Performance and Stability Limits at Near-Unity Aspect Ratio in the PEGASUS Toroidal Experiment

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1 Performance and Stability Limits at Near-Unity Aspect Ratio in the R. Fonck, S. Diem, G. Garstka, M. Kissick, B. Lewicki, C. Ostrander, P. Probert, M. Reinke, A. Sontag, K. Tritz, E. Unterberg University of Wisconsin, Madison, Wisconsin, USA

2 Abstract The is a mid-sized extremely-low aspect ratio (A) spherical torus (ST). It has the dual roles of exploring limits of ST behavior as A approaches 1 and studying the physics of ST plasmas in the tokamak-spheromak overlap regime. Major parameters are R = m, A = , I p.15 MA, and B T <.1 T. High beta plasmas are produced at very low toroidal field by ohmic heating. Values of b t > % have been obtained, and the operational space of b t vs I p /ab T is similar to that observed for NBI-heated START discharges. Achievable plasma current is subject to an apparent limit of I p /I TF ~ 1. Access to higher-i p appears to be restricted by the appearance of large internal MHD activity, including m/n=/1 and 3/ modes, which extend over a large region of low shear. Recent experiments have begun to access ideal stability limits, with disruptions observed as q 95 approaches 5, in agreement with numerical predictions for external kink mode onset. Work Supported by U.S. DoE Grant No. DE-FG-9ER5375.

3 Pegasus is a mid-sized spherical torus Major Parameters: - R =. -.5 m - A = B t.7 T - I p.15 MA - k = Dt pulse = 1-3 ms - <n e > = 1-5x1 19 m -3 - b t % High strength solenoid magnet is enabling technology

4 Role of PEGASUS in the Fusion Community 1 TS-3, Spheromaks 1 1 PEGASUS NSTX, MAST CDX-U, HIT, TST-M, Globus-M, ETE START.1 MEDUSA Aspect Ratio Conventional Tokamaks 5 START PEGASUS Increase I p /I TF 1 Increase Aux. Heating 15 I N =I p /ab to [MA/(m T)]

5 PEGASUS Faces a Variety of Stability Issues Resistive internal modes can be especially severe at low-a - Low T e at startup increases h faster mode growth - Broad low-shear region provides little stabilization larger saturated island width - Confinement degradation dissipates limited OH flux y N External kink limits more severe for STs - q y for n = 1 kink stability as A Ø - could cause limit for low-tf operations at A ~ 1 8 k = 1. R/a = 1.8 R/a = 1. R/a = 1.5 R/a = 1. R/a = 1.3 R/a = 1. 3 q y

6 Vacuum vessel interior hardware EBW antenna New centerstack armor Extensive magnetic diagnostics Outboard limiter HHFW antenna Segmented divertor plates

7 Pegasus diagnostic set Presently Operating Diagnostics Diagnostic Capability Measures Core Flux Loops () V L, Y pol Wall Flux loops () Vessel currents Int. Flux loops () Y pol Rogowski Coils () I p Diamagnetic Loop () F tor / b p B p, Mirnov Coils (5) B r, B z / MHD activity VUV (SPRED) central chord Impurity monitor Filterscopes central chord Oxygen, Carbon, VB, D a Interferometer single chord N e l High Res. Camera 1 fps Plasma shape/position -D SXR Camera Internal Shape/ j(r) Poloidal SXR Diode Array (19) MHD Activity Near-Future Diagnostics Diagnostic Capability Measures Status Tangential CCD PHA single chord T e (t) In Development Tangential Bolometer Array ~ chords P rad Testing Ross Filters chords T e (t) Testing -Color X-ray chords T e Testing Tangential VB Array ~ chords Z eff (R,t), N e (R,t) Testing DNB N e (R,t), T e (R,t), j(r) Proposed EBW Radiometer T e (t) Proposed

8 Equilibrium reconstruction is a primary analysis tool A new equilibrium code has been developed for Pegasus - Robust, cross-platform, easy incorporation of new diagnostics Uses a two-step iterative method to determine equilibrium - Gauss-Seidel multigrid relaxation to solve Grad-Shafranov equation - Levenberg-Marquardt method to minimize c Benchmarked against existing codes Sample reconstruction: False-Color CCD Image Poloidal Flux Plot Fit Results I p 151. ka R.35 m a.9 m A 1. k 1.8 RB t.3 T-m b t 1% l i.35 q.8 q Safety Factor. Current Density.. y N y N Pressure R (m) y N..8 1.

9 Equilibrium Diagnostics Sufficient for Global Parameter Determination Installed Magnetics Flux Loops () Poloidal Mirnov Coils ( + 1) LFS Toroidal Mirnov Coils () HFS Toroidal Mirnov Coils (7) External Wall Loops () Total (88) Plasma - diagnostic separation ª a for many discharges - Flux loops and B-field measurements constrain plasma geometry - Diamagnetic loop constrains stored energy fi pressure - Wall flux loops constrain wall currents

10 Monte Carlo Analysis Gives Uncertainty in Fit Parameters Uncertainty estimate technique: - single time-slice of discharge reconstructed 1 times - Gaussian noise added to measurement data Gaussian width from diagnostic uncertainty starting c ~ 8 x final c - s of fit parameter distributions gives uncertainty Parameter I p R l i b t b p q 95 q Rel. Uncertainty ± % ± % ± 9% ± 15% ± 15% ± % ± % Variety of discharges analyzed - wide range of fit parameters covered: 75 ka < I p < 15 ka 8% < b t < 18%. < l i <..3 m < R <.33 m..5 l i = 9 % - no significant variation in relative uncertainty l i fiuncertainty determined by diagnostic uncertainties s li 1 1 b t (%) s b t b t = 15 %

11 Equilibrium Reconstructions Show low-a Characteristics High-b t (Ohmic): b t > 1% High-b N (Ohmic): b N > High I p /I TF : I p /I TF ~ 1 High-k (natural): k > High field windup: high q a at low TF Paramagnetic: b p =.3 at e =.83; G/G vac ~ 1.5 on axis

12 PEGASUS is Accessing High-bt ST Regime High b t achieved at high density and low toroidal field - All results achieved with ohmic heating only - Highest normalized currents achieved at low field 3 1 Conventional Tokamaks START (Sykes-EPS 1) I N = I /(ab t ) P 8 1

13 Low-l i Indicates Unrelaxed Current Profile High I p and short pulse length result in low l i Plasma Duration Time (ms) START (Hender PoP 99) q 95 Some hints of increasing l i as pulse length increases -t R is on the order of discharge length or greater t R ~ 3 ms for following conditions: Z eff =, n e = n i = x 1 19 T e = T i =15 ev (linear profile) a = 5 cm - these conditions typical for t ~ 5 ms into discharge Time (ms)

14 Toroidal field utilization exhibits a soft limit around unity Maximum plasma current generally does not exceed rod current This holds for a variety of loop voltage waveforms Appears to relate to two factors: - Increased V-s consumption required for breakdown at lower TF - Large-scale resistive MHD during current ramp (exacerbated by low l i?).1.1 I p =I tf Pegasus Data TF Rod Current (MA).1.1

15 What Factors Contribute to I p ~ I TF Limit: Volt-seconds or MHD? Volt-second effects: - total flux available to drive plasma inherent limit due to v loop waveform - late start up decreases availability at low-tf - efficiency of flux usage MHD effects: - large m/n = /1 and 3/ tearing modes present in most discharges known to degrade plasma confinement - low-shear & high-h lead to quick growth of large modes g =.55 t R 3 /5 t A / 5 Ê Án a Ë R aq' q ˆ / 5 ( ad' ) / 5 t R = m a h w s µ q q '

16 Rotating /1 Mode Observed in Most Discharges Mode present in most significant discharg Outboard midplane Mirnov Frequency is typically -1 khz - no evidence of mode locking Island width estimates indicate w > 1 cm w = db B t qr n dq dr

17 Toroidal mode numbers are readily identified Toroidal Mirnov Signals f= The -coil LFS array is used to obtain values of n - Uneven coil spacing allows for resolution up to n=1 Spectral techniques are used to extract resonant frequencies and phase delays - Cross-power gives spectrum - Cross-phase gives phase shift Time (ms).18 Sample Cross-Power Spectrum Reconstructed Toroidal Mode Numbers 1 1. n= (7. khz) 5.5 n=1 (3.5 khz). Frequency (Hz) Physical Toroidal Angle (xp) 1.

18 Perturbed Field Magnitude at the Wall /1 mode is poloidally asymmetric Poloidal and toroidal phase analyses clearly indicate mode is m=/n=1 Toroidicity of mode is seen in large phase shifts along centerstack - Roughly 1.5 wavelengths observed across 1º poloidally Mode is typically strongest on the plasma outboard - As plasma grows, LFS signal increases and HFS signal decreases = Gauss. 1.5 /1 Poloidal Phase at the Wall Centerstack Coils 1. Outboard Coils Outboard Coils Physical Poloidal Angle (xp) 1.

19 Higher Current Discharges Exhibit Greater Variety of Modes /1 and 3/ modes correlate with q passing through and 1.5 respectively - low central shear allows modes to have large radial extent I p 8 db / /1 / Time (s)

20 MHD activity appears to limit plasma performance I p db F dia l i High MHD Shot Low MHD Shot Reduction in MHD typically results in improved plasma performance In High MHD Case: - l i stays low (.3) - Stored energy stays < 1 J - Ejima coefficient >.8 In Low MHD Case: - li climbs higher (despite higher V loop ) - Stored energy climbs to J - Ejima coefficient ~. 1.. W C E Reduction of /1 mode was important for improved plasma performance Further data analysis is ongoing Time (s) Time (s)

21 MHD Amplitude Increases at Lower TF MHD amplitude measured with core Mirnov - all discharges core limited Fluctuations increase rapidly at low TF I p /I TF ~ I p Fluctuations relatively constant at constant TF I TF =15 ka I p

22 In Some Discharges I p Exceeds I TF (a).. 1. R (m) Shot 197 (b) I p 157 ka R.9 m a.5 m A 1.17 k 1. B t (axis).1 T b t 9% l i.3 q 1.5 q (c).. 1. (d).. 1. (e).. 1. y N Discharge appears to be V-s limited

23 Increased Magnetic Shear Reduces MHD Amplitude Mode stabilized as rational surface moves to higher shear region ~ B / Bpol Time (ms) q = Time (ms) Similar stabilization observed 1 for several shots - both /1 and 3/ modes y N fiincreased magnetic shear helps to mitigate confinement degrading MHD 8 rational surface

24 I p ~ I TF Limit Due to Combination of Factors Decreased V-s at lower TF reduces ultimate plasma current - % decrease in V-s explains ~ half of drop in plasma current Increased MHD at lower TF degrades plasma - large tearing modes dissipate input flux - mode onset is related to appearance of q = surface onset at lower I p for lower TF - mitigated by lower h, increased shear

25 I p /I TF ~ 1 limit arises from large-scale internal modes resonant in regions of low shear q = pr B t m RI p 1+k f(a) f ( A) = È 1 + b + l i Í p A Î Í I p ( r) = pr j( r) B t 1 +k fi m Rj ( ) B t = m I TF pr fi q ~ 1 I TF 1+k A I assume j(r) = j p I p ~ 1 1 Ê 1+k ˆ Á I TF A që For PEGASUS: A ~ 1. k ~ ~ : I p ~ I TF 1 ~ 1 fi I p /I TF ~ 1 reflects limit due to q

26 Abrupt Discharge Termination Due to Apparent Edge Kink Mode q 95 Æ 5 as large MHD event terminates discharge 7.. shot 135 shot 1351 shot 135 shot time (ms) 1 11 Shot 1357 is typical of these discharges time (ms) 1 1 1

27 External kink modes observed in highest-current shots Higher-current discharges (15 ka class) often terminate in abrupt disruptions - Lower-current shots have IREs followed by gradual plasma termination n=1 fluctuations are observed on Mirnov coils immediately prior to disruption - Dominant frequency is roughly 1 khz - Mode observed a few 1 ms before IRE Observed disruptions are associated with edge kink limits - Oscillations not observed until q 95 5 Calculated free-boundary energy (DCON) approaches zero as oscillations begin - Negative value indicates instability to external kink Consistent with theoretical understanding of ideal kink stability at near-unity A - As AÆ1, unstable q a increases - Roles of finite b, low l i under study Plasma Current q 95.1 Free- Boundary Energy..1. Time (s) MHD Amplitude

28 A variety of computational tools are being implemented Equilibrium code Wall currents code Energy confinement code DCON: ideal stability analysis TSC: predictive discharge modelling GATO: instability growth rates NIMROD: resistive MHD analysis Preliminary Model of Resistive Stability (NIMROD) 3 Study of Kink Stability (DCON) Stable Mercier / Ideal internal kink External kink Evolution of J(r) during TF rampdown (TSC) q 95

29 Planned upgrades will allow further study of low-q high-b plasmas Goals require increased control of plasma conditions - Density control and shot reproducibility = between-shot gettering - Improved equilibrium field control Suppression of large internal MHD modes - Increasing I p ramp time = increased programmable V-sec from ohmic solenoid - Attain higher T e () during formation = increased B T, improved position control - HHFW heating = increased RF power operation, improved position control - Maintain q() > during plasma formation = increased B T - Maintain I p ramp time = increased programmable V-sec from ohmic solenoid - Maintain high q 95 during formation = increased B T w/rampdown - Controlled gas puff for edge cooling = continuous gettering - Separatrix operation = energize divertor coils Access to very high b T regime - Increase T e () during formation = increased B T w/fast-rampdown - Increase I p and N e = increased V-sec - High-power HHFW heating = increased RF power operation

30 New power supplies will provide dramatically improved waveform control Supplies will use electrolytic capacitors switched by GTOs or IGBTs - Switches modulate power to coil - Provide very flexible waveform control Represents a major improvement over resonantly-driven coil sets - TF: much higher I rod and fast rampdown capability - OH: enables near full use of magnet flux and real V loop control - EF: active position control TF Waveform with Fast Rampdown GTO Drive Assembly 8 Four Quadrant Ohmic Switch Electrolytic Drive Bank 3.kV 38mF Ignitron Ringing Assembly Present and New Loop Voltage Waveforms L-C resonant charge (present waveform) Effective plasma time (present waveform) Bipolar switched mw 18m W 5uH OH Solenoid time (ms) time (ms)

31 Summary PEGASUS is a university-scale spherical torus plasma experiment designed to explore the limits of plasma behavior as aspect ratio is reduced to near unity Results from ohmic operation at very low field include values of b t of ~% and toroidal field utilization factors up to and slightly above 1 Large-scale low m/n MHD activity is observed in all high-power plasmas; this activity is believed to be resistive in nature and is a limiting mechanism in the current Pegasus configuration Experiments have begun to find evidence of external kink limits at very-low-a, with q 95 =5 found to be unstable for low l i plasmas Upgrades will provide improved plasma performance to higher I p /I TF by increasing control over toroidal field, loop voltage, and radial position