High-Resolution Detection and 3D Magnetic Control of the Helical Boundary of a Wall-Stabilized Tokamak Plasma

Transcription

1 1 EX/P4-19 High-Resolution Detection and 3D Magnetic Control of the Helical Boundary of a Wall-Stabilized Tokamak Plasma J. P. Levesque, N. Rath, D. Shiraki, S. Angelini, J. Bialek, P. Byrne, B. DeBono, M. E. Mauel, G. A. Navratil, Q. Peng, D. Rhodes and C. Stoafer Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA Corresponding Author: JPL2131@columbia.edu Abstract: We report high-resolution detection of the time-evolving, three-dimensional (3D) plasma magnetic structure of wall-stabilized tokamak discharges in the High Beta Tokamak Extended Pulse (HBT-EP) device. Measurements and control experiments are conducted using a newly-installed adjustable conducting wall made up of 20 independent, movable, wall segments that have been precision located and equipped with 120 modular control coils and 216 poloidal and radial magnetic sensors. The control coils are energized with high-power solid-state amplifiers, and massively-parallel, high-throughput feedback control experiments can be performed using low-latency connections between input and output CompactPCI modules and a graphics processing unit (GPU). The time evolution of unstable and saturated wall-stabilized external kink modes are studied in detail with and without applying magnetic perturbations with the control coils. The 3D dynamic structure of the magnetic field surrounding the plasma is defined with biorthogonal decomposition using the full set of magnetic sensors without the need to fit either a Fourier or a model-based basis. Naturally occurring external kinks are composed of independent helical modes, frequently having m/n = 3/1 and 6/2 helicity, that are seen to modulate each other in time. When magnetic perturbations are applied by energizing the control coils, the resonant magnetic response can be either linear, saturated, or disruptive depending upon the amplitude of the applied perturbation and on plasma s current profile and rotation rate. Active feedback experiments have been conducted using 40 magnetic sensors and 40 control coils, and initial results show mode amplification and suppression as a function of feedback phase angle. 1 Introduction Understanding and control of the plasma s 3D helical structure are important to optimizing the performance of external kink/resistive wall mode feedback systems [1, 2], error field correction [3], and edge localized mode (ELM) mitigation [4]. MHD control physics and knowledge of the plasma s multimode response [5, 6] to magnetic perturbations are relevant to successful operation of ITER and future burning plasma experiments [7].

2 EX/P FIG. 1: Schematic of the new instrumented control wall in HBT-EP. 120 control coils of varying angular extent surround the plasma, and 236 in-vessel magnetic sensors allow detailed measurement of the 3D magnetic structure evolution. The High Beta Tokamak Extended Pulse (HBT-EP) is designed to study β-limiting MHD instabilities [8, 9]. A fast start-up ( 9 ka in 100 µs) followed by a current ramp of 2.5 ka/ms creates strong current gradients near the plasma edge, producing currentdriven kink modes. The unique adjustable conducting wall in HBT-EP has allowed detailed studies of kink stabilization as a function of the wall geometry [10, 11, 12, 13]. Passive kink stability can be studied by moving the wall itself, instead of simply changing the location of the plasma with respect to a fixed wall. HBT-EP has also pioneered the use of active magnetic feedback to control the resistive wall mode (RWM) [14, 15, 16, 17, 18]. RWMs have been suppressed or enhanced as a function of feedback parameters. This paper describes recent experimental results focusing on kink mode rigidity [13], high-resolution MHD spectroscopy [19, 20], and feedback using a graphics processing unit (GPU) based control system [21]. Naturally occurring 3/1 and 6/2 kink modes are observed to exhibit non-rigid behavior. Applied 3D fields have been large enough to induce nonlinear effects including major disruptions and saturation of the resonant plasma response. Initial feedback experiments with the new control system produce mode amplification or suppression, accompanied by acceleration or deceleration of the mode. 2 High-Resolution Measurements and Mode Control Multimode kink structures in HBT-EP can be characterized accurately using the new set of 216 magnetic sensors that were installed close to the plasma surface in Figure 1 shows the upgraded sensor set with all passive-stabilizing wall segments in their standard fully-inserted positions. All sensors are pickup coils, measuring B/ t via a voltage induced around a loops of wire. Both the radial and poloidal magnetic fields are recorded with high-speed digitizers allowing reconstruction of the time-evolving helical field from

3 3 EX/P4-19 the wall to the plasma surface and comparison with the 3D electromagnetic code, VALEN [22]. Simultaneous measurements of B r and B θ allows calculation of the magnetic stress tensor and torque on perturbed currents from the wall or externally applied fields. In addition to the pickup coils, 20 sensors on a movable radial array measure B θ directly through the Hall effect. Three distinct sets of 40 active coils of varying toroidal extent are mounted on the wall segments for applying non-axisymmetric control fields. Currents in the coils are controlled by 40 independent amplifier outputs, and allow application of radial fields up to 70 G at the plasma surface. Further details of the sensors and control system are given in Reference [9]. 3 Non-rigidity of Kink Modes In HBT-EP, external kink structures are strongly linked to resonances with the edge safety factor. Transitions between different poloidal mode numbers as the edge-q changes are expected since the q = m/n resonant surface moves. Long-wavelength n = 1 modes are typically the most unstable perturbations, however we have observed many interesting cases where harmonics of the dominant mode, sharing the same helicity, become significant. The harmonics are often independent of the primary mode, and can sometimes dominate the overall mode structure for brief periods. An exemplary case showing interaction of a dominant m/n = 3/1 mode with a secondary 6/2 mode is seen in Figure 2. Between 4 and 5 ms, the edge safety factor is measured to be relatively constant near 2.7. Poloidal field fluctuations during 4 5 ms are shown in Figure 2(a-b). The contour plots clearly reveal a rotating 3/1 structure dominant for most of the time window. However, near 4.2 ms and 4.4 ms the mode behavior changes. After 4.2 ms the mode briefly becomes less coherent. At 4.4 ms a higher-order mode structure becomes apparent with roughly double the spatial frequency. The 3/1 mode then grows until around 4.7 ms, followed by decay through the end of the time window. One can also see modulations of the 3/1 mode during ms. Biorthogonal decomposition [20, 23] of all poloidal sensors and radial feedback sensors produces the empirical poloidal mode structures shown in Figure 2(c-d). Spatial mode structures are clearly 3/1 and 6/2 quadrature pairs. Amplitude and phase of the mode pairs are shown in Figure 2(e-h). Although the modes have the same helicity and resonate with the same rational surface, the phase plots in Figure 2(g-h) show independent rotations the 3/1 mode slows down while the 6/2 speeds up. The 6/2 phase appears coherent during the whole time window, in spite of its low amplitude most of the time. Neither the phase nor amplitude of the 6/2 simply track with the 3/1 mode, indicating non-rigid multimode behavior. Between 4.2 and 4.7 ms there is exponential growth of the dominant 3/1 mode while the 6/2 remains at low amplitude. However, at 4.4 ms, the 6/2 mode rapidly grows at the expense of the 3/1. The 6/2 mode then decays, and the 3/1 grows again. There are no abrupt changes in equilibrium parameters at this time which might explain the interchanging mode amplitudes. After 4.6 ms the 6/2 mode modulates the 3/1, as quick bursts of 6/2 activity are accompanied by reductions in 3/1 amplitude.

4 EX/P FIG. 2: Contour plots of δb θ versus poloidal angle (a) and toroidal angle (b), primarily showing rotating m/n = 3/1 activity. Biorthogonal decomposition of the sensor data gives the poloidal spatial modes in (c-d). Toroidal mode numbers are n = 1 and n = 2. Amplitude and phase of each mode are shown in (e-h). 4 Response to Stationary Applied Fields When the control coils are energized, high-resolution measurements are made of the complex, multimode dynamics of the plasma response to the applied magnetic perturbation. Rapid step-changes in the magnetic perturbation from the control coils have been applied with sufficient strength to allow investigation of both the plasma s linear and nonlinear responses [19, 20]. The active coils gridded in the poloidal and toroidal directions provide enough m- and n-resolution to determine that the plasma responds to the resonant 3/1 component of the applied field. Three regimes of plasma response have been observed when applying 3/1-resonant fields. These regimes depend on the edge safety factor and resonant magnetic perturbation (RMP) amplitude, as seen in Figure 3. A linear response is observed when applying fields below Br 3/1 /B T = Applying fields with Br 3/1 /B T > typically causes a disruption during the RMP. In the intermediate range of RMP amplitudes, the response depends on q ; a linear response is seen at lower q, while a saturated response is seen for higher q. Enhanced interaction of the perturbed plasma with the limiting surfaces may be responsible for the observed amplitude saturation.

5 5 EX/P4-19 FIG. 3: Plasma response versus applied 3/1 resonant magnetic perturbation amplitude for two ranges of time-averaged q. Low-q discharges have only linear and disruptive responses, while high-q discharges have an additional saturation regime. Naturally occurring rotating perturbations are present while the RMPs are applied. Although the applied fields are spatially resonant with the pre-existing modes, the temporal evolution of the externally driven stationary mode is approximately independent of the natural mode. This is consistent with predictions of a linear single-helicity model that incorporates both the RWM and viscous kink mode dynamics [15, 19]. 5 Magnetic Feedback When high-resolution measurements are used as input to real-time feedback, we observe mode acceleration, deceleration, suppression, and amplification. The dynamic phase response illustrates the importance of phase control and low latency. Figure 4 shows an example of high-throughput active control of the rotating m/n = 3/1 external kink for two different settings of the programmed feedback phase. Feedback is observed to increase

6 EX/P FIG. 4: Wall-stabilized kink dynamics measured during active magnetic feedback for two discharges having oppositely programmed control phases, φ. Contour plots of δb θ versus poloidal angle are shown in (a-b). Feedback is active during 2 4 ms. Amplitude and rotation frequency of the 3/1 mode are shown in (c-d). coherence and amplify the mode when phased to accelerate the closed-loop mode dynamics. When the feedback phase is inverted for suppression, the mode rotation decelerates, associated with a changing latency-induced phase lag. Full 3D VALEN characterization of the stabilizing wall and multimode coupling between the sensors and control coils are in progress and will be used to explore optimized multimode control methods. Averaging the feedback performance over many shots gives the results in Figure 5. This scan applies to feedback on n = 1 modes with no restrictions on poloidal mode number the phase and amplitude for four groups of 10 δb θ feedback sensors and control coils at different poloidal angles are treated separately. However, the applied rotation frequencies for the separate groups are coupled in order to avoid rotational shear. Control system latency and amplifier transfer functions are considered when determining output phase of the applied field. The results presented represent the preliminary experiments with the new GPU-based feedback system, which allows a wide range of processing options within the input-output cycle [21].

7 7 EX/P4-19 FIG. 5: (a) Mode amplitudes as a function of feedback phase angle. Clear excitation is seen at 180, while slight suppression occurs at 0. (b) Frequency spectrum of measured n = 1 modes without feedback, along with amplifying and suppressive feedback phasing. Feedback can enhance or reduce the modes while also changing the mode rotation frequency. 6 Summary HBT-EP experiments are focused on measurement and control of the 3D plasma boundary. Non-rigid behavior of coexistent m/n = 3/1 and 6/2 modes is observed in typical discharges. Application of stationary RMPs is found to produce three regimes of plasma response which depend on the edge safety factor and RMP amplitude. Linear and disruptive responses are seen for lower q values, while a saturated response occurs at higher q. Initial feedback experiments with a new GPU-based control system have shown amplification and suppression of n = 1 kink modes depending on the applied feedback phase angle. Further experiments aimed at optimizing feedback performance are in progress. 7 Acknowledgments This work was supported by U.S. Department of Energy Grant DE-FG02-86ER53222.

8 EX/P References [1] SABBAGH, S.A., et al., Nuc. Fusion, 50 (2010) [2] CHU, M.S., OKABAYASHI, M., Plasma Phys. Contr. Fus. 52 (2010) [3] PARK, J.-K., et al., Phys. Rev. Lett. 99 (2007) [4] EVANS, T.E., et al., Nuc. Fusion 48 (2008) [5] LANCTOT, M.J., et al., Phys. Plasmas 18 (2011) [6] BARUZZO, M., et al., Nuc. Fusion 51 (2011) [7] HENDER, T.C., et al., Nuc. Fusion 47 (2007) S128. [8] SANKAR, M.K. VIJAYA, et al., Journal of Fusion Energy 12 (1993) 303. [9] MAURER, D.A., et al., Plasma Phys. Contr. Fus., 53 (2011) [10] IVERS, T.H., et al., Phys. Plasmas 3 (1996) [11] KOMBARGI, R., The Influence of a Conducting Wall on Disruptions in HBT-EP, PhD Thesis, Columbia University, (1997). [12] EISNER, E.C., The Effects of Wall Coverage, Symmetry, and Plasma-Wall Separation on the Stability of Tokamak Plasmas, PhD Thesis, Columbia University, (1998). [13] LEVESQUE, J.P., Multimode Structure of Resistive Wall Modes near the Ideal Wall Stability Limit, PhD Thesis, Columbia University, (2012). [14] CATES, C., et al., Phys. Plasmas 7 (2000) [15] MAUEL, M.E., et al., Nuc. Fusion 45 (2005) 285. [16] KLEIN, A.J., et al., Phys. Plasmas 12 (2005) [17] PEDERSEN, T.S., et al., Nuc. Fusion 47 (2007) [18] HANSON, J.M., et al., Phys. Plasmas 16 (2009) [19] SHIRAKI, D., High-Resolution MHD Spectroscopy of External Kinks in a Tokamak Plasma, PhD Thesis, Columbia University, (2012). [20] MAURER, D.A., et al., Phys. Plasmas 19 (2012) [21] RATH, N., et al., High-speed, multi-input, multi-output control using GPU processing in the HBT-EP tokamak, Fus. Eng. and Design, (2012) (Article in Press). [22] BIALEK, J., et al., Phys. Plasmas 8 (2001) [23] DUDOK DE WIT, T., et al., Phys. Plasmas 1 (1994) 3288.