This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344"

LLNL-PRES-641496"

Resistive-MHD simulations of Coaxial Helicity Injection (CHI) in

NSTX !

Bick Hooper, LLNL

NIMROD Team Meeting"Boulder, CO"

August 13-15, 2013"

Acknowledgements

This work was done in collaboration with: Carl Sovinec, University of Washington Roger Raman, University of Washington and NSTX Fatima Ebrahimi, PPPL and University of New Hampshire Jon Menard, PPPL

2  

Comparing simulations with experiment

There are some differences between the simulation results and experiment: • The injector current decays more slowly in the

simulation than in the experiment • The volume of close flux is large but smaller than

experiment I will discuss the differences at the end of the talk

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NSTX: Shot shows expanding flux bubble!

See R. Raman, et al. Phys. Rev. Letters 97, 175002 (2006)"

4  

Boundary conditions for helicity injection!• Rate-of-change of net toroidal flux –– equals Vinj –

Vabs

• Absorber voltage –– determined by requiring the total vacuum toroidal flux to be constant, corresponding to a constant ITF

• Bϕ – Bϕ,vac << Bϕ,vac à Vinj – Vabs << Vinj

• Discharge (injector) current –– measured by the change in RBϕ just above the injector slot

• Toroidal flux –– carried in by ExB flow at the injector and out by ExB flow at the absorber

• Equating flows of vacuum toroidal flux yields

!

Erabs = Er

inj rinj,minrabs,min

drB"r2B2rinj ,min

rinj ,max

#

drB"r2B2rabs,min

rabs,max

#

This generalizes the model used in HIT-II: R.A. Bayliss, C.R. Sovinec, and A.J. Redd, Phys. Plasmas 18, 094502 (2011).

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Simulation –– A narrow injection slot narrows the injected current!

Injection slot!

Finite elements generate additional resolution!

A narrow slot was found to be important in the experiment –– guided the simulations!

Current flow in flux bubble!

The narrow slot generates a narrow distribution of injected current"

Vertical current inside radius R at the bottom of the flux conserver!Wide slot (11 cm)! Narrow slot (4 cm)!

6  

Absorber Coils –– not used in these simulations

ISSUE:    The  absorber  slot  boundary  condi7on  requires  an  outward  EXB  flow    

Experiment:    Poloidal-­‐field  coils  shield  absorber  slot  from  plasma    Simula7on:    ExB  out-­‐flow  at  the  extractor  slot  ––  generates  plasma  flows  in  plasma  outside  the  flux  bubble    •  Absorber  coils  energized  ––  Problem  as  the  bubble  approaches  NSTX  top    

–  Flows  forced  to  small  R  by  absorber  magne7c  fields  ––  cross  B-­‐field  to  reach  absorber  

–  Flows  interact  with  bubble  –  Result  –  Current  not  fully  localized  in  surface  layer    

•  Absorber  coils  not  energized  ––  Flow  reaches  absorber  slot  along  B    

–  Negligible  interac7on  with  bubble  –  Injector  and  toroidal  currents  largely  localized  in  the  bubble  –  Experimental  problems  with  breakdown  do  not  occur  in  simula7ons        

Conclusion:    No  absorber  coils  in  present  simula7ons  

7  

Two simulations –– used in the present study

hi-­‐temp    High-­‐temperature,  “high  quality”  discharge  without  radia7on  cooling  and  with  a  low  thermal  conduc7vity  across  the  mag.  field    •  Used  to  show  plasma  evolu7on  under  good  condi7ons  

 low-­‐temp    Low-­‐temperature  discharge  with  radia7on  cooling  

 •  Used  to  study  reconnec7on  and  X-­‐point  forma7on  physics  

8  

Discharge  currents  and  voltages  

hi-­‐temp   low-­‐temp  

Temperature  profiles  at  z  =  0  

Note:    The  glitches  shortly  aVer  9  ms  are  when  the  X-­‐point  forms  

t  =  9  ms  

Flux-surface evolution – hi-temp – similar to exp.

9  

7.0  ms  

8.5  ms  

9.7  ms  

7.0  ms  

10.0  ms  

8.5  ms  

13.1  ms  

Note  X-­‐point  forma7on  at  boXom  of  NSTX  

low-temp –– “simpler” flux configuration at 9 ms Use to analyze X-point formation

10  

hi-­‐temp  has  two  shallow  (<0.1  mWb)  regions  of  closed  flux  •  High  temperature    

–  small  magneNc  diffusion  coefficient    –  current  is  well  localized  to  the  surface  

of  the  flux  bubble  •  Flat  poloidal  flux  ––  allows  some  flux  

surface  closure    low-­‐temp  forms  a  finger  of  flux  above  the  injector  slot  ––  easier  analysis  

X-point forms by 9.120 ms

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t = 9.006 ms ! t = 9.060 ms ! t = 9.120 ms ! t = 9.216 ms !

ReconnecNon  is  underway  by  9.060  ms  

Flux-surface formation correlates with flow reduction from injector slot

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Poincáre  puncture  plots  

Poloidal  flow  vectors  

9.060  ms  

9.006  ms    

•  No  closed  flux  surfaces    

•  Flow  from  the  injector  slot  supports  the  flux  “bubble”    

9.060  ms    

•  Closed  flux  surfaces  at  large  z  

 

•  Injector  voltage  and  ExB  velocity  are  small  

 

•  Li`le  flow  from  the  injector  slot  

9.006  ms  

Temperatures are low in flux plume –– flux closure heats plasma locally

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t = 9.006 ms! t = 9.060 ms!

Magnetic diffusion!!!!!!!Diffusion distance in 50 µs is!!!!Distances are similar to those in the plume!

Dm = 411 Te3/2

! 5 m2 s at 20 eV! 40 m2 /s at 5 eV

!x " 0.01 m at 20 eV" 0.04 m at 5 eV

5.4 eV!

15.3 eV!

4 eV!

12.1 eV!

20.3 eV!

25.5 eV!

Magnetic pressure analysis

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! pB2

2" B p #!B p "

B!2

rr̂

$

%&&

'

())= 0

B p !"Br # 0

!!r2B!0"B! +"B!

2 + Br2 + Bz

2( ) ! "22B!0"B! +"B!

2

r

!W ! 2B"0!B" +!B"2 + Br

2 + Bz2 " #4

B"0!B" +!B"2 2

r$ dr + const.

The  evolving  configura7on  is  in  quasi  magne7c-­‐force  balance  

The    magne7c  curvature  in  the  “finger”  is  small  un7l  the  X-­‐point  forms  

Set                                                  ––  The  terms  in              cancel  so  B! = B!0 +"B! B! 02

Integrate  over  r  to  get  twice  the  magne7c  pressure  due  to  the  plasma  

δBϕ at 9.006 ms (before X-point formation starts)

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“Background”  from  injected  current  near  the  surface  of  the  stretched  poloidal  flux.    

Scales  approx.  as  1/r      ContribuNon  from  currents  driven  by  the  plasma  flow  in  the  flux-­‐finger  

Plasma-magnetic fields before and during reconnection !

16  

9.006  ms  

9.060  ms  

•  δBϕ  drops  as  the  flow  from  the  slot  ceases    

•  The  width  of  the  “flux-­‐finger”  decreases  as  the  poloidal  field  reconnects  at  the  null  line  

Magnetic pressure before and during reconnection !

17  

9.006  ms  

9.060  ms  

•  Before  reconnecNon  the  magneNc  pressure  varies  smoothly  through  the  flux-­‐finger  

       •  During  reconnecNon  the  magneNc  

pressure  adjacent  to  the  poloidal-­‐field  null  exceeds  pressure  at  the  null,  driving  flow  and  field-­‐lines  into  the  null  

Magnetic fields following poloidal-field reconnection !

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9.216  ms  

•  The  radial  “cut”  is  below  the  X-­‐point  and  thus  in  the  private-­‐flux  region  

•  The  fields  vary  smoothly  and  there  is  no  poloidal-­‐field  null  •  The  curvature  is  not  negligible  ager  the  X-­‐point  forms    Conclusions    •  X-­‐point  formaNon  is  “triggered”  by  the  drop  of  toroidal  flux  carried  by  the  

flow  from  the    injector  slot  •  The  reconnecNon  is  axisymmetric  and  thus  characterized  as  “Sweet-­‐Parker”  

Following flux-closure – current evolution in hi-temp!

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10.0  ms  

13.1  ms  

•  Following  closure  the  toroidal  current  confined  in  the  closed  flux  is  ≈  13%.    It  increases  with  Nme  =>  100%  at          ≈  13.5  ms  

 

•  With  constant  boundary  flux  the  enclosed  current  remains  constant  ––  the  ohmic  drive  due  to  the  changing  poloidal  flux  is  important  

 

•  The  injector  current  goes  to  zero  at  the  same  Nme  as  the  enclosed  current  =  100%  

 

•  Ager  ≈  13.5  ms  the  closed  flux  is  “leaning”  on  the  central  column  

The enclosed net toroidal flux = net injected toroidal flux at the same time !

20  

•  The  net  toroidal  flux  injecNon  rate  =    Vinj  –  Vabs    <<    Vinj    

 •  The  toroidal  flux  outside  the  closed  flux  =>  0  when  the  injector  current  =  0  

Remaining differences with experiment include!

21  

Injector  current    

•  Experiment:  Iinj  =  0  at  t  =  11.5  ms  (Itor  =  154  kA)  Itor  =  106  kA  at  13.5  ms    •  SimulaNon  Iinj  =  0  at  t  =13.5  ms      Itor  =  118  kA  at  13.5  ms    Closed  volume  at  9  ms    

•  Vol(exp.)  >  Vol(sim.)  •  Experiment:  Rmax  ≈  1.5  m  at  midplane  •  SimulaNon:  Rmax  ≈  1.3  m  at  midplane    Density  spaNal  distribuNon    

•  Experiment:  High  density  in  current  channel,  low  density  inside  flux  bubble  •  SimulaNon:  Uniform  density        ImpuriNes    

•  Experiment:  Important  •  SimulaNon:  Included  but  model  needs  improvement    Absorber  coils    

•  Experiment:  On  •  SimulaNon:  Off  

Summary!

22  

•  Coaxial  Helicity  Injec7on  in  NSTX  reproduces  many  of  features  of  the  experiment  

 –  Flux-­‐bubble  forma7on  and  general  characteris7cs  –  X-­‐point  forma7on  and  flux  surface  closure  soon  aVer  reduc7on  in  injector  voltage  

–  Long-­‐lived  closed  flux  surfaces  suitable  for  start-­‐up  plasmas    

•  Several  differences  remain  which  will  be  addressed  in  the  coming  months  

   The  next  goal  of  the  study  is  to  beXer  reproduce  the  laboratory  results