NIMROD Applications for MHDControl

Carl SovinecUniversity of Wisconsin-Madison

for theNIMROD Team (https://nimrodteam.org)

16th Workshop on MHD Stability ControlSan Diego, CA Nov. 20-22, 2011

Outline• Introduction of NIMROD• Control and control-related applications

• RF/MHD modeling• Disruption mitigation• Imposed asymmetry

• Relevant model development• Concluding remarks

Introduction: NIMROD is a nonlinear macroscopicdynamics code for multi-scale plasma studies.

It has been applied to many configurations including:• Tokamak tearing and ELMS (above)• MHD jets (above right) and space physics• Basic plasma phenomena (below right)• Alternates (below)

S. Kruger, TX-Corp

C. Carey, WI

P. Zhu, WI

2006 Milestone

R. Milroy, WA

The implementation considers 3D nonlinear dynamicswithin a geometrically 2D domain.

• The fundamental dependent fields,V, B, n, and T (or Ti and Te), areevolved in time from initial conditionsusing fluid-based models.

• Variations over the poloidal planeare represented on a mesh ofspectral elements.

R

Z

1 1.5 2 2.5

-1

-0.5

0

0.5

1

• Variations over the periodic (toroidalor straight) coordinate are representedby finite Fourier series.

Examples of meshes used for DIII-D tearing(left) and for MRX reconnection (right).

Two-fluid sawtooth evolution of kineticfluctuation energies. (Comp. has 0≤n≤42.)

Computations related to control include sources orboundary conditions that model the physical system.

• Volumetric sources of momentum density (fluid or electron) andenergy density have been used.• Fluxes and fields applied at the wall may be symmetric orasymmetric.

CAD drawing of the HIT-SI spheromak chamber (left)and NIMROD mesh and injector Bz (in color) used insimulation (right). [Izzo and Akcay, Univ. WA]

• A common symmetricflux is the applicationof Eφ from loopvoltage.

• An example ofasymmetric fields andfluxes are the time-dependent conditionsused to model HIT-SIinjectors.

Control-related applications: To date, the twoapplications most closely tied to plasma control areRF/MHD coupling and disruption mitigation.• The RF/MHD effort seeks to model ECCD stabilization of tearing modesas a part of comprehensive simulation capability.• The project is led by Tom Jenkins of Tech-X in collaboration with DaltonSchnack, Eric Held, and Bob Harvey as part of SWIM.• Initial work demonstrated island suppression with an ad hoc, toroidallysymmetric current drive. [Jenkins, PoP 17, 12502, 2010]

Application ofsymmetric sourceaffects magneticislands over theresistive time-scale.

Recent development couples GENRAY ray-tracing andQLCALC diffusion calculation for localized deposition.

GENRAY ray bundle interceptingNIMROD data plane.

• SWIM’s Integrated Plasma Simulator (IPS)is used to coordinate computations.• Present logic is intended to model an idealsystem that targets the island O-point.• Future work will implement more realisticcontrol logic.• Predicting power requirements for ITER isthe primary physics objective.

Temperature contours before (left) and justafter (right) ECCD feedback on 2/1 island.

n≥1 Fourier modeenergy (~ island width)

n=1n=2n=3

NIMROD magnetic fluctuation energiesrespond to simulated control.

MGIsimulationofDIII‐DwithNeinjection:

1

2

2.30ms 2.63ms

Nedensityshowsefficientmixingintocoreduetoflowsassociatedwith1/1mode,furtherenhancingcorecooling.

Disruption mitigation: Simulations of MGI track impuritydensity and incorporate radiative cooling.

• Val Izzo uses ‘NIMRAD’ to investigate MHD mixing and resulting efficiency.• The computations couple NIMROD and the KPRAD radiation code.• Validation studies have been conducted using Te and ne profiles from DIII-Dand C-MOD. [Izzo, et al., PoP 15, 56109, 2008]

1)InjectedNecoolsedge,triggersMHD

2)DestructionoffluxsurfacesreducesTegradient

3)CoreTedropsrapidlyduetom=1/n=1mode

Te profiles for DIII-D Ne MGI.

3

ExampleREorbitscalculatedduringNIMRODrun;typicallythousandspersimulation.

Whenmagneticfieldsbecomestochastic,REsescape,strikingouterdivertor.

NIMRODpredictedRElossratesshowexpectedrelationshiptoDIII‐DmeasuredREcurrent(withoneexception).

• Tracer electrons evolved with collisions, ∇B and curvature drifts, bremm-strahlung and synchrotron radiation predict confinement and strike points.

Test‐particlemodelcalculatesrunawayelectron(RE)driftorbitsasMHDfieldsevolve.

Additionofn=3RMPsqualitativelychangesTQMHD,butdoesnotincreaseRElosses

ChangingRMPsymmetryton=1orn=2doesnotimproveuponno‐RMPcase

Afterpromptloss,appliedRMPfieldshavenoeffectonremainingconfinedREs.

DIII‐Dexperimentsshowedambiguouseffectsofapplyingn=3RMPsbeforeTQ,i.e.noclearbenefit.AsinNIMROD,post‐TQRMPshadnoeffect.

NonlinearcomputationswithREtracingandRMPpredictlittleenhancementoflossesduringthermalquenchinDIII‐D.

Imposed asymmetry: Simulations are being used toinvestigate possible benefits of imposing 3D fields.

• Izzo’s DIII-D simulation with n=3 RMP investigates MHD density pump-out.

density(m

‐3)

PoloidalVelocity Density(norotation)Plasmaresponse(norotation) Highedgerotation

LargetoroidalrotationneartheedgescreenstheRMPfieldsandeliminatesthedensitypump‐outeffect.

FinalDensityProfiles

A new RMP study uses circular cross-section toroidalgeometry to facilitate analytical comparisons for ELMs.• Ping Zhu previously performed analytics and computations for anintermediate ballooning regime (no RMP). [Zhu, NF 49, 95009, 2009]• The new study adds RMP perturbations.

The problem setup has uniform pressure within apedestal region.

Evolution of perturbed kineticenergy shows RMP effects prior toballooning saturation.

• Poincaré surfaces (not shown)have islands before ballooningsaturation, a stochastic layer after.

Computations of the Compact Toroidal Hybrid considerflux-surface evolution with large 3D shaping.

• Auburn’s CTH is a heliotron that can have significantrotational transform from plasma current.• While imposed magnetic fields are asymmetric,helical coils lie outside a toroidally symmetric surface.• Mark Schlutt (WI) has incorporated vacuum fieldsprovided by Jonathan Hebert (Auburn) into NIMRODboundary conditions. Auburn CTH experiment.

Evolution of Jφ profile shows currentpenetration for applied Vloop = 4 V.

time

Evolution of rotational transformindicates 2/1 activity late in time.

time

Magnetic topology evolution shows 2/1 island formationprior to loss of flux surfaces.

vacuum t = 9 ms

t = 12 ms• These 0-β, fixed-resistivitycomputations show behavior thatappears qualitatively similar to theexperiment.

• After convergence testing, nextsteps include temperature evolutionto model realistic resistivity profilesthat change in time. Poincaré surfaces show growth of closed-

flux volume then island development.

A study of field-error penetration uses straight cylindricalgeometry for verification.

• Andrea Montgomery (WI) has implemented boundary conditions for a thinresistive wall with a helical coil located outside the resistive wall.• Simple analytical profiles of the form are used toselect a stable resonant mode.

!

q(r) = q0 1+ r a( )2"[ ]1/"

Poincaré surface from alinear computation withoutflow indicates perturbationamplitude.

A linear computation withflow shows significantshielding.

Nonlinear effects with thesame flow and perturbationinduce locking.

A series of nonlinear computations demonstrates ‘sub-critical’ locking behavior.

Nonlinear results on k⋅〈V〉 as theperturbation amplitude is varied.

Sketch of different classes of lockingbehavior for flows that are above andbelow the critical rate.

• Locking information from Waelbroeck, PFB 1, 1989 and Fitzpatrick PoP 5,1998 will be adapted for verifying these large-island cylindrical results.• Computations for less-stable, larger-S (7×107) conditions maintain smallerislands and will be used for verifying small-island behavior.• Testing the response in toroidal geometry is the next computational step.

Relevant model development: Our computations are basedon single- and two-fluid plasma models.

!

"n

"t+# $ nV( ) = 0

!

mn"

"t+V #$

%

& '

(

) * V = J+B,$ nT-

-

. ,$ #/

!

3

2n"

"t+V# $%

&

' (

)

* + T# = ,nT# % $V# ,% $q# +Q#

!

"B

"t= #$% &J#V %B+

1

neJ%B#

Te

ne$n+

me

ne2

"

"tJ

'

( )

*

+ ,

!

µ0J = "#B

!

" #B = 0

Faraday’s / Ohm’s law

low-ω Ampere’s law

flow evolution

particle continuity

temperature evolution

divergence constraint• Closures for stress (Π) and heat flux (q) often use relations for collisionalplasma for practical modeling.

!

"gv =mipi

4eBˆ b #W $ I+ 3ˆ b ̂ b ( )% I+ 3ˆ b ̂ b ( ) $W# ˆ b [ ] , W & 'V +'V

T %2

3I' $V

(

) *

+

, -

!

"|| =pi#i

2

ˆ b $W $ ˆ b ( ) I% 3ˆ b ̂ b ( )

!

"# ~ $3pimi

2

10e2B2%i

W has been treated as $ nmi& isoW or $ nmi&kin'V

!

" for collisional plasma is a combination of "gv, "||, and "# .

Kinetic modeling of energetic ions is available, andmajority-species drift kinetics is under development.

W

• Charlson Kim (WA) implemented and verified PIC-based δf computationfor minority energetic particles; drift and full-Lorentz options are available.• A relatively recent application is Dylan Brennan’s (U-Tulsa) study of energetic-ion effects on 2/1 tearing in large tokamaks.• Eric Held is developing drift-kineticmodeling with a complete linearizedCoulomb collision operator for neoclassicaleffects in 3D evolution.• Comparison of bootstrap current over aNIMROD 2D spatial domain with results fromE. Belli’s 1-spatial-D NEO code provides animportant verification.• Full RF/MHD coupling will incorporate DKmodeling a la Hegna&Callen, PoP 16,112501, 2009. Comparisons of NEO’s flux-surface

averaged bootstrap current withresults from NIMROD’s DKE solution.

Concluding Remarks• Many current NIMROD modeling applications are related toplasma control, either directly or indirectly.

• The applications include boundary conditions or sourcesthat model how external controls influence magnetizedplasma over long time-scales.

• Many NIMROD applications are conducted by universityfaculty, staff, and students.

• To benefit all applications, significant active development ofNIMROD continues after more than 15 years.

No

Read NIMROD data (synthetic Mirnov)

Can identifymode, ω, γ?

Roughoutlineofcontrolsystemlogic

No

Over thresholdamplitude? Already on?

Already on?

Yes NoNo

Turn OFF

YesYes

Find O-point

Calculate newGENRAY input

parameters

Turn ON

Yes

Send newinputs toGENRAY

Hierarchy of control systems desired:“Dumb system”: Mirnov coils only (for detection)Experimental mimicking system: Implement system similar to DIII-DOptimized control system: What we want to provide“Perfect system”: Hit the O-point exactly (what we are doing in this talk)

Send PCSstatus toNIMROD

Below thresholdamplitude?

Yes No