(Inductive tokamak plasma initial start-up)

(Inductive tokamak plasma initial start-up) 24. 6. 7. (tapl1.kaist.ac.kr)

Outline Conventional inductive tokamak plasma start-up Inductive outer PF coil-only plasma start-up

Inductive plasma start-up in tokamaks Flux change Φ( t) t Central solenoid I OH ( t) t r Φ B ( t) E = Faraday s law t I ( t) ˆ φ Φ ( t) ˆ φ E ˆ φ OH B φ = Vloop ˆ φ 2πR Electron acceleration I OH e/n collision Townsend avalanche E φ Breakdown Plasma current build-up, I p (t) I OH t Power transfer by transformer action Primary: Solenoid current Secondary: plasma current Importance of pre-ionization

Why inductive (ohmic) current drive? Ohmic solenoid: work horse for fusion energy for decades. Based on simple physics principle very well-understood cf) Non-inductive CD schemes: still pretty much in the physics-proving stages. Simple hardware system Cheap power cost ($/kw) Iron core versus air core Provides a good target plasma for high power auxiliary plasma heating. May be challenging in engineering for low aspect ratio devices such as spherical tori.

Typical I p ramp-up configurations D-IIID NSTX I p control V loop control (~1 MA/s) t = -3 ms: gas injection t = -2 ms: ECH injection -7 < t < 3 ms: E-field turn-on, Field null control t = ms: plasma start t = 2 3 ms: position feedback control Limited plasma @ inner wall I p ~ 2 ka w/ V loop = 3 V, κ > 1.3 R/a = 1.67/.67 m B T = 2 T

Important factors in plasma start-up E-field strength (loop voltage) Magnetic flux (volt-sec) consumption Magnetic structure (field null) Vacuum vessel and conducting structure material Pre-ionization Prefill gas pressure Wall condition (impurity)

V loop dependence I p 3 2 1 I p 3 2 1 V loop 3 2 1 D α 3 2 1 As V loop, I p ramp-up rate As V loop, breakdown is delayed. Breakdown time time @ initial D α peaks. E >.25 V/m for breakdown ITER requirement: E ~.3 V/m Breakdown time τ bd e -CE

V loop dependence cont d JET I p (inverted) l i Normalized plasma internal inductance l i 2µ B 2 p V V 2 Bp dv 2µ where B p = r r Bp dl r dl

Flux consumption Starting from the Poynting theorem, total flux consumption at the plasma t S = Φind + Φ res t 1 I d 1 dt' 2 2 Vsdt' = Li I p dt' + Φ p Inductive flux (mag. config. establish.) t I p R p dt' Resistive flux (ohmic dissipation) Total flux from the coil Φ tot Φ = where t V dt loop ' = b p = t 1 d Φind = I dt' ext Φ ind p V L I = µ R + Φ res 2 B p dv dt' 2µ b ln I a p + Φ : flux btwn flux loop and plasma surface ext Φ res t = I p R p dt' : determined from the measured (or obtained by EFIT) Φ ind and Φ ext Ejima coefficient Φres CE µ R I p

A double-swing solenoid flux of NSTX is.7 V-s. Spherical tori have small ohmic solenoid. Flux consumption optimization is more important than in conventional tokamaks.

NSTX Influence of impurity Wall conditioning Baking of graphite tiles to 35 C/15 C Boronization (5% trimethyl boron + 95% helium GD) Reduction of flux consumption after boronization Before boronization After Ejima-Wesley coefficient Φres + Φind CE W µ R I p Ejima coefficient Φres CE µ R I p

Importance of pre-ionization ISX-B with ECH pre-ionization V res > Use of pre-ionization: Removal of the initial V loop peak Larger I p ramp rate Slightly larger average n e Reduction of V-s usage by 3% owing to a substantial reduction in V res. V res Means of pre-ionization: ECH Fast wave Lower hybrid wave etc.

Importance of pre-ionization cont d KAIST-TOKAMAK Pre-ionization using a 2.45 GHz, 1 kw microwave source (not ECH) Breakdown at lower V loop Flux saving Earlier breakdown V loop (V) 14 12 1 8 6 4 2 Without pre-ionization 6.1 V 9.4 V ~1 ms Loop voltage Without breakdown Pre-ionization 1 2 3 4 5 Time (ms) I p (ka) 14 12 1 8 6 4 2 Plasma current ~1 ms Pre-ionization Without pre-ionization 1 2 3 4 5 Time (ms)

Importance of pre-ionization cont d KAIST-TOKAMAK Major Axis Images of ECH plasmas Minor Axis 53 cm ms 33.3 ms 66.6 ms 1 ms 133 ms 166 ms

Importance of pre-ionization cont d DIII-D ECH pre-ionization and pre-heating allow prompt and reliable start-up. Prompt breakdown (indicated in D α emission) (n e ) av > 2 1 12 cm -3 during pre-ionization V loop = 3 V Higher ramp-up rate D α Larger density ECH (6 GHz, 6-85 kw) Earlier burnthrough

Importance of pre-ionization cont d DIII-D Higher ramp rate at the same V loop 4% ~65 kw Time (ms) V s = V res + V ind = I p R p + d(l i I p )/dt (Constant V loop control period) V res : V ind = 55% : 45% di p /dt >, V res ~ const I p & R p or n e & T e Reduction of V res by ECH di p /dt (inductive flux consumption increased)

RF power dependence As P ECH, V res and di p /dt DIII-D

RF power dependence cont d PETULA-B (France) In the presence of LHCD, significant reduction of loop voltage. Total flux consumption decreased due to resistive flux saving. I p waveform kept constant for comparison. w/o RF w/ RF

Influence of prefill pressure Non-assisted ohmic start-up (V loop = 3 V) di p /dt almost const. DIII-D ECH-assisted ohmic start-up (V loop = 3 V) Prefill pressure: (2.2-9) 1-5 torr As p, breakdown and current rise significantly delayed. No breakdown at p > 9 1-5 torr Always prompt breakdown Wide prefill pressure operating range

Influence of prefill pressure cont d Breakdown time (V loop = 3 V) DIII-D Hard X-ray emission for ohmic shots (V loop = 3 V,.3 V/m).3 V/m 2 ms Always prompt breakdown with ECH Wide prefill pressure operating range Hard X-rays from runaway electrons due to long breakdown delays No hard X-ray emission with ECH

Influence of stray magnetic fields Transverse magnetic field structure by a central solenoid B R B z B Flux Central solenoid

Vessel eddy currents JET Eddy current B z by I eddy

Compensated Mod-B contours (in G) Influence of stray magnetic fields cont d DIII-D For reliable ohmic breakdown, EB φ B > 1 3 (V/m)

Example of evolution (NSTX) Coil current Coil voltage NSTX vv and coils PF2 PF3 PF1 PF5 CS

Evolution of B and V loop B contours V loop contours

Evolution of B vector and breakdown contours Transverse B-vector Breakdown contours Consistent with visible camera pictures

Inductive PF coil-only tokamak plasma start-up scheme In collaboration with PPPL (USA), Kurchatov (Russia) Submitted to Nucl. Fusion and PPCF Will be presented at 24 IAEA meeting

Motivation Ohmic solenoid has been the work horse of fusion research. Attractive fusion CTF and power plant design requires OH elimination Compact CTF requires elimination of OH regardless of R/a. ARIES-AT and ARIES-ST design assumes no OH. PF coils have been used to start-up the plasma. Plasma In-board region Conventional ohmic solenoid R a Out-board region Elimination of ohmic solenoid #1 MAST (START): PF coils + radial compression Plasma Plasma #2 JT-6U: Aggressive application of rf Midplane R a a #3 Plasma start-up using appropriate combination of out-board / outer PF coils. Major axis

< 2% of total flux from VT in Strong pre-ionization with 4 MW RF

Null field generation using out-board induction coils Plasma Midplane Plasma R a a #1 #3 #2 Small radius PF coil #1 produces a peaked B V profile. Large radius PF coil #2 produces a flat B V profile. Near-midplane trim PF coil #3 produces a follow B V profile. Z Major axis Plasma #1 Initial plasma #2 #3 R Null field region 2 BZ BZ, 2 R R matched Field null region 2 BZ BZ BZ,, = 2 R R

Numerical modeling performed for NSST Several configurations possible flexibility to accommodate the needs for a particular device Case 1 Case 2 Case 3 Case 4 Case 5 #1 #1 #1 #1 #1 #2 #2 #2 #2 #3_1 #2 #3 #3 #3_1 #3_1 #3_2 #3_2 #3_2 Coil #1 down Coil #3 on mid-plane Coil #2 moved up Coil #3 off mid-plane With more contoured vacuum vessel To give sufficient access to blankets To further increase access to blankets

Case 5 for sufficient mid-plane space for the blanket access Coil #1 (+16 MA-t) Coil #2 (-1 MA-t) Mid-plane vertical field profiles Coil #3_1 (-3.7 MA-t) Coil #3_2 (+6.7 MA-t) Net vertical field profile Available flux 2 BZ BZ, 2 R R matched Field null region 2 BZ BZ BZ,, = 2 R R

Case 5 cont d Flux contours Mod-B contours (Gauss) Radial profile of flux Plasma axis Significant amount of volt-sec available for current ramp-up: ~4.5 V-s at R = 1.75 m Generation of good quality multi-pole field null Excellent out-board access (~1.8 m vertical spacing) Suitable for the interchangeable blanket modules for CTF.

Dynamic calculation for start-up scenario Coil Current (ka) 5 4 3 2 1 Pre-magnetization Flux swing Breakdown 1 2 3 4 5 6 7 Time (s) Typical start-up procedure Pre-magnetization phase Flux swing phase Breakdown phase Requirements of start-up Sufficient electric field Field null structure Lloyd condition for successful breakdown (B. Lloyd et al., Nucl. Fusion 31, 231 (1991)) Without preionization BT E 1 kv/m B With sufficient pre-ionization BT E.1 kv/m B Eddy currents induced in various conducting structures

Development of start-up simulation code NULLB Circuit equations w/o plasma Axi-symmetric 2-D calculation Field structure, loop voltage, flux, coil current waveform, etc TSTART -D power and particle balance equations Plasma parameters (I p, T e, T i, n e, n i, etc) Waveform of each coil Field Structure Neutral Flux Change Ion (main atom, impurity) Loop Voltage Plasma current Electron

Dynamic electromagnetic code (NULLB) Set-up of a set of circuit equations including structure eddy currents (1 st order time-dependent differential equations) dii + + di j did Li dt IiRi Mij dt + Mid dt = Eigen-expansion method for solving the circuit equations Least squares method for optimization under constraints Constraints Lloyd breakdown condition Multi-pole field null E 1 kv/m B Magnetic flux for further current rising Max coil current limited by power supply Max coil voltage limited by power supply Coil temperature heated by coil current BT

Evolution of plasma parameters (TSTART) Electron related terms Electron power balance 3 2 d ( n κ T ) = P + P ( P + P ) P P dt e e OH ECRH Dion Drad equi brem ( P + P + P + P ) P I e ion line RRE DRE con Electron particle balance ( ) n n n Z = + e D I I I Ion related terms Ion power balance 3 2 d ( n κ T ) = P P P dt i i i equi CX con Plasma current related terms Ohmic input power P OH ηi I R I V = = = A V V 2 2 p p p p res 2 p p Ion particle balance dnd V n Sn n dt V τ n = e p Plasma current evolution di V I R = dt L p p p D p

Time-dependent calculation for NSST NULLB PF coil current PF coil bias voltage PF Current (ka/turn) 25 2 15 1 5-5 -1-15 -2-25 PF1 PF2 PF3-1 PF3-2 -2. -1.5-1. -.5..5 PF Voltage (kv) 7 6 5 4 3 2 1-1 -2-3 -4-5 -2. -1.5-1. -.5..5 PF1 PF2 PF3-1 PF3-2 Time (s) Time (s)

Flux Magnetic Flux (Wb) 4.38 4.36 4.34 4.32 4.3 4.28 4.26 NSST plasma evolution.48.485.49.495.5.55 Time (s) Magnetic Flux at 2.35m Loop Voltage (V) -7. -6.5-6. -5.5-5. -4.5-4. -3.5 Loop voltage -3..48.485.49.495.5.55 Time (s) Loop Voltage at 2.35m Plasma starts at.483 s Plasma current 14 Plasma Current 25 Vertical field B v _calculated B v _needed Plasma Current (ka) 12 1 8 6 4 2 B v (G) 2 15 1 5-2.48.485.49.495.5.55.48.485.49.495.5.55 Time (s) 2x1-5 torr prefill pressure Time (s)

E*B t /B p contours BT E B.1 kv/m Note) Outermost contour =.1 kv/m required in the presence of sufficient pre-ionization ~6 cm Large volume of low stray field region Breakdown contour shape sustains ~2 ms!

Simulation for NSTX +2 ka/turn Static calculation Flux contours Dynamic calculation - 2 ka/t +2.8 ka/t

Simulation for NSTX PF current (ka/turn) 2 15 1 5-5 -1-15 -2 PF2 PF3 PF4 PF5 PF current -5-4 -3-2 -1 1 Bias Voltage (kv) 1.5 1..5. -.5-1. -1.5-2. -2.5-3. PF2 PF3 PF4 PF5 PF voltage -5-4 -3-2 -1 1 Time (ms) Time (ms) PF current (-3 ms) PF voltage (-3 ms) PF current (ka/turn) 2 15 1 5-5 -1-15 -2 5 1 15 2 25 3 Bias Voltage (kv) 1.5 1..5. -.5-1. -1.5-2. -2.5 Under 3 kv -3. 5 1 15 2 25 3 Time (ms) Time (ms)

Time-dependent calculation with vacuum vessel eddy currents considered BT Evolution of E contours T B P EB t /B perp =.1 kv/m 23 ms 24 ms 25 ms ~ 3 cm 26 ms 27 ms 28 ms Lloyd s condition, with strong pre-ionization, E T B T /B P.12 kv/m satisfied in a significant volume.

NSTX time-dependent calculation cont d PF current (ka/turn) Coil current Loop voltage Flux vs time (at 1.4 m) 2 PF3 15 1 PF2 5-5 PF5 Null -1-15 PF4-2 -5 5 1 15 2 25 3 Time (ms) Loop Voltage (V) 9 8 7 6 5 4 3 2 1 23 24 25 26 27 28 29 3 Time (ms).14.13.12.11.1.9 23 24 25 26 27 28 29 3 Magnetic Flux (Wb).15 Time (ms) Significant V-s is available for current ramp-up. Vertical field and field index in the initial start-up phase seems to be right. Equilibrium calculation is on-going (DINA or TSC). Full ramp-up scenario will require bi-polar PF5. But initial breakdown experiment to ~1 ka should be possible with the existing power supplies.

Force balance calculation 1 2. 1.6 2. 1.6 I p (ka) 8 6 4 2 23 24 25 26 27 28 29 3 Time (ms) R (m) 1.2.8.4 Plasma Position Field Index 1.2.8.4.. 23 24 25 26 27 28 29 3 Time (ms) Field Index B z (Gauss) -1-2 -3 Calculated B z Required B z for I p -4 23 24 25 26 27 28 29 3 Time (ms) DINA

Summary An analysis for developing an out-board PF-only inductive start-up scheme was performed. A combination of out-board PF coils placed outside the vacuum vessel is shown to create a good quality field null region while retaining significant volt-second capability for current ramp-up. For NSST, ~5 V-s possible for ramping the current to a few MAs. For NSTX, ~.12 V-s possible for I p ~ a few hundred ka. The concept provides sufficient flexibility to accommodate the needs for a particular device. NSTX can be utilized as a test-bed for elaborating the concept. - A quality multi-pole field null can be produced at R 1.4 m with the current machine capabilities. - Dynamic calculation including structure eddy currents shows sustainment of field null for over 5 ms. - Experiment under plan in 24.