Investigation of microtearing modes for electron transport in NSTX

Presented by

King-Lap WongCo-authors: D. Mikkelsen, J. Krommes, K. Tritz, D.R. Smith, S.

KayeITPA Meeting PPPL

Oct. 5-7, 2009

NSTXNSTX Supported by

College W&MColorado Sch MinesColumbia UCompXGeneral AtomicsINELJohns Hopkins ULANLLLNLLodestarMITNova PhotonicsNew York UOld Dominion UORNLPPPLPSIPrinceton UPurdue USNLThink Tank, Inc.UC DavisUC IrvineUCLAUCSDU ColoradoU IllinoisU MarylandU RochesterU WashingtonU Wisconsin

Culham Sci CtrU St. Andrews

York UChubu UFukui U

Hiroshima UHyogo UKyoto U

Kyushu UKyushu Tokai U

NIFSNiigata UU Tokyo

JAEAHebrew UIoffe Inst

RRC Kurchatov InstTRINITI

KBSIKAIST

POSTECHASIPP

ENEA, FrascatiCEA, Cadarache

IPP, JülichIPP, Garching

ASCR, Czech RepU Quebec

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Outline

• Introduction

• Properties of microtearing modes

• Proposed experiment on NSTX

• Some ideas for AUG

• Summary

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Introduction

Anomalous e due to imperfect magnetic surfaces:• Magnetic islands - Kerst 1962, Rosenbluth, Sadeev, Taylor 1966

• Magnetic braiding - Stix 1973

e in stochastic magnetic field - R & R 1978, Stix 1978

• Lc~ qR for tokamak - Kadomtsev 1978, Krommes 1983

• properties of microtearing - Drake, Gladd, D’Ippolito, Connor 1980 -1990

• In conventional tokamaks, microtearing can only be found at the edge (D-

III 1987, CMOD 1999)

• In STs, microtearing can be the dominant instability - Redi 2003,

Applegate 2004

• Microtearing can explain measured e at r/a>0.5 in NSTX, Wong - 2007

• Microtearing can be unstable at the outer core of AUG, Told - 2008

Can we find experimental evidence of this instability ?

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Properties of microtearing modes

• High-m (m~10-20) tearing modes (k||=0)

• Driven mainly by Te

’ is actually negative at high m (stabilizing)

Different from ITG modes :

Er Br || mode structure k direction

Microtearing odd even extended electron drift

ITG even odd ballooning ion drift

Br has even parity - creates magnetic islands at q=m/n

• In slab geometry, microtearing instability requires: [Wesson, “Tokamaks”, 1987]

(a) e= dlnTe/dlnne > 0.3

(b) collision rate must exceed electron diamagnetic freq., ei > ★e

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Distinguishing between microtearing and resistive ballooning modes

• Frequency

microtearing: = ★e + c ★T , 0 < c < 1

resistive ballooning: << ★e

• Mode structure

microtearing: k|| = 0 mode structure extended along B

resistive ballooning: k|| ≠ 0,

mode amplitude peaks on low field side, because the

bad curvature plays an important role

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Growth rate of microtearing modes (NSTX#116313, 0.9s)

many unstable modes broadband spectrum expected

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K-L Wong, APS-07,

NI1.00004, p 7

Comparison between etheory

and eexp

Put B/B=e/LT, get e = (e/LT)2 Rve(mfp/Lc)= (e/LT)2ve2/(eiq)

Use parameters from #116313A11 at 0.9s, Lc= qR

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K-L Wong, APS-07,

NI1.00004, p 8

Microtearing modes are stable at low ei (< ★e )

•Reduce transport by lowering ne and raising Te

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Scaling of E with ei in NSTX

• In beam heated plasmas, Te(0) < 1 keV, ne(0) < 1014 cm-3

• In HHFW heated plasmas, Te(0) < 5 keV, ne(0) < 3x1013 cm-3

• NSTX data base appear to support microtearing mode as the

dominant cause of electron heat loss in many beam heated

plasmas – see K. Tritz’s presentation

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Transition to global stochasticitymany possibilities, but they are not equally probable

• Landau-Hopf scenario - the power spectrum should have finite discrete

frequencies (finite no. modes)

- not observed in experiment highly unlikely

• Ruelle-Takens scenario - broadband noise (chaos) appear in power

spectrum after a few bifurcations likely to be the case

• Don’t expect to see linear growth of a coherent single mode

prepare to deal with stochastic magnetic field over an

extended region (fully developed magnetic turbulence)

• Lesson learned from TEM/ITG: need to work with plasma in stochastic B.

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Mirnov loop lacks spatial resolution- not too useful for broadband high m,n fluctuations deep inside the plasma

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Work with the tools we have: the X-ray camera

Ref: Stutman et al., RSI 74,1982 (2003)

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X-ray emissivity

• For Maxwellian electrons in NSTX plasmas, X-ray emission is

dominated by collisional excitation of impurity ions1; dielectronic

recombination2 is small; bremsstrahlung3(ff) and radiative

recombination4 (fb) are very small

• Emissivity for both (1), (2) & (3) scale like ~ ne nz (Z e)2 √Te

is approximately constant on a flux surface for NSTX plasmas

- see Stutman et al., RSI 74,1982 (2003)

• Te & ne fluctuations - Te & ne give rise to which may be

measurable in NSTX

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Crude estimates

• Take parameters from #116313, r/a=0.5, t=0.9s

• Island full width: ∆r = 4 ( bmn R r q / m s )1/2 ~ 0.85 cm

• Put r ≤ ∆r / 2 ~ 0.4 cm, Ln ~ 50 cm, LT ~ 35 cm,

• get ~ r / Ln + 0.5 r / LT ~ 1.4%

~ 1% is not too difficult to detect if we have a

diagnostic that can do local measurements

• However, all we have is an X-ray camera for

line-of-sight measurements - difficult !

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SVD analysis

• Ref: T. Dudok de Wit et al., PoP 1, 3228(1994)

• Expand the discrete signal (n x m matrix) y(xj, ti) into a set of modes

that are orthogonal in time and space

y(xj, ti) = k=1 K Ak k(xj) k(ti), K = min(n,m)

• Chrono = temporal eigenfunction = k(ti)

• Topo = spatial eigenfunction = k(xj)

• Weight distribution: Ak (≥0), k =1, 2, ….. K

• Construct the matrix Yi j = y(xj, ti) and use IDL subroutine to do SVD

analysis - program written by David Smith

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SVD result (#116313,1.002-1.003s)

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Preliminary SVD results (15 Ch SXR)

• Topo frequently exhibits wave-packet structure although the camera

spatial resolution is marginal

• Chrono usually consists of irregular / intermittent bursts

• No sign of single mode growth - has temporal resolution

- fNyquist= 300kHz , i.e., Landau’s Scenario NOT observed

• No single frequency signal observed - usually see broadband fully

developed turbulence (Ruelle-Takens scenario ?)

• A lot more data / work are needed

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Need data from all 46 channels

• Need to do cross correlations of ij (xij) for xij on same flux

surface

• New software capabilities (new tools) needed:

Overlay plots of flux surfaces (from EFIT or TRANSP)

and X-ray viewing chords

Search for coherent structures, correlation lengths etc,

Don’t expect quick success from this experiment

- need to stop & think every step along the way

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De and the X-ray energy spectrum

• Kinetic eq: ∂f/∂t = e/m E∂f/∂v + C(f) + LDeLf

L = ∂/∂x - (eEA/m)/v2

E - applied electric field(1st order), EA - ambipolar electric field

• Perturbative solution: f = f(0) + f(1) + f(2) + ….

• 0-th order: 0 = C(f(0)) local Maxwellian

• 1st order: 0 = C(f(1)) - e/m E ∂f(0)/∂v Spitzer resistivity

• 2nd order: 0 = C(f(2)) + LDeLf(0) - e/m E ∂f(1)/∂v

and f(2) gives information on De

• Ref: K. Molvig et al., PRL 41, 1240 (1978) – formulation looks fine, result is questionable

First step: Use X-ray spectrometer to look for non-Maxwellian fe(v)

2nd step: Measure f(r,v,t) with PILATUS detector modules and solve for De

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Some ideas for AUG – more hardware capability

• Heat pulse propagation expt with ECH & ECE for Te(r,t) - directly determine e.

• Use fast electrons from ECH at high_B side as trace particles and measure spatial diffusion of trace particles due to stochastic B – DM ?

• Measure f(r,v,t) with PILATUS detector modules and solve for De

• Tangential viewing port

will be helpful if Ee~100keV

Cross-polarization scattering

to measure B ?

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Summary

• Identification of a single microtearing mode in linear growth phase is difficult

– not expected based on current knowledge: Can MSE and / or JHU’s technique

work? - Probably not, but … Never hurt to

try.

• Need to prepare for fully developed turbulence – plasma in stochastic magnetic field

Need theoretical input: Do we know how to describe the plasma equilibrium ?

Ref: Reiman et al., Nucl.Fusion(2007); Krommes et al., J. Plasma Physics (1983).

• For ST’s (NSTX / MAST):

X-ray spectrometer may provide some evidence of non-Maxwellian fe(v)

Multi-chord imaging can provide more info’ – PILATUS has the best chance

• For AUG:

ECH + ECE provides new capabilities not available on STs PILATUS with

tangential view possible?

• PPPL owns two PILATUS (now on CMOD), asking for a 3rd one

Are they available for collaborative microtearing expts ?21