1. 24th IAEA Fusion Energy Conference, San Diego, USA October 8-13, 2012
Dynamo Current Drive
ICC/1-1Ra
Progress on HIT-SI and Imposed Dynamo Current Drive T. R. Jarboe, C. Akcay, D. A. Ennis, C. J. Hansen, N. K. Hicks,
A. C. Hossack, G. J. Marklin, B. A. Nelson, R. J. Smith, B. S. Victor
University of Washington, Seattle, WA 98195, USA
ICC/1-1Rb
Flow and Magnetic Field Profiles in the HIST Spherical Torus Plasmas Sustained by Double Pulsing Coaxial Helicity Injection M. Nagata, T. Higashi, M. Ishihara, T. Hanao, K. Ito, K. Matumoto,
Y. Kikuchi, and N. Fukumoto, T. Kanki* Univerisity of Hyogo, Himeji, Hyogo , Japan *Japan Coast Guard Academy, Kure, Hiroshima , Japan
24th IAEA Fusion Energy Conference, San Diego, USA October 8-13, 2012 1

2. Outline Explanation of dynamo current drive Prediction of model
Experimental data
Possible implications for tokamaks
Summary

3. Both experiments drive edge current directly and produce current and flux amplification by dynamo current drive.
HIST
HIT-SI

4. Dynamo current drive can be understood based on well known concepts.
Electrons are frozen to magnetic fields.
Magnetic fluctuations can be considered separately from equilibrium (mean dynamo theory).
Field lines have tension.
Massless electrons transmit force to ions.
In the externally driven regions dynamo force brakes electrons so the force is in the direction of the current giving ion velocity in that direction.
In the dynamo driven region the force is with the electron flow resulting ion flow against the current.

5. Fluctuations crossing flux surfaces give cross-field current drive effect.
Fluctuations drives mean current.
BBll tension on the flux surface provides the force that drives current inside the flux surface.

6. Three conditions must be met for dynamo current drive to form and sustain an equilibrium.
Externally driven current must be higher speed than dynamo driven equilibrium current.
Cross-field fluctuations must be strong enough to drive the current.
Can be produce by instability.
Can be imposed externally.
The driven current must be in a region that supports an equilibrium.

7. Non-inductive current start-up CHI start-up and OH coupling ramp-up
Progress on Coaxial Helicity Injection
Coaxial Helicity Injection
Transient-CHI
Steady-state CHI
Non-inductive current start-up
Dynamo current drive
(ST: HIT-II)
CHI start-up and OH coupling ramp-up
(ST: HIT-II, NSTX-CHI; See EX-P2-10)
Muti-pulsing CHI (better time averaged confinement)
ST: HIST
Spheromak: SSPX
NSTX-CHI (PPPL)
HIT-II (UW)
HIST (U.Hyogo,Japan)
SSPX (LLNL)

8. HIST sustains current and flux amplification in mean-field closed flux surfaces by dynamo
Current amplification
Dynamo Fluctuation
2nd CHI pulse
HIST

9. MHD and Hall dynamo electric fields balance in the parallel mean-field Ohm’s law
MHD dynamo
Hall dynamo
Electron dynamics
Anti-dynamo
Dynamo
ExB drift
Diamagnetic drift
Core
Edge
MHD dynamo
Core
Hall dynamo
Two fluid effect is large
Separatrix
(Driven region)
HIST

10. Poloidal shear flow is generated by CHI
Observation of Zonal flow–like
poloidal flow profile
Self-Generation of radial electric field Er
Poloidal flow
Diamagnetic drift is significant
Itf
Toroidal flow
Poloidal shear flow layer
ion
Density It . It Er
Steep gradient
Reduction of dB
HIST
Separatrix

11. Imposed Dynamo Current Drive (IDCD) is a major advance toward fusion power.
Current driving fluctuations are imposed (not produced by instability).
A stable equilibrium can be sustained.
Current profile can be controlled.
The following data validates model:
Toroidal current versus time
Current profile
Injector impedance scaling with j/n of spheromak.

12. On HIT-SI the injectors drive the edge and impose the fluctuations
On HIT-SI the injectors drive the edge and impose the fluctuations. Imposed dynamo model predicts current time dependence. Data also validate 2-fluid XMHD simulation by NIMROD.
HIT-SI
T.R. Jarboe et al., Nucl. Fusion 52 (2012)

13. IDCD equation models the toroidal current with the same fitting parameter across a range of shots.13
HIT-SI

14. Imposed dynamo model predicts current profile
The required B decreases as the minor radius decreases.
Inside the dynamo driven region the imposed B increases as the minor radius decreases.
The excess drive results in a constant j/B in the dynamo driven region*.
j/B r a
For more on NIMROD simulation see
PSI-Center poster TH/P2-02
transition
*T.R. Jarboe et al., Nucl. Fusion 52 (2012)
HIT-SI

15. Data validate imposed-dynamo prediction
Data validate imposed-dynamo prediction* that injector impedance  spheromak j/n
IDCD is engaged during the time between the vertical blue lines.
*T.R. Jarboe et al., Nucl. Fusion 52 (2012)
HIT-SI

16. Two-Fluid resistive MHD seems to capture the physics of HIST and HIT-SI
MHD and Hall dynamo electric fields balance in the parallel mean-field Ohm’s law.
Poloidal shear flow generated by CHI is consistent with two-fluid dynamo.
HIT:
Imposed dynamo model is two-fluid.
Two-fluid simulations show good agreement:
n=1 to n=0 transition rate correct
Current gain only 30% low
Profile shape agrees with data as well as might be expected considering:
Injectors modeled as boundary conditions
Assumed constant density, resistivity, and viscosity

17. On a reactor and ITER the required injector parameters and fluctuation levels are quite modest.
Present HIT-SI
ARIES-AT
ITER
Itor (kA) 55
12,800
15,000
Temp. (eV) 6
18,000
8,100
Vinj (Volts)
500
630
830
Iinj (kA) 18 11
L/R (s)
0.0003
605
454
Brms /B
0.16
0.0001
Dynamo action should have the following effects on tokamaks:
Fluctuations flatten the j/B profile.
Locked RWM can stop plasma current.
RMPs change the edge equilibrium and rotation along with confinement.
Fluctuations that change rotate also change the current profile.
Low level uncontrolled fluctuation can randomly modify the equilibrium.

18. Summary of dynamo current drive
Dynamo current drive is a power efficient and cost effective method of sustaining plasma current.
Mean closed flux has been sustained by coaxial helicity injection and by imposed dynamo current drive.
With imposed dynamo current drive the current driving fluctuations are imposed externally (not produced by instability)
A stable equilibrium can be sustained
Current profile can be controlled
The amplitude of the fluctuations required for current drive in a reactor is quite low B/B  10-4.
Method may be compatible with sufficient confinement
Normal uncontrolled fluctuations not only affect confinement but also the equilibrium profile

19. The Taylor state that includes the injector fields can be used to predict the imposed B
Br  B vs. Time
Data:
Taylor:

20. HIT-SI imposes excess fluctuation inside the separatrix

21. HIT-SI3 provides a definitive test of profile control
B2 required for constant 
B2 produced (Taylor)
B2
Injectors 120o out of phase
Injectors in
phase
B2
HIT-SI3 

22. Injector requirements are nearly constant
Injector requirements are nearly constant. rplas/rgi decreases with machine size
Parameters for sustaining various plasmas with IDCD. The injector frequency is 80 kHz and a Zeff= 2 is used. alfv is the wavelength of the Alfvén wave at 80 kHz. On the two tokamaks the gyro-radius is the poloidal gyro-radius to approximate the banana width.
Parameter
Present HIT-SI
SSPX
HIT-PoP
HIT-POW
ARIES-AT
ITER
n (1019 m-3)
2.5 10
3.3 20
a (m)
0.25
0.6
1.8
1.3 2
R0 (m)
0.84
2.52
5.2
6.2
B (T)
.044
0.8
0.28
4.0
5.8
5.3
Itor (kA) 55
1000
850
37,000
12,800
15,000
Tpeak (eV)
500
18,000
8,100
Vinj (Volts)
1200
400
770
630
830
Iinj (kA) 18 11 6 15
L/R (s)
0.0003
0.051
0.76
903
605
454
rgi (mm) 8 3 4
rplas/rgi 12
100
3.1
rflux/rgi 9
1.5
0.30
0.024
.004
.005
alfv/a 63 25 62 52
Brms /B
0.16
0.006
.003
0.0002
0.0001
The plasma oscillates about the mean flux surface by rplas because of the first order term jB in mean dynamo theory. It time averages to zero but has finite amplitude. [T.R. Jarboe et al., Nucl. Fusion 52 (2012) ]

23. Place three injectors on one side.
Future Plans
Place three injectors on one side.
Drives plasma rotation for stability
Injectors have same preferred direction
Injectors easy to shield from DC spheromak fields
Thicker plate gives better injector opening
Using higher power surface treatment
Try perforated plate backed by a pumped chamber for density control
HIT-SI3

24. Limitations of HIT-SI Density builds in time and spoils performance.
Limits the temperature because of pressure limit
Excessive wall loading can damage insulator.
Limits the time of a shot and the power 
Limits the spheromak current
Limits Temperature and density
rplas/rgi too large for a confinement experiment (fundamental problem with all previous spheromak experiments).

25. Experiment to test and develop IDCD with sufficient confinement
HIT-PoP is designed to be TF-coil free, high-beta (>10%), and DCON stable with an IDCD sustained equilibrium
Cryro-pumping
Experiment to test and develop IDCD with sufficient confinement

26. The science is now advanced to the point it is ready for a new Dynomak device
A TF-coil free, high-beta (>10%), and DCON stable with an IDCD sustained equilibrium seems possible.
Thus, formation, sustainment, equilibrium, stability, and confinement are all in hand.
The goal of this dedicated current drive experiment will be to demonstrate good confinement while sustaining by IDCD.

27. Achieving sufficient confinement is expected
A stable equilibrium will be sustained having better confinement than previously sustained unstable configurations.
The amplitude of the plasma motion due to dynamo will be about an ion gyro radius. In previous experiments the amplitude was greater then the minor radius, unacceptably high.
Decaying spheromaks and RFPs have shown good confinement.
The fluctuations will be controlled to be only as large as necessary. Presently they are too large near the magnetic axis.
The fluctuations needed for the reactor seem acceptably low.
A larger machine will allow the development of good confinement.
Validated two-fluid NIMROD simulations show transient flux surface formation with only a current gain of 6 for an IDCD sustained equilibria. The experiment will have over 40 gain. With more optimal fluctuation profile sufficient confinement likely.
Required fluctuations at the magnetic axis are much less than for a transformer driven RFP. (The largest fluctuations are required in the externally driven region, which is around the magnetic axis on the RFP)
Will use much better (than previous spheromaks) density control
1 second pulse will allow time for good confinement to develop

28. The Dynomak experiment
Ip = 850 kA
a = 0.6 m
T = 1 keV
n = 3.3 x 1019 m-1
tpulse= 1 s
3 m

29. Current amplification of 3 achieved at 36.8 kHz
Figure shown on same scale as results from 14.5 kHz
Still working on increasing power at this frequency

30. Density evolution similar at 14.5 and 36.8 kHz
Fueling rate of 36.8 kHz shot is ~50% of the 14.5 kHz shot
Similar ratio of δne/ne at both frequencies

31. Two fluid MHD simulations results are similar to data

32. Fluctuations are too large at smaller r to expect good confinement
B (unfiltered)
Fluctuations are too large at smaller r to expect good confinement
Bpol (averaged over a cycle)
Btor (averaged over a cycle)

33. Injector requirements are nearly constant
Injector requirements are nearly constant. rplas/rgi decreases with machine size
Parameter
Present HIT-SI
SSPX
HIT-PoP
HIT-POW
ARIES-AT
ITER
n (1019 m-3)
2.5 10
3.3 20
a (m)
0.25
0.6
1.8
1.3 2
R0 (m)
0.84
2.52
5.2
6.2
B (T)
.044
0.8
0.28
4.0
5.8
5.3
Itor (kA) 55
1000
850
37,000
12,800
15,000
Temp. (eV) 6
250
500
18,000
8,100
Vinj (Volts)
1200
400
770
630
830
Iinj (kA) 18 11 15
L/R (s)
0.0003
0.051
0.76
903
605
454
rgi (mm) 8 3 4
rplas/rgi 12
100
3.1
rflux/rgi 9
1.5
0.30
0.024
.004
.005
alfv/a 63 25 62 52
Brms /B
0.16
0.006
.003
0.0002
0.0001

34. Helicity and power always injected