Choongki Sung, Y. S. Park, Hyunyeong Lee, J. Kang and Y. S. Hwang Development of Continuous Merging Scenario for Start-up and Formation of Spherical Tokamak Plasmas 2009 American Physical Society Nov. 4. 2009, Atlanta Choongki Sung, Y. S. Park, Hyunyeong Lee, J. Kang and Y. S. Hwang NUPLEX, Dept. of Nuclear Engineering, Seoul National University, 599, Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea sck83@snu.ac.kr

1 2 3 4 5 Contents Introduction & Motivation Concept of Partial Solenoid Operation 3 Start-up Analysis 4 AC Plasma Injection Scenario 5 Conclusion

Introduction : Spherical Tokamak Facility in SNU (will be constructed) Chamber Specification Initial phase Future Chamber radius [m] 0.8m (middle) 0.6m (up & down) Chamber height [m] 2.4m Toroidal B field [T] 0.1T 0.3T Major radius [m] 0.3m 0.4m Minor radius [m] 0.2m Aspect ratio 1.5 1.3 Plasma current [kA] 30kA 100kA qedge 4.6 5.1 First target 30kA plasma (R=0.3m, a=0.2m, A=1.5)

Motivation : Existing Solenoid-free ST start-up Existing solenoid-free start-up concepts Compression-Merging method : Use in-vessel PF coil’s swing Disadvantage Impurity due to in-vessel PF coil Engineering constraints Double Null Merging (DNM) : Use Outer PF coil’s swing Disadvantage : Hard to get equilibrium [1] Not effective as much as conventional solenoid start-up. However, ST has not sufficient space for solenoid. Thus, we need innovative concept for generating first target plasma. [1] : P. Micozzi, the 11th workshop on spherical torus, St. Peterburg, 2005

Partial Solenoid Operation : Efficient Solenoid Start-up in ST PF coil Solenoid start-up The most effective method for start-up High shaping and equilibrium ability by PF coils Hard to keep low aspect ratio Difficult to apply to Spherical Tokamak Partial solenoid operation TF coil Keeping solenoid start-up’s merits maintaining low aspect ratio Possible to be effective start-up method in ST

Start-up Analysis : Considerations at each phase Merging two plasmas (6kA) Breakdown by partial solenoids Equilibrium state of merged plasmas (12kA) Breakdown phase Sufficient pre-ionization (ECH at R=0.33m) Null region formation at both ends Induce sufficient loop voltage for breakdown Pressure driven current in the middle [2] ECH ECH Merging Phase 12kA Transport two plasmas to the middle region ECH Equilibrium phase Radial & vertical force balance [2] C. B. Forest et al., Phy. Rev. Lett. 68, 3559 (1992)

Start-up Analysis : Null Region Formation Null region formation in partial solenoid geometry. Despite of asymmetry, high quality null is formed. Partial solenoid can supply more volt-sec to null region than normal double null merging by PF coils. PF#3 8.96kAturns PF#4 -0.2kAturns 10G PF#5 -0.2kAturns 5G 20G PF#6 6.08kAturns PF#2 98kAturns PF#7 0Aturns 15G B-null region (B < 20G) : 0.25<r<0.5, 0.87<z<1.1 PF#8 0Aturns PF#1 5.45MAturns

Start-up Analysis : Lloyd Condition for Breakdown with pre-ionization (for pre-ionization, ECH used at r=0.33) Lloyd Condition depending on time t=0.1ms t= 0.17ms Z [m] Z [m] R [m] R [m] : Expected plasma center (R=0.33, Z=1m) During 0.17ms, Lloyd condition is satisfied in large region. Successful breakdown is possible within 0.17ms. [3] B. Lloyd et al., Nucl. Fusion 31, 2031 (1991)

Start-up Analysis: Vsec Requirement for current ramp up Volt-second (Vsec) requirement : flux produced by coils : flux consumed by the plasma during current ramp up : external consumed flux : internal consumed flux : inductive component due to magnetic field in plasma : resistive component due to resistive consumption is calculated by analytic model[4] by Poynting method : Ejima coefficient ( ≈ 0.4 at 4~5kA/ms) [4] S. P. Hirshman and H. Neilson, Phys. Fluids 29, 790 (1986)

Start-up Analysis : Required Vsec for Small Plasma Considerations for setting small plasma parameters Major radius is set to 0.33m which is ECH resonance zone (BΦ = 875G) Plasma current is limited by q value (q>2 due to current drive instability) Plasma current is set to 6kA which is near the maximum current value. (qedge =2.21 when Ip=6kA) Small Plasma Required Vsec to ramp up 6kA plasma Assumption : li=1.2 βpol=0.1 ∆Ψext [Vsec] 0.0032 ∆Ψind [Vsec] 0.0015 ∆Ψres [Vsec] (100% margin) 0.0020 ∆Ψtot [Vsec] 0.0067 Small Plasma

Start-up Analysis : Single Filament Model for Plasma Plasma can be treated like single filament which has its own resistance and inductance. Plasma resistance Spitzer resistivity Effective charge Coulomb logarithm Resistivity factor, ex) , when Plasma resistance Plasma inductance : internal inductance(=0.5 for flat current profile)

Start-up Analysis : Governing Equations for Start-up Simulation Circuit equation including plasma filament Balance equations[5] Electron Power Balance Ion Power Balance Ion Particle Balance Neutral Particle Balance Plasma filament’s resistance is affected by electron temperature and density. These properties are updated from balance equations at each time step. [5] B. Lloyd et al., Plasma Phys. Control Fusion 38, 1627 (1996)

Start-up Analysis : Initial Condition for Start-up Simulation From ECRH pre-ionization 10% ionization is assumed. ( ) Electron will be heated. ( ) Te(0)=10eV, Ti(0)=1eV Initial Neutral Density from Paschen’s law (Stoletow point, ) In hydrogen case, minimum required E is 2.4V/m operation pressure will be (Particle confinement time) is set to 0.1ms. Impurity : two impurities (O(2%),C(1%)) No external gas influx. ψ(recycling coefficient) is set to 1.01.

Start-up Analysis : Plasma Initiation Result Result of Plasma initiation simulation Plasma current increases up to 6kA keeping proper ramp-up rate (4~ 5kA/ms) in assumed initial condition. This simulation will be used to interpret experiment results as well as design study.

Start-up Analysis : Equilibrium phase PF #2 Suppose plasma current will be 12kA by merging two 6kA plasmas. PF #3 PF #1 PF #4 Plasma parameter PF #5 PF #6 R [m] 0.3 a [m] 0.2 Ip [kA] 12 n index 0.076 q0 1.006 q95 5.962 PF #7 PF coils PF #1 PF #2 PF #3 PF #4 0At PF #5 PF #6 PF #7 -5.3kAt -1.78kAt Merged ST plasma can be in equilibrium. PF #6 and #7’s main role is to get an equilibrium.

Current Ramp-up method : Long solenoid for ramp-up Partial solenoid Merged plasma (A=1.5, Ip=12kA) need current ramp-up to reach first target plasma (A=1.5, Ip=30kA). Another method for supplying loop voltage into plasma is required. Possible Solutions 1. Another solenoid for sustaining (tentative solution) 2. Non-inductive current drive (ultimate solution) Solenoid for ramp-up (Long solenoid) At initial phase, long solenoid will be used to ramp-up plasma current, non-inductive current drive system will be installed in the future. Long solenoid will be thin to keep low aspect ratio.

Current Ramp-up Method : New Current Ramp-up Scheme in Partial Solenoid Operation PF #1 -0.044kAt PF #1 -0.044kAt PF #1 -0.044kA Small Plasma Solenoid 0A +40kAt 0A PF #2 -0.45kAt PF #2 -0.449kAt PF #2 -0.449kA PF #3 -1.83kAt PF #3 -1.833kAt PF #3 -1.833kA PF #4 -6.55kAt PF #4 -6.546kAt PF #4 -6.546kA 12kA 12kA 21kA Solenoid charging Solenoid swing down Plasma injection +40kAt 0A Solenoid 0A Small Plasma Continuous injection for sustaining may be possible through AC operation of partial solenoids.

Outline of AC Plasma Injection Scenario Feature of operation scenario Plasma injection for ramping-up plasma current and sustaining by AC operation of partial solenoid Outline of operation scenario Expected Plasma current during start-up Initiating main plasma (12kA) by merging two small plasma (6kA) Ramping-up main plasma (21kA) by injecting two small plasma (4.5kA) Ramping-up main plasma current (30kA ) Then, 30kA ST plasma is generated. Charging up partial solenoids Charging up partial solenoids

Plasma Parameters in AC Plasma Injection Scenario Plasma parameters considered in the simulation at each phase Main plasma Small plasma Major radius (R) [m] 0.3 0.33 Minor radius (a) [m] 0.2 0.1 elongation (κ) 2 1 Plasma current (Ip) [kA] 12 21 30 4.5 6 qedge value 11.6 6.62 4.64 2.95 2.21 Murakami limit [1018m-3] 2.58 4.53 6.47 9.0 12.0 Greenwald limit [1018m-3] 4.77 8.36 11.9 14.3 19.1 Toroidal B-field [T] 0.096 T at R=0.33m

AC Plasma Injection : Solenoid for AC Plasma Injection Obstacles in AC plasma injection I. Sustaining merged plasma : Plasma should exist until next injection event II. Partial solenoid charging : Charging solenoid will induce reverse toroidal E field against plasma current, resulting in plasma current decrease First of all, the means to supply voltsec to maintain merged plasma current is required. Long solenoid can be used. Negative effect due to solenoid charging should be investigated.

Investigation of Negative Effect due to Partial Solenoid Charging-up Plasma sustaining simulation Single filament plasma is used at simulation. (R=0.3m, a=0.2m, Ip=12kA) No V-sec consumption from long solenoid. Plasma decay w/o charging 12kA to 10.9kA (only ohmic decay) 0.01Vs charging 12kA to 10.8kA 0.02Vs charging 12kA to 10.7kA Negative effect due to partial solenoid charging is not severe. Most Long solenoid’s Vsec will be consumed to compensate ohmic decay.

AC Plasma Injection : Confirmation of Long Solenoid’s Role Plasma Sustaining Simulation based on circuit equation Assuming Plasma as one filament (R=0.3 m, a=0.2m, resistance obtained from Spitzer resistivity) 12kA plasma case 21kA plasma case Long Solenoid can compensate negative effect from solenoid charging-up and sustain plasma current.

AC Plasma Injection : Equilibrium Analysis at each phase 30kA ramp-up scenario through AC merging 5.4MAt 3.5MAt 3.5MAt 452kAt 452kAt 0At 50kAt 0At 50kAt 0At Solenoid charging Solenoid charging Merging Merging 12kA 12kA 21kA 21kA 30kA Ip[A] = 12kA R[m]= 0.37 a[m] = 0.20 Ip[A] = 12kA R[m]= 0.37 a[m] = 0.20 Ip[A] = 21kA R[m]= 0.35 a[m] = 0.20 Ip[A] = 21kA R[m]= 0.35 a[m] = 0.20 Ip[A] = 30kA R[m]= 0.30 a[m] = 0.20 Plasma can be in equilibrium at each phase in operation scenario.

Comparison of Charged Voltsec to Consumed Voltsec during AC Plasma Injection Suppose 12kA main plasma initiation by merging two 6kA plasmas and merging time is 1ms from MAST results[6] ① : Solenoid charging-up phase (12kA main plasma sustaining) ② : Plasma current ramp-up by merging (ramp up from 12kA to 21kA) ③ : Solenoid charging-up phase (21kA main plasma sustaining) ④ : Plasma current ramp-up by merging (ramp up from 21kA to 30kA) ① ② ③ ④ Long Solenoid Partial Solenoid Total Consumed Vsec [Wb] 0.0031 Wb (12kA sustaining) 0.0043 Wb (21kA sustaining) 0.01 Wb x 2 (at each phase ) 0.0251 Wb (0.005Wb required to ramp-up 4.5kA plasma) Through AC plasma injection, Charged Vsec is larger than consumed Vsec. Effective Vsec production scheme during operation

Total Volt-second Consumption in AC Plasma Injection Scenario Long Solenoid Partial Solenoid Total Consumed Vsec [Wb] 0.0031 Wb (12kA sustaining) 0.0043 Wb (21kA sustaining) 0.01 Wb x 2 (at each phase ) 0.0251 Wb (0.005Wb required to ramp-up 4.5kA plasma) Comparison of Volt-second consumption Long solenoid ramp-up method AC plasma injection method Total Vsec 0.0146 Wb 0.0274 Wb AC plasma injection method will consume more Vsec than long solenoid ramp-up method. However, consumed Vsec in partial solenoid can be supplied during operation through AC operation of partial solenoids.

Voltsec Consumption by Long Solenoid Depending on Ramp-up Method Volt-second consumption by long solenoid in long solenoid ramp-up method : Volt second consumed to ramp up from 12kA to 30kA Difference between Volt second consumption to ramp up from 0 to 30kA and Volt second consumption to ramp up from 0 to 12kA 0.0244 Wb (0A to 30kA) – 0.0098 Wb (0A to 12kA) = 0.0146 Wb Comparison of Volt-second consumption by long solenoid Long solenoid ramp-up method AC plasma injection method Total Vsec 0.0146 Wb 0.0074 Wb Through AC plasma injection method, we can save the Vsec consumed by long solenoid. AC plasma injection method may be a powerful scheme for breakdown and sustaining plasma in terms of Vsec consumption.

Conclusion Start-up in partial solenoid operation is studied, and possible start-up scheme is found. AC plasma injection is developed for alternative ramp-up and sustaining scheme in partial solenoid operation. AC plasma injection will be effective method to supply volt-second during operation. Partial solenoid operation scenario will be tested by experiment in near future. Design of ST facility in SNU is in progress.

Appendix : ST Facility in SNU (in construction) - Chamber Design Chamber Specification Chamber radius [m] 0.8 (middle) 0.6 (up & down) Chamber height [m] 2.4 Toroidal B field [T] 0.0875 T at r=0.33m Chamber consists of three small chambers to facilitate assembly procedure, adjusting chamber design and plasma control.

Appendix : ST Facility in SNU (in construction) : TF coil & PF coil Multi turn coils (8 turns) Use car batteries connected in parallel to apply required current (18000A) Ripple field is accounted in design Toroidal Field Coil PF coil Thin pancake coils Flexible to modify position Considering breakdown and equilibrium phase Poloidal Field Coil

Expected ST Facility in SNU : Potential Research Topics Super X Divertor [7] Magnetic Reconnection [8] Various advanced fusion research topics will be studied. Divertor Engineering (ex) Super-X divertor, radiative divertor Magnetic Reconnection (ex) Reconnection physics from merging experiment Wave Current Drive, High-β operation, … [7] P. Valanju et al., Super X divertor for NSTX, (2008) [8]http://cer.ucsd.edu/