presented by j.e. menard princeton plasma physics laboratory mhd sfg meeting thursday, may 19, 2005...

Presented by J.E. Menard Princeton Plasma Physics Laboratory

MHD SFG Meeting Thursday, May 19, 2005

nearly identical to my talk at:2005 International Sherwood Fusion Theory Conference

April 11-13, 2005Stateline, Nevada, USA

This work supported by the US DoE, UK EPSRC, and EURATOM

Unique MHD Properties of Spherical Torus Plasmas

Supported by

J.E. Menard – MHD SFG – 5/19/20052

Special thanks to contributors to this talk:

J. Bialek, S.A. Sabbagh, A. Sontag, W. Zhu (Columbia University)

M.S. Chu, R.J. La Haye, P.B. Snyder (General Atomics)

D. Stutman, K. Tritz (Johns Hopkins University)

A.H. Glasser, X.Z. Tang (Los Alamos National Laboratory)

H. Strauss (New York University)

R. Maingi, Y.-K.M. Peng (Oak Ridge National Laboratory)

E. Belova, J. Breslau, E.D. Fredrickson, G. Fu, D.A. Gates, J. Manickam, S.S. Medley, M. Ono, W. Park (PPPL)

W. Heidbrink (University of California – Irvine)

R. Betti, L. Guazzotto (University of Rochester)

T. Jarboe, R. Raman (University of Washington)

R. Fonck, C. Hegna (University of Wisconsin – Madison)

R. Buttery, S. Saarelma, A. Sykes, H.R. Wilson (Culham Science Centre – United Kingdom)

Y. Ono, Y. Takase (University of Tokyo - Japan)

and the entire NSTX Research Team

Columbia UComp-X

General AtomicsINEL

Johns Hopkins ULANLLLNL

LodestarMIT

Nova PhotonicsNYU

ORNLPPPL

PSISNL

UC DavisUC Irvine

UCLAUCSD

U MarylandU Rochester

U WashingtonU Wisconsin

Culham Sci CtrHiroshima U

HISTKyushu Tokai U

Niigata UTsukuba U

U TokyoJAERI

Ioffe InstTRINITI

KBSIKAIST

ENEA, FrascatiCEA, Cadarache

IPP, JülichIPP, Garching

U Quebec


World Spherical Torus (ST) Community Continues to Grow in Experiments and Research Goals

Lowered cost, very high , and low-A physics attract high interest

• HIST• LATE• NUCTE-ST• TS3,4• TST-2• UTST• All Japan ST• SUNIST

MAST •Globus-M •

GUTTA •Proto-Sphera •

STPC-EX •KTM •

HIT-SI •Pegasus •

CDX-U/LTX •NSTX •

ETE •

19 ST research centers world-wide(M. Peng – ORNL)


NSTX (USA) and MAST (UK) are investigating low-collisionality toroidal plasmas at low aspect ratio

NSTX MAST

Close-fitting passive stabilizers:

Wall stabilization of external kink

Internal poloidal field coils:

Plasma formation w/o solenoid

Typical Parameters

Aspect ratio A < 1.6Elongation < 2.7Triangularity < 0.8Major radius R0 0.85m

Plasma Current Ip < 1.5MA

Toroidal Field BT0 < 0.6T

Poloidal flux < 1WbPulse Length < 1.5sNBI Heating < 7MW

Te, Ti = 1-4keVne = 1019-1020m-3

e, i 0.1, 1

S (Lundquist #) = 107 (core)Pr (Prandtl #) = 10-100

R0 a


Largest STs operate in unique MHD parameter regime

• Low–A configuration access to high – Configuration generates strong natural shaping– Higher stability limits with broad pressure and current profiles – Diamagnetic frequency comparable to ideal mode growth rates

• Neutral Beam Injection (NBI) heating dominant– Largest STs presently have uni-directional beam injection– Large toroidal rotation inseparable from high – n, p profiles decoupled from flux surfaces– Flow-shearing rates comparable to ideal growth rates– Large population of energetic ions produced

• Fast ions constitute 15-50% of total stored energy• Vfast / VAlfvén = 2-4 strong drive for energetic particle modes• Parameters potentially relevant for ITER fast-ion physics

The ST is an unique & important platform for testing MHD theory and simulation


ST configuration allows access to high plasmas

• Troyon scaling Max(T) ~ N IP / aBT

• Low A higher IP / aBT at same q* (i.e. same kink stability)• Low A also has higher N limit w.r.t. kink & ballooning modes

PEGASUS: Explore plasma limits as A1

Paramagnetic plasma: local 50%, diamagnetic: local 100%


STs can produce strongly-shaped plasmas• Natural elongation increases rapidly with decreasing A and li• Low-li plasma stability enhanced by large edge magnetic shear at low-A• Elongation up to 2.6 at =0.5 achieved in NSTX at low li = 0.5-0.6

– NSTX will increase from 0.5 0.8 at high this year

• Low A needs high and to maximize T at high P(i.e. bootstrap fraction)

TRANSP Up to 60% non-inductive current fraction w/ fBS = 50% at T = 15-20%

Internal Inductance

Higher yields simultaneously higher T and fBS 0.51/2P

(elongation)

20042002-03

Control system upgrade higher

(D. Gates - PPPL)

T (%) 0.51/2P


Unidirectional beam-heating drives large toroidal rotation

Ne()

Model ne(,R) w/

matches ne dataIncludes fast-ion p and

nD

107540 at t=333ms

Solid curves: Model ns(,R) w/ rotation

Dashed curves: Ns(density w/o

rotation

MS = v / vsound = 0.4-0.8, MA = v / vA = 0.2-0.5 (higher in ST)

Force balance + neutrality ne(,R) = Ne() exp(M2() (R2–R02)/2T())

Centrifugal effects evident in ne(R) profiles:


Presently studying role of flow in equilibrium reconstructions and effect of p-anisotropy

FLOW code ( L. Guazzotto – U. Roch.) Density profile shift in a static plasma for

varying anisotropy for an NSTX-like equilibrium

EFIT w/ rotation + MSE (S. Sabbagh, CU)

Phys. Plasmas, Vol. 11, No. 2, February 2004-2

-1

1

2

0

Z(m

)

0.5 2.01.0 1.5R(m)

0.0

114444t=0.257s

iso-surface

p iso-surface

(no p-anisotropy)

Developing stability code for arbitrary flow and


ST configuration impacts full spectrum of MHD activity

ST MHD areas treated in this presentation:

• Internal kink mode

• Resistive Wall Mode (RWM)

• Edge Localized Modes (ELM)

• Neoclassical Tearing Modes (NTM)

• Alfvén Eigenmodes (*AE)

• Solenoid-free ST plasma formation



• Internal kink mode– Flow-shearing rate ~ Mode linear w/o rotation– Rotation + enhanced * possible saturation mechanism?

• Resistive Wall Mode (RWM)– Low A, high edge-q, and large vSound / vAlfvén impact critical

– Higher plasma (lower S) may impact RWM scaling

• Edge Localized Modes (ELM)– Strong intrinsic shaping enhances pedestal stability– Larger rotational shear may also enhance stability

• Neoclassical Tearing Modes (NTM)– Low-A enhances toroidal curvature effects– Toroidal mode coupling stronger, q=1 radius larger

• Alfvén Eigenmodes (*AE) and Energetic Particle Modes (EPM)– Intrinsically large vfast / vA and fast enhanced instability drive– Resonances at 1st ci harmonic

• Solenoid-free ST plasma formation– Coaxial helicity injection and electron beam injection – Plasma merging/compression and PF-coil direct induction


Sawteeth are rare in NSTX at high- and with large rotation

Neutron rate ½ expected value during mode activity, but sometimes recovers

Instead, 1/1 mode saturates - Why? • degrades fast-ion confinement• flattens core rotation profile

108103

(Submitted for publication in Nuc. Fus. – J. Menard )


SXR data consistent w/ rapid growth saturation

227ms 228ms 229ms

230ms 240ms 270ms

(USXR data from Stutman & Tritz - JHU)

Island model h fit to SXR

SXR data (line-integrated)


Sheared rotation is stabilizing, but mode flattens profile

M3DM3D resistive MHD code Sheared rotation slows mode growth by factor of 2-3

Core flattening observed in M3D and experiment even w/o complete reconnection

Complete collapse of profile and island locking disruption

W. Park - PPPL


Larger BP / B in ST enhances damping from modes

• Neoclassical Toroidal Viscosity (NTV) good candidate to explain core rotation flattening

(K.C. Shaing et al., Phys. Fluids 29 (1986) 521, also Lazzaro, Sabbagh, Zhu…)

• Larger BP / B in ST larger ratio of brm,n/ B

• 1/1 mode NTV needed to match evolutiondiamonds measured lines calculated

(Example shown: Coupled 1/1 + 2/1 modes at high-

NTV apparently explains flattening from 1/1

Important to develop and include improved viscosity models in non-linear MHD simulations

mode

2,1,2

NTV i,

~m n

m n r

m n

bT T

B

2 2 1(on island only)NTV EMR R r T T S

t r r r

Torque balance

Damping

Without NTV

With NTV

W. Zhu – Columbia Univ.


Diamagnetic effects may contribute to saturation of the 1/1 mode at high

• 1/1 island displaces core enhanced p and q in reconnection region– Locally enhanced *i and *e stabilizing, higher shear destabilizing– Rogers and Zakharov: quasi-linear model with high-A, circular plasma, no rotation– Significant non-linear stabilization possible for ST parameters for range of q-shear

• High increased *iAiA

i /a

A = R0/a = aspect ratio

i = ion skin depth

a = minor radius

Model predictions:- Mode stable for 0 < 0.5 *i

- Low / high shear no saturation

- Shear s 0.1-0.2 allows saturated 0 / rq=1 0.5similar to measured displacement

• MSE will allow q measurement this year

Preliminary M3D result * and may

synergistically contribute to saturation (W. Park) B. Rogers and L. Zakharov

Phys. Plasmas 2 (9), September 1995

0 / *i

0 / rq=1

108103


MHD Counter 2Fuids Co 2Fuids

Saturation with hot spot pulled away from x-point

Crash faster than MHD case

MA=+-0.3 MA=-0.3 MA=+0.3

Temperature


Saturated 1/1 modes observed late in longest-duration discharges this year

Sawteeth (?)

400ms 1/1 mode


Rotation flattening from 1/1 observed, rotation decays gradually thereafter


Plasma J-profile appears nearly time-invariant late in saturation phase.

Preliminary MSE EFITs consistent with q(0) < 1



• Internal kink mode– Flow-shearing rate ~ linear w/o rotation– Rotation + enhanced * possible saturation mechanism?


– Higher plasma (lower S) may impact RWM scaling• Edge Localized Modes (ELM)

– Strong intrinsic shaping enhances pedestal stability– Larger rotational shear may also enhance stability





Wall stabilization physics understanding is key to sustained plasma operation at maximum

• High t < 40%, N = 6.8 reached

N

li

N/li = 12 68

4

10

wall stabilized

• Global MHD modes can lead to rotation damping, collapse• Physics of sustained stabilization is applicable to ITER

• Operation with N / Nno-wall > 1.3

at highest N for pulse >> wall

-25-20-15-10

-505

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

N

01234567

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

DCON

W0

10

20

0.6 0.70.50.40.30.20.10.0t(s)

n=1 (no-wall)n=1 (wall)

112402

wall stabilized

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

EFIT

core plasma rotation(x10 kHz)

(S. Sabbagh, CU)


ST research will improve our understanding of rotational stabilization of the RWM

• Drift Kinetic Theory:– Trapped-particle effects at finite significantly weaken ion Landau damping – Toroidal inertia enhancement modifies eigenfunction when / A > 1 / 4q2

• Experimental crit consistent with scaling / q2 – why?

• ST has higher sound / A distinguish between s and A scaling?• Is stabilizing dissipation localized to resonant surfaces, or more global?

– Attempting to answer these questions w/ NSTX / DIII-D similarity experiments

(R. La Haye – GA)

(A. Sontag - CU)


Active control of RWM in ST geometry will complement research at higher aspect ratio

20.0 0.2 0.4 0.6 0.8 1.0

1

0

-1

N = 5.0114024

R

Z

R0+ aR0- a

DCON

R0+ a R0+ aR0- a

B (

arb)

RWM eigenfunction strongly ballooning

at high , low-A outboard coils effective

Like (present) ITER design, NSTX feedback system must deal with external mid-plane coils and nearby (blanket-like) passive plates VALEN code

J. Bialek – CU

S. Sabbagh – CU, A. Glasser - LANL (Equilibria used have Nno-wall = 5.1; Nwall = 6.9)

Feedback stabilize RWM at C = 68% without rotation


MARS code calculations for NSTX indicate plasma 0 destabilizing for RWM

• 0 increases WALL for large WALL

• Also apparent lowering of no-wall limit

Ideal plasma

ResistivePlasma

= 0

• 0 required for benchmarking/comparison to M3D- Studying interplay between resistivity and dissipation

• Will test Bondeson/Chu kinetic damping model in MARS for NSTX- Kinetic damping model applicable to low-A needed

No-walllimit

Ideal-walllimit

Chalmers, GA, PPPL


M3D simulations examining role of plasma and rotation

Perturbed Poloidal flux at

0.05 Av

R

Saturates at

0w/ collisional viscosity

7.1,5 0 qN

Resistive plasma / resistive wall mode (RPRWM) growth rate scaling:

9/43/1~ w

(H. Strauss - NYU)

1

.001

0.1

.001e

e

eWALL

e

610

310w

1/3

4/9w

w

RWM interacts w/ tearing / EM -ballooning mode

Wall Plasma

similar to analytic scaling Finn 1995; Betti 1998

Better dissipation models needed


(From P.B. Snyder - GA)

ELITE code

Coupled peeling-kink and ballooning modes explain many features of Edge-Localized-Modes (ELMs) in H-mode pedestal


5

4.2

3.3

A=2.5

Collisionality, triangularity, and aspect ratio impact ELM stability

Aspect ratio varied via R scan at fixed BT, IP, a, shape

Need to extend stability scans to lower A, include 0, *, rotation…

P.B. Snyder, et al., Plasma Phys. Control. Fusion 46 (2004) A131–A141


Sheared rotation predicted to enhance ELM stability in ST

• Experimental profiles analyzed w/ ELITE Expt. marginal pped 2 kPa - consistent with analysis

10% variation in threshold with n and equilibrium qsurf

=m-nqsurf

Mode number n=6

pped = 2kPa

(From S. Saarelma,

H.R. Wilson – Culham, UK)

• Sheared edge rotation stabilizing– High-n modes most easily stabilized– 10-20% increase in stable pped

depending on n-number and rotation

Expt. vped


Model of ELM cycle including sheared rotation:

4. Hyper-exponential growth as dv/dr 0

ELM crash

1. p < sheared-velocity limit stable 2. p > sheared-velocity limit unstable

3. Instability reduces rotation shear

Extension of Cowley / Wilson non-linear ballooning model to include rotation

Filament-like

structure

A. Kirk, et al.,

PRL, June 2004

3/2 NTM used to study stabilizing role of curvatureFrom R. J. Buttery, et al. PRL 88, 25 March 2002, p. 125005-1 (Culham - UK)

2941

At higher p get 2/1 NTM:– earlier excitations do not grow– usually requires H mode and high p

• Sawteeth briefly reduce p

• high enough p 3/2 NTM

• 3/2 mode reduces energy confinement time:

– W 3.0kJ (11%)

Chang & Callen ‘belt’ model predicts: W 2.4kJ

MAST Discharge

incomplete pressure flattening

w>~wd

bootstrap term (drive)

requires low collisionality

ion polarisation effects

w>wpol

“classical”resistive

tearing index (assumed stabilizing)

Stabilization terms require minimum island size

Evolution described by modified Rutherford Eqn.

field curvature shape and aspect ratio dependence

25.022222 )2.0(/1 w

a

ww

a

ww

a

wdt

dw

rpol

d

GGJ

d

bsPr

Ratio aGGJ / abs 3/2 important as 1

Curvature term cancels 60% of BS drive for MAST case

saturation

dwdt

w

seed

Glasser-Greene-Johnson term aGGJ DR

Equation from O. SauterPhys. Plasmas 4, May 1997

Evolution can be well fit using modified Rutherford eqn.

• TM size responds to p step down, and fit is < 0 NTM

• Island width too large w/o GGJ term ( would be too negative)

• Fit to decay requires either ion polarisationion polarisation or finite island transportfinite island transport model

(noise level)Isla

nd

siz

e (c

m)

/

p x

15

models

3730

data

p

NBI (800kW)

sawtooth/ELM transients

q-profile measurements needed for NSTX this yearM.R. Eqn. derived for low-A & high- (C. Hegna – PoP 1999) will also be used

Sawtooth seeding of TM strong in ST, not fully understood

Sawtooth increases existing n=2 NTM width

n=

1 a

mp

litu

de

n=

2

am

plitu

de

30

20

10

00.6

0.4

0.2

0.0

0.40 0.42 0.44 0.46 0.48 0.50Time (s)

Fre

quen

cy (

kHz)

n=2 Amplitude (G) simulated B

111383

n=2

0.1

0.0

Width/a

Sawtooth can excite n=2 on NSTX also… but, n=2 width can also decrease post-crash

(R.J. Buttery)(E. Fredrickson)

• On MAST, sawtooth readily excites 3/2 NTM close to NTM marginal

• Large q=1 surface radius and stronger magnetic coupling likely important

n=1


The ST inherently accesses unique region of parameter space for fast-ion-driven MHD

• Typical operational scenarios have:– Low B, high ne lower VA

– High fast and high vfast/VA

Strong drive for Alfvénic modes Excellent tests for theory/simulation

0

1

2

3

4

5

6

fast(0) / tot(0)

Vfa

st/V

Alfv

én

0.0 0.2 0.4 0.6

ITER NSTX

ARIES-ST (design)

0.8

CTF

CAE/GAE (HYM, Nova-k)

TAE/rTAE (M3D-k,Nova-k)

“fishbones” (M3D-k)

109022

0.1 0.2 0.3 0.40

100

500

1500

2500

Time (sec)

Fre

quen

cy (

kHz)

• Broad spectrum of modes often unstable simultaneously:– CAE: 1-3MHz (Compressional)

– GAE: 0.3-1MHz (Global)

– TAE: 50-150kHz (Toroidal)

– Fishbone: 5-100kHz

DIII-D


ST & standard tokamak can test A-dependence of fast-ion MHD by operating in similar (low BT) parameter regime

• At B(0) 0.5-0.6T, NSTX & DIII-D observe:– EPM, TAE and CAE– Fast ion losses from EPM and TAE– Modes unstable when fast-ion β is high

• Differences:– NSTX TAE has lower n (from R scaling)– Rapidly chirping/bursting (100kHz10kHz)

EPM much more common on NSTX• Also observed on START/MAST ST feature?

NSTX 107335.0140

DIII-D 109855.1035

(Fredrickson - PPPL

Heidbrink - UCI)


Non-linear TAE simulations reproduce many features observed in NSTX data

• M3D Nonlinear Hybrid simulations:– Mode growth and decay times are

approximately 50 - 100s

– Bursting/chirping behavior results from:• Non-linear modification of fast-ion distribution• Change in mode structure

2

0

-2

t = 0.267

108530

200 s

Data

Simulation

t=0.0 t=336

(G. Fu - PPPL)

n=2

Simulations Mode moves

radially outward during

amplitude saturation phase


GAE/CAE unstable at higher k|| and high vfast / vA > 2

• HYM simulations of GAE and CAE– Nonlinear, global, fully kinetic ions– Beam ions treated with full-orbit f method

• GAE found to be most unstable ( < 10-2 ci)– = 0.3-0.5ci just below the lower edge of

the Alfven continuum < MIN(A)– 2 n 7, several m unstable for each n– Localized near magnetic axis– B|| B / 3

• Higher-n modes more compressional (CAE)– B|| > B – = 0.4-0.7 ci

– 7 n 10, weakly unstable compared to GAE

– Localized near outboard midplane

0|||| ciVk Beam ion resonance condition:

(Electron Landau and thermal ion cyclotron damping weak)

VZ

VR

(E. Belova - PPPL)


Impact of fast-ion MHD on confinement can be significant

Bursting/chirping EPMs

correlate w/ large fast ion loss

CAE bursts coincident w/

EPM onset suggest

CAE-induced fast ion transport

Are CAE modes large

enough to stochastically

heat thermal ions?

(Gates, White - PPPL)Phys. Rev. Lett. 87, 205003 (2001)

(Fredrickson - PPPL)

Need internal measurement of CAE B to assess role in fast-ion transport & stochastic heating









• Solenoid-free ST plasma formation– Coaxial helicity injection (CHI) and electron beam injection – Merging/compression (MC) and PF-coil direct induction


Transient Coaxial Helicity Injection (CHI)

• Method attempts to force axisymmetric reconnection at injector to create equilibrium with closed flux surfaces

(R. Raman – U. Washington)(Camera images – C. Bush)


Experiment (NSTX, Raman, et al)Fast camera view

3D Simulation (CHIP code, NESRC 256 CPUs)-averaged poloidal flux; n=1 helical kink

CHI is helical instability cascading to relaxation

Tang and Boozer, PoP, May 2004

Significant OH flux savings has been

achieved on HIT-II using transient CHI

Understanding from CHIP code (X. Tang - LANL)• Line-tied kink driven unstable on open field lines

• Kink drives dynamo VLOOP in closed-flux region

• Closed-flux modes driven unstable by J-gradient relaxation and current penetration


• Use MST-style gun current sources to inject helical current in divertor region

• Current amplification up to ~ 20

• Merging / reconnection (?) above threshold power

• Closed flux surfaces requires field, gun optimization

Noninductive ST Plasma Formation: Current Injectors in Divertor

(R. Fonck – U. Wisconsin)

30ms 30ms


Merging/Compression: plasma rings formed on or near ‘induction’ coils, then merged together

Recent scheme proposed by TS-3/4 team - ‘Double Null Merging’ (DNM) - produces plasma at X-point rather than coil surface to reduce impurities

Coils

ECH

SmallTokamak

Coils

ST

ST

High-ST

(TS-5 Proposal - Y. Takase, Y. Ono – U. Tokyo)

Magnetic reconnection heats ions creating high- plasma

M/C method w/o X-point already used on START and MAST in U.K.

SmallTokamak


MAST recently produced 1st example of 300kA DNM plasma

Plasma is dense (91019m-3) and hot (~0.5keV)

(From A. Sykes – Culham, UK)A B

C D

E F

MAST benefits from internal coils; NSTX will test with external coils


20kA tokamak formed using outboard PF coil induction

• HHFW antenna used as ionization source in outboard field null

• BZ ramp supplies loop voltage and vertical field

• BZ and BR evolution will be optimized to keep plasma in high VLOOP region DINA modeling

8ms

9ms

10ms

114405

R 0 Low VLOOP(Camera images – C. Bush)


The ST is a unique & important platform for testing MHD theory and simulation

• Low–A high + strong intrinsic shaping

• NBI drives near-Alfvénic rotation + *AE modes

Unique ST features highlight MHD theory needs:

• 1/1 mode Non-linear evolution with flow, 2-fluid, hot particles • RWM Self-consistent kinetic damping in general geometry + • ELM Rotation, , and * effects + non-linear evolution • NTM 2-fluid treatment for high-, general geometry + seeding• *AE, EPM Self-consistent non-linear treatment of multiple *AE• IP creation Dynamo, relaxation, reconnection high IP w/ closed


I think we all agree that…

From Horizon Casino


Backup Material

Fitted parameters close to theoretical values

• ’ adjusted to match saturated island size • field curvature fixed to theory - bootstrap allowed to vary

Quantity

Theory Fit: Ion

polarisation Fit: Island transport

Model

r' -2m? -6.5 -6.5 match saturated size

aGGJ 3.2 3.2 3.2 resistive interchange with CHEASE code

abs 5.2 5.62 5.66 r (ms) 530+ 100 100

Fokker-Planck code (arbitrary R/a and )

apol (cm2) uncertain 7.4 0

wd (cm) 1.5-3.5 0 1.45 conductive/convective transport models

+r usually reduced in conventional tokamak fits

• Good match to predicted drive - confirms BS/GGJ physics

• Field curvature stabilises 60% of bootstrap drive• r reduced - island affecting resistivity?

presented by j.e. menard princeton plasma physics laboratory mhd sfg meeting thursday, may 19, 2005...

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