the flux surfaces generate a 3D stability ballooning boundary in (s, a, y). This can be used to tailor the plasma profiles to achieve the 2nd region of stability or optimize the b for the 1st region. Linear Non-Ideal low-n

42 PEST-III is an outgrowth of the PEST-II code that is used to calculate resistive instabilities. It uses singular finite element techniques to compute the jump in the logarithmic derivative of global mode eigenfunctions across singular surfaces. This information gives the quantity known as delta-prime, which determines the stability with respect to resistive instabilities. This delta-prime also enters into the theory for the evolution of the neo-classical tearing mode. Linear low-n MHD + Particles The NOVA-K code (and its non-perturbative version NOVA-KN) computes stability of global MHD and non-mhd modes in the presence of energetic particles such as NBI and ICRF heated particles and alpha particles for tokamaks with noncircular flux surfaces. The NOVA-K code makes use of a kinetic-mhd formalism that includes kinetic effect through particle pressure in the momentum equation. The plasma pressure is calculated from the particle distribution governed by the gyrokinetic equation including finite orbit width and Larmor radius effects. The NOVA-KN code includes particle perturbed pressure into the eigenmode equation and solves it iteratively for the mode structure and eigenfrequency. Linear high-n MHD + Particles The HINST code computes space structure and stability of high-n modes such as TAE and ballooning modes in the presence of energetic particles such as NBI and ICRF heated particles and alpha particles for high beta tokamaks with noncircular flux surfaces. The HINST code makes use of the Ballooning in poloidal and Fourier in radial directions formalism to determine the global mode structure and stability. It can be used in two forms to provide the local (1D in ballooning variable) and the global solutions (2D in ballooning and radial variables). It is non-perturbative and includes such effects as particle finite orbit width and Larmor radius. Vacuum and Active Feedback In the VACUUM code, the magnetic scalar potential is solved from Laplace's equation using a collocation-green's function method to calculate the vacuum contribution to dw for three topologically distinct wall shapes - toroidal, spherical, and segmented. It calculates the vacuum response in either a Fourier or a Finite representation in the poloidal angle. It also reads the output from stability codes and calculates the eddy current pattern on the shells and also simulates the Mirnov loop readings. A thin resistive shell is now an option and the coding for feedback simulations is being added. 8. Facility PPPL has designed and fabricated technologically challenging hardware additions to the C-Mod facility where needed to allow extension of the plasma parameter space or diagnostic capability

43 8.1. Highlights of Recent Research Rework of 4 ICRF transmitters PPPL RF engineers provided active participation in the rework of C-Mod s ICRF transmitters for enhanced reliability and performance. Circuit improvements and spare components were brought from the PPPL ICRF system on TFTR, and our engineers spent weeks working with their C-Mod counterparts to perform modifications and final checkout Fabrication, installation, upgrading of 4-strap ICRF antenna Bringing our experience from experiments performed on the PLT and TFTR tokamaks, the ICRF group at PPPL designed and fabricated a new 4-strap antenna intended for high-power ICRF heating and current drive on C-Mod. Available port and interior space resulted in an extremely compact, high power density design. Active participation in its operation and the retrofits performed as the result of the detection of operating deficiencies have helped to raise its power level above 3 MW so far, with no deleterious effects on the plasma

44 Ongoing ICRF engineering support The PPPL RF engineering group provides active support to the C-Mod ICRF (and LH) experiments through close communication with C-Mod engineers, resulting in exchange of ideas and experience, and hands-on participation in hardware modification and transmitter retuning Completion of LHCD launcher

45 Again bringing experience from PPPL experiments, this time LH and LHCD studies on PBX, our RF group designed and fabricated a Lower Hybrid launcher to provide ~2 MW of directed wave power for C-Mod experiments. This launcher will be used in conjunction with C- Mod s 4.6 GHz RF power system, and will be utilized to provide the off-axis current drive crucial to C-Mod s Advanced Tokamak program Proposed Research LHCD launcher #1 installation and commissioning The commissioning of the new LH system essentially consists in confirming the accuracy of the phasing system and determining the best radial position of the front end of the launcher for best coupling. All this is obtained by monitoring the reflection coefficient in each waveguide and the total value for various phasings