1. 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 , 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 , Korea

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

3. 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)

4. 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

5. 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

6. 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)

7. 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

8. 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)

9. 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)

10. 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

11. 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)

12. 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)

13. 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.

14. 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.

15. 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.

16. 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.

17. Current Ramp-up Method : New Current Ramp-up Scheme in Partial Solenoid Operation
PF # kAt
PF # kAt
PF # kA
Small Plasma
Solenoid 0A
+40kAt 0A
PF # kAt
PF # kAt
PF # kA
PF # kAt
PF # kAt
PF # kA
PF # kAt
PF # kAt
PF # kA
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.

18. 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

19. 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

20. 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.

21. 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.

22. 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.

23. 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.

24. 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]
Wb (12kA sustaining)
Wb (21kA sustaining)
0.01 Wb x 2
(at each phase ) 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

25. Total Volt-second Consumption in AC Plasma Injection Scenario
Long Solenoid
Partial Solenoid
Total
Consumed Vsec [Wb]
Wb (12kA sustaining)
Wb (21kA sustaining)
0.01 Wb x 2
(at each phase ) 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 Wb 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.

26. 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
Wb (0A to 30kA) – Wb (0A to 12kA) = Wb
Comparison of Volt-second consumption by long solenoid
Long solenoid ramp-up method
AC plasma injection method
Total Vsec Wb 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.

27. 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.

28. 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]
T at r=0.33m
Chamber consists of three small chambers to facilitate assembly procedure, adjusting chamber design and plasma control.

29. 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

30. 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]