Evidence for Magnetic Relaxation in Coaxial Helicity Injection Discharges in the HIT II Spherical Torus A. J. Redd Aerospace & Energetics Research University of Washington Seattle, Washington USA 24 Innovative Confinement Concepts Workshop University of Wisconsin Madison Madison, WI USA May 25, 24
24 Innovative Confinement Concepts Workshop May 25, 24 HIT Personnel Faculty and Staff Thomas R. Jarboe George R. Andexler John A. Rogers Brian A. Nelson Matthew B. Fishburn Dzung Tran Roger Raman Susan Griffith Aaron J. Redd Daniel E. Lotz Roger J. Smith Dennis Peterson Graduate Students William T. Hamp R. Griff O Neill Valerie A. Izzo Paul E. Sieck Undergraduates Rabih Aboul Hosn Ellen Griffin Chris Pihl Rorm Arestun James Newman Joshua Proctor Anna Askren Nora Nguyen Aaron Siirila James Deville Edwin Penniman Jed Smith
24 Innovative Confinement Concepts Workshop May 25, 24 Summary New Coaxial Helicity Injection (CHI) regime on HIT II Toroidal plasma current I p up to 35 ka I p greater than I TF in some discharges ( 12%) Global magnetic measurements indicate that measured I p can be up to 6 times the wrap-up current q a I INJ Internal magnetic measurements show: Buildup of poloidal flux and formation of closed-flux core Relaxation of the current density profile High paramagnetism (up to 4% of vacuum field) Current ramp-up rate correlates with the pitch in the magnetic field across the injector
24 Innovative Confinement Concepts Workshop May 25, 24 The HIT II Spherical Torus HIT II Engineering Parameters: Major Radius R =.3 m Minor Radius a =.2 m Aspect Ratio A = 1.5 Elongation κ = 1.75 6 mwb Ohmic Flux Available Active poloidal-flux boundary feedback control system (response time < 1 ms)
24 Innovative Confinement Concepts Workshop May 25, 24 The HIT II Spherical Torus HIT II plasma parameters achieved: Ohmic CHI CHI Startup Pulse Length 6 ms 25 ms 4 ms Peak Current 3 ka 35 ka 3 ka Density n e 5 1 19 m 3 1 1 1 19 m 3 5 1 19 m 3 HIT diagnostic systems include: Internal magnetic and Langmuir probes Scannable two-chord FIR interferometer 16-channel Ion Doppler Spectrometer, scannable single-chord Multi-point Thomson Scattering Pair of VUV spectrometers (OVI/OV ratio) H-α visible light detectors Surface magnetic triple probes Bolometer (total radiated power) SPRED Single-chord Z eff measurement
24 Innovative Confinement Concepts Workshop May 25, 24 I p (ka) I INJ (ka) V INJ (kv) P RAD (MW) CHI-driven I p up to 353 ka 4 HIT-II Low-I TF DND CHI Shot #3386 Peak I 3 p = 353 ka (I p /I TF = 77%) 2 1 6 4 2 Toroidal Plasma Current Injector Current 1.5 Injector Voltage 1..5. 8 6 4 2 1 2 3 4 Time (ms) Radiated Power I p is total (open- and closed-flux) toroidal plasma current.
24 Innovative Confinement Concepts Workshop May 25, 24 I p (ka) I (ka) V INJ (kv) P RAD (MW) CHI-driven I p Above 3 ka 4 HIT-II Low-I TF DND CHI Shot #29478 Peak I 3 p = 33 ka (I p /I TF = 7%) 2 1 6 4 2 Toroidal Plasma Current Poloidal Wall Current Injector Current 1.5 Injector Voltage 1..5. 8 6 4 2 Radiated Power 1 2 3 4 5 6 Time (ms) I p is total (open- and closed-flux) toroidal plasma current.
24 Innovative Confinement Concepts Workshop May 25, 24 I (ka) I (ka) V INJ (kv) P RAD (MW) CHI-driven I p up to 12% of I TF 3 HIT-II Low-I TF DND CHI Shot #29988 Peak I p = 21 ka (I p /I TF = 12%) Toroidal Plasma Current 2 1 TF Current 6 Injector Current 4 2 Poloidal Wall Current 1.5 Injector Voltage (Late Breakdown) 1..5. 4 3 2 1 Radiated Power 1 2 3 4 5 Time (ms) I p is total (open- and closed-flux) toroidal plasma current.
24 Innovative Confinement Concepts Workshop May 25, 24 Optimum I TF for CHI-Driven I p on HIT II I p (ka) 4 3 2 Peak Toroidal Plasma Current versus TF Current 1..2.4.6.8 TF Current (MA) Peak plasma current I p in 37 shots, versus corresponding I TF I p can be maximized for I TF 5 ka Wall conditions can produce significant shot-to-shot variations, and can limit plasma performance early in a run campaign
24 Innovative Confinement Concepts Workshop May 25, 24 CHI-Driven I p Consistent With Taylor Relaxation λ TOK (m -1 ) 8 6 4 2 Peak Tokamak Lambda vs Injector Lambda 2 4 Injector Lambda (m -1 ) 6 8 Peak λ TOK in 37 shots, versus post-formation λ INJ where λ INJ µ I INJ ψ INJ and λ TOK µ I p φ TF Solid line is λ TOK =λ INJ, dashed line is λ TOK =(1.1)λ INJ Generally, λ TOK λ INJ, which agrees with Taylor relaxation
24 Innovative Confinement Concepts Workshop May 25, 24 I p Up To 6 Times Wrap-up Current q a I INJ I (ka) I (ka) I (ka) 3 HIT-II Low-B T Discharge #29133 Plasma Current I p 2 1 3 I INJ (solid) and edge-q*i INJ 2 1 3 I BANK (solid) and edge-q*i BANK 2 1 1 2 3 4 5 Time (ms) Discharge #29133: peak I p was 29 ka, while I TF 47 ka, for peak I p /I TF of 62%. Peak I p /qi INJ 6, while peak I p /qi BANK is nearly 2.
24 Innovative Confinement Concepts Workshop May 25, 24 I p Can Be Many Times q a I INJ I (ka) I (ka) I (ka) 3 HIT-II Low-B T Discharge #29988 I p (solid) and TF Current 2 1 3 I INJ (solid) and edge-q*i INJ 2 1 3 I BANK (solid) and edge-q*i BANK 2 1 1 2 3 4 5 Time (ms) Discharge #29988: peak I p was 21 ka, while I TF 175 ka, for peak I p /I TF of 12%.
24 Innovative Confinement Concepts Workshop May 25, 24 I p (ka) T i (ev) v TOR (km/sec) IDS-Measured T i up to 3 ev 3 HIT-II Low-B T Discharge #29141 Toroidal Plasma Current 2 1 4 Chord-Averaged Ion Temperature 3 2 1 2 Chord-Averaged Toroidal Velocity -2-4 1 2 3 4 Time (ms) 5 6 T i and v TOR measured by single-chord Ion Doppler Spectroscopy, tuned to OV emission (278 nm) on edge chord (impact parameter of.44 m). Negative v TOR is counter to I p.
24 Innovative Confinement Concepts Workshop May 25, 24 Internal Magnetic Probe Array Each probe stem contains 5 or 8 magnetic triple probes, with Boron-Nitride sheaths, stem axes spaced 35 mm apart Three probe stems are spaced poloidally and toroidally to enable calculations of the current density J Shallow probing (9 mm insertion) was found to be only slightly perturbing for these discharges Deeper probing (15 mm insertion) significantly degraded plasma performance, generally reducing peak I p by 2%
24 Innovative Confinement Concepts Workshop May 25, 24 I p (ka) ψ POL (mwb) Probes Show Poloidal Flux Generation 3 HIT-II Low-B T Discharge #29388 Toroidal Plasma Current I p 2 1 2 15 1 5 Probes at 9 mm insertion Innermost Probe: R =.42 m Measured Poloidal Fluxes 1 2 3 4 5 6 Time (ms) Rapid rise in I p corresponds to the bubble-burst, and probe-measured flux is simply the injector flux ψ INJ (6. mwb, lower dashed line) Slow post-formation rise in I p corresponds to increasing probe-measured flux. Peak measured flux is larger than the total vacuum flux that could be in the confinement region ( 11 mwb, upper dashed line)
24 Innovative Confinement Concepts Workshop May 25, 24 Vacuum Fluxes for HIT II CHI Shot #29388 Discharge #29388 flux boundaries are Unbalanced Double-Null Divertor, with: Injector flux ψ INJ = 6. mwb Absorber null flux ψ INJ = 2.5 mwb Vertical flux up to 4. mwb at midplane Internal magnetic probes can have up to 2 mwb of vertical flux behind the tips for 15mm insertion (as shown) Open flux in confinement region may be up to 11 mwb for 9 mm insertion, assuming ψ INJ is completely drawn out.
24 Innovative Confinement Concepts Workshop May 25, 24 Current Density Relaxes Inward I p (ka) 3 HIT-II Low-B T Discharge #29388 Plasma Current I 2 p 1 Probes at 9 mm insertion 1 2 3 4 5 6 Time (ms).8 Toroidal Current Density J T (MA/m 2 ).6.4.2. at t=3.3 ms at t=1.7 ms at t=1. ms.4.42.44.46.48.5 Major Radius (m) J(R) is initially hollow. During slow I p rise, current density migrates inward.
24 Innovative Confinement Concepts Workshop May 25, 24 Low-TF Plasmas Can Be Strongly Paramagnetic I p (ka) B T (mt) B T /B T-VAC (%) HIT-II Low-I TF DND CHI Shot #351 25 Toroidal Plasma Current 2 15 1 5 Probes at 9 mm insertion 5 Vacuum-Subtracted Toroidal Fields 4 at R=.42 3 at R=.44 2 at R=.47 m 1 5 Relative Paramagnetism (% of Vacuum) 4 3 2 1 1 2 3 4 Time (ms) Paramagnetic toroidal fields reach 4% of the vacuum toroidal fields.
24 Innovative Confinement Concepts Workshop May 25, 24 Note the Slow I p Rise After Formation 3 HIT-II Low-B T Discharge #29968 Toroidal Plasma Current I p (ka) 2 1 1 2 3 4 5 Time (ms) Initial fast rise in I p is related to bubble-burst, and probing indicates that the current is flowing on open field lines Slower post-formation rise in I p is related to relaxation and the formation of a closed-flux core This current rise di p /dt correlates with high injector flux, relative to the toroidal field
24 Innovative Confinement Concepts Workshop May 25, 24 Even for High B T, Increasing ψ INJ Allows Relaxation and Current Build-Up 3 Toroidal Plasma Current I p (ka) 2 1 Discharge #29473, ψ INJ =1. mwb Discharge #29465, ψ INJ =1.8 mwb Discharge #29469, ψ INJ =11.9 mwb 1 2 3 4 5 Time (ms) Shot series with relatively high toroidal field (I TF 8 ka)
24 Innovative Confinement Concepts Workshop May 25, 24 Current Ramp-up Rate Correlates with Injector Field-Line Pitch I p /I TF di p /dt (ka/ms) 1.2 Ratio of I p to I TF.8.4. 12 Post-Formation Current Ramp-up di p /dt 8 4 1 2 3 4 5 Approximate Field Pitch Across Injector (degrees) ( ) pitch tan 1 2 Bp INJ B T where B p INJ is the poloidal field due to the injector flux and B T is the vacuum toroidal field in the injector. Data plotted for 37 discharges.
24 Innovative Confinement Concepts Workshop May 25, 24 A Minimum Field Pitch May Be Needed for Relaxation to Overcome Resistive Decay Relaxation rates vary with field-line geometry: Antiparallel field lines reconnect faster than parallel field lines. [Y. Ono et al, Phys. Fluids B 5, 3691 (1993)] Strong toroidal fields in a Spherical Tokamak Fields are nearly parallel in the HIT II injector Slow magnetic relaxation rate Decreasing I TF and/or increasing ψ INJ will increase the magnetic field pitch in the injector region Experimentally, there is a minimum field pitch needed for significant buildup of the toroidal plasma current Minimum relaxation rate needed to overcome resistive decay
24 Innovative Confinement Concepts Workshop May 25, 24 Summary New HIT II CHI operating regime has been explored: Toroidal plasma current I p up to 35 ka I p greater than I TF in some discharges ( 12%) Consistent with Taylor relaxation (λ TOK λ INJ ) I p can be up to 6 times the wrap-up current q a I INJ Relatively high temperatures: IDS T i typically 1-3 ev and MPTS T e up to 1 ev Internal magnetic measurements show: Buildup of poloidal flux and formation of closed-flux core Relaxation of the current density profile Strongly paramagnetic at low TF (up to 4% of vacuum) Current ramp-up rate correlates with injector field-line pitch Excess TF inhibits relaxation and current drive
24 Innovative Confinement Concepts Workshop May 25, 24 Continue analysis: Future Work Discharges with NSTX-like injector geometry Do these discharges follow the field-pitch scalings? More detailed probing results: Overall scalings? n=1 mode structure? Formation dynamics? Correlate (if possible) other discharge features: HXR pulses, slow P RAD oscillations EFIT equilibrium reconstructions, with and without fitting to internal probe measurements Do corresponding CHI studies on NSTX
24 Innovative Confinement Concepts Workshop May 25, 24 Magnetic Helicity Magnetic helicity is a measure of flux linkage. The helicity K is defined by: K (A B) dv = (A dl) (B ds) For two flux tubes, φ 1 and φ 2 : K = (A 1 dl 1 ) (B 1 ds 1 ) + 1 2 (A 2 dl 2 ) (B 2 ds 2 ) That is, K = φ 2 φ 1 + φ 1 φ 2 = 2φ 1 φ 2 In a tokamak, K I p I TF
24 Innovative Confinement Concepts Workshop May 25, 24 Helicity and CHI Current Drive Coaxial Helicity Injection (CHI) injects toroidal flux φ TOR which links the poloidal flux ψ inj Insulator I tf ψ inj V inj V inj injects φ TOR which links ψ inj K = 2V inj ψ inj
24 Innovative Confinement Concepts Workshop May 25, 24 Model for ST CHI Injector As described in: Jarboe, Fusion Technology 15, 7 (1989), and Nelson et al., Nuclear Fusion 34, 1111 (1994) Describes a CHI discharge in terms of current flowing on open flux connecting the injector electrodes. Injector flux remains in the injector unless the injected current passes a threshold: the bubble-burst current. Above this threshold, the injector flux is drawn into the confinement region, and the steady-state injector current will be clamped to the bubble-burst value. For large A, the bubble-burst I inj is I inj = χ2 ψ 2 inj µ 2 d2 I TF where χ is a dimensionless number, ψ inj is the injector flux, d is the inter-electrode distance, and I TF is the current generating the TF. The measured electrode voltage can be affected by rapid changes in the field-line lengths.
24 Innovative Confinement Concepts Workshop May 25, 24 Empirical CHI Scaling Studies Utilized sets of single-null CHI discharges with variations in injector flux magnitude ψ INJ, toroidal field current I TF and injector geometry (effectively, d). Found that, as expected, the injector current scales as I INJ ψ 2 INJ/I TF and that open-flux toroidal plasma current scales as I p ψ INJ That is, the open-flux toroidal plasma current has no dependence on I TF The injector current did not scale as 1/d 2. Instead, given ψ INJ and I TF, the injector current was minimized for an NSTX-like injector flux geometry.
24 Innovative Confinement Concepts Workshop May 25, 24 I INJ Scales as ψ 2 INJ /I TF 2 15 HIT-like 6.5 mwb, Both guns, Inner puff, V SB = 94% Injector Current vs TF I INJ (ka) 1 5 I inj = C/I TF Each point is a 1ms interval in a single discharge.2.3.4.5.6.7.8 TF Current (MA) I INJ (ka) 25 2 15 1 Injector Current vs Ψ inj t = 2. ms in all shots, avgd over 1. ms I inj = C*Ψ inj 2 5 Bottom gun, Inner and Top gun puff 2 4 6 8 1 12 14 Injector Flux (mwb)
24 Innovative Confinement Concepts Workshop May 25, 24 I INJ Minimized for NSTX-like Injector 15 Plasma Current I p (ka) 1 5 Each point represents 1 ms interval in one discharge 1 Rows at 9%, Both Guns, Both Puffs 12 Injector Current 9 I INJ (ka) 6 3 Bank Current minus Wall Current 25 Current Multiplication Factor 2 I p /I INJ Z INJ (mω) 15 1 5 Plasma Current divided by Injector Current 16 Injector Impedance 12 8 4 HIT-Like NSTX-Like Wide-Inj Injector Geometry