MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA Energetic Particle Driven MHD in Spherical Tokamaks. M Gryaznevich.

M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA

MAST

Energetic Particle Driven MHD in Energetic Particle Driven MHD in Spherical Tokamaks. Spherical Tokamaks.

M Gryaznevich

EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB, UK

Acknowledgements:S Sharapov, S Pinches, H Berk, B Breizman, R Martin, V Shevchenko, R Akers and MAST & NBI teams

This work was funded jointly by the United Kingdom Engineering and Physical Sciences Research Council and by EURATOM.


MAST

ST research - present statusST research - present status

MAST and ASDEX-Upgrade

NSTX and DIII-D

MAST(UK), NSTX, Pegasus, CDX-U, HIT-II (US), Globus-M (RF), ETE(Brazil), TST-2 (Japan) and other STs are operating, demonstrating many of the predicted advantages of this concept and providing physics basis for Next Step ST devices

Comparison of large STs with conventional aspect ratio tokamaks of similar size

* G Voss, STW 2003; ** H Wilson, Lyon 2002


MAST

- particle physics constraints for burning plasmas:- particle physics constraints for burning plasmas:

ST vs conventional tokamak ST vs conventional tokamak

• Radial diffusion and other losses of -particles due to EPD MHD modes

may lead to degradation of performance

• Possible excessive heat loading due to -particle losses caused by EPD

MHD modes and constraints connected with the load on the plasma-facing

components are also very important

• Physics of burning plasma is mainly determined by heating of bulk

plasma by -particles, which in the absence of other -particle losses is

characterised by sd - -particle slowing down time

• These are equally valid for both STs and conventional aspect ratio tokamaks


MAST

• Radial diffusion: classical diffusion is low, diff >> sd

• In present-day STs the use of low magnetic fields, and plasma densities comparable to those of conventional tokamaks, implies a lower Alfvén speed and hence a lower beam energy threshold for the excitation of Alfvénic instabilities (via the fundamental vbeam = vA resonance)

• To prevent first orbit losses of -particles in burning ST the plasma current should be

Ip > 5.4 (R/a)-1/2 (k2+1)/2k ~ 5MA Putvinskii, Rev.Pl.Phys., 18 (1993) 239

Heidbrink & Sadler NF 34 (1994) 535 empirical estimate gives even smaller value of ~ 1.4MA

• “Ripple” loss of -particles is small in STs due to toroidal magnet design (note poloidal ripple effect, Yavorskij, Lyon 2002), but may increase in high- regime.

• So mainly anomalous losses may be important, caused, for example, by stochastic diffusion due to EPD Alfven Eigenmodes Berk et al, Ph.Pl. 3 (1996) 1827

D

anom N2 (B/B)2, where N - number of eigenmodes, B - field perturbation

- particle physics constraints for burning ST plasmas:- particle physics constraints for burning ST plasmas:


MAST

• Different types of EPD MHD activity have been observed in NBI-heated

START, MAST and NSTX plasmas:chirping modes

fishbones

fixed-frequency modes in AE frequency range

modes at frequencies above AE frequency range

Energetic Particle Driven MHD in STsEnergetic Particle Driven MHD in STs

• Three main regimes of EPD modes in STs:

low- regime (chirping modes, TAE, fishbones)

higher- (t ~ 5 - 15%) regime, when TAEs are suppressed by the -effect

high- (t(0) ~ 100%) regime

• We will discuss effect of EPD MHD on fast particles and thermal plasma in STs in these three regimes


MAST

Structure of the ideal MHD continuum spectrum for n = 1 START shot #35305,

t = 26.3ms from CSCAS, t = 3%

Im() = 1 corresponds to f ~ 540kHz

Ideal MHD radial velocity eigenfunctions corresponding to TAE (n = 1, f = 180 kHz), from MISHKA-1 Mikhailovskii et al, Pl.Ph.Rep 23 (1997) 844

• at least 36 Alfvén eigenmodes were found in these simulationsSharapov, STW 1996

q(r)

n(r)/n(0)

2

1

00 r/a 1

Im(

) =

R

0/c

A(0

)

TAE

EAE

NAE

m=1

m=2m=3,4,5...

r/a

Alfvén eigenmodesAlfvén eigenmodes in STs. in STs. LowLow- regime McClements, Gryaznevich, Sharapov PPCF 41 (1999) 661

• Multiple AEs are likely to exist if >> S with number of modes ~ r/(RS)>>1 Candy et al., Ph.Lett. A215 (1997) 299


MAST

Alfvén eigenmodes drive, theory & experimentAlfvén eigenmodes drive, theory & experiment

• Fast particle distribution is calculated using the Monte-Carlo code LOCUST (Akers et al, EPS98). Analysis shows that the drive for AE is determined by the radial gradient of fast ion pressure and the stationary bump-on-tail distribution function

LOCUST contour plots of beam ion distribution at the edge (top) and plasma centre (bottom), START

shot #35096, t = 5%

NPA flux spectra of beam ions, measured (dots) and simulated at different chords,

START shot 35096, t = 5%

birth energies

• Fast ion losses themselves may produce bump-on tail, causing EPM excitation (as observed on NSTX, Medley, STW2003)


MAST

Multiple modes within the TAE gap frequency range, fA = cA/4qR0 ~ 200kHz

have been observed on START at low t

Mirnov coil spectrogram of TAE mode on START (a), and Fourier power spectrum at t ~ 26ms (b) observed during early stage of discharge, START, shot #35305

Time, ms Frequency, kHz

Po

we

r, a

.u.

Fre

qu

en

cy,

kHz

(a) (b)

PNBI ~ 0.5 - 0.3 MW, E0 ~ 30keV, t < 3%, f ~ 14kHz

dominant n = 1, m = 1,2

details: Hender et al, Ph Pl 6 (1999) 1958, McClements et al, PPCF 41 (1999) 661

Experimental results, EPD modes. Experimental results, EPD modes. LowLow- regime on START


MAST

f, kHz

200

150

100

50

020 30 40 50 60 70 t,ms

TAE frequency range

EAE frequency range

small Internal Reconnection event

Typical MAST 1 MA shot #2493, MHD during current ramp, ne ~ 2.5 1019m-3

PNBI ~ 0.65MW, E0 = 28keV, t < 5 %

Experimental results, EPD modes. Experimental results, EPD modes. LowLow- regime on MAST


MAST

Fourier power spectrum at t ~ 72ms, #2884

“pitchfork” splitting

• new on MAST: long-lasting ( > 20ms) modes without fine spectrum in TAE frequency ranges have been observed.

Fourier power spectrum at t ~ 124ms, #2885


f, kHz 300

150

0

40 80 120 t,ms

f, kHz 300

200

100 80 100 120 140 t,ms

• new on MAST: long-lasting (> 20ms) modes with fine “pitchfork” spectrum in TAE and EAE frequency ranges have been seen. Note that chirping modes at t ~ 80ms start from the TAE frequency. (recently also observed on NSTX, Fredrickson, Ph.Pl.2003, 2852)


MAST

• more modes, more complicated (multiple - n) mode structure than on START

Typical outer midplane Mirnov coil spectrogram in a NB heated discharge #4636, t < 2.5%

• these multiple-n modes may cause enhanced fast ion transport, more efficiently than single-n modes of similar amplitude

as observed on NSTX, Fredrickson, Ph.Pl. (2003), 2852f, kHz

400

200

0 20 40 50 60 70 80 90 100 120 130 140 150 t,ms



MAST

New features of chirping modes have been found on MAST

Chirping modes may start from a continuous mode frequency

MAST #9171, t < 2%

Chirping modes may end as a continuous mode

MAST #9110, t ~ 4 - 5%

65 55 85 t,ms

f, kHz

200

100

0

f, kHz 200

100

0140 150 160 170 t,ms



MAST

MAST shot #5547. NBI D to D; ~ 1.2MW during current ramp. Bt ~ 0.42 T, t < 2.5 %

Mirnov outer coils, R=1.85m, z=0

• chirping modes with n = 3, 2 and 1 (only n = 1 observed on START)

f, kHz 200

100

070 74 78 t,ms54 58 62 t,ms

f, kHz 400

200

0

dB/dt

n = 2

n = 1

n = 359.0 60.0 t,ms 70.0 72.0 74.0 t,ms

New features of chirping modes on MASTNew features of chirping modes on MAST


MAST

New features of chirping modes on MASTNew features of chirping modes on MAST• Characteristics of chirping modes change when NBI is applied during current ramp-up phase

MAST #9128, 1.2MW, 40 keV NBI during Ip ramp-up at

4MA/s. Modes chirp up and down in frequency t < 2.5 %

MAST #9109, 1.2MW, 40 keV NBI at Ip flat-top. Typical

chirping modes - frequency chirps down, t < 3 %

NBI

f, kHz 200

100

0100 110 120 130 t,ms

NBI

f, kHz 200

100

0 60 70 80 t,ms


MAST

MAST #5568, NBH during Ip ramp at 7MA/s in DND regime, PNBI ~1MW, ENBI ~40keV,

Bt=0.52T, ne ~1.5 1019m-3, no sawteeth, q(0)efit > 2, liefit ~ 0.5 - 0.7, t < 3%


Ip

PNBI

SXR

q(0)

liefit

Bt

MHD

ne8a_


MAST

spectrogram of bursts with simultaneous chirping-down and chirping-up frequency (MAST, NBH shot #5568)


64 66 68 70 72 ms

f, 140kHz 120

100

80

• Non-linear theory shows a symmetric chirping of “usual” AE frequency due to the “hole-clump” generation in the distribution function Berk, Breizman, Petviashvili, Phys Lett A234 (1997) 213

• Previously in majority of cases (START, early MAST discharges) only chirping-down modes have been observed. This may have been caused by the deficit of fast ions above the resonance velocity.

• Recently, bursts with simultaneous chirping-down and chirping-up frequency were observed:

Theory


MAST

- Plasma should be near the linear instability threshold:

L - d << L

- Collisional effects should be sufficiently weak. This means, that the up-chirping modes are likely to be observed at lower densities or higher temperatures.

• For a “hole-clump” mechanism, several conditions should be satisfied:

40 50 60 70 80 90 100 110 120 t,ms

f, kHz 300

200

100

0



MAST

• the rate of a frequency change of a sweeping phase space structure driven by

resonant particles is uniquely determined by its amplitude through the relation: = C b

3/2 t1/2 , C 1 for a single resonance

Berk et al., Phys. Plasmas, 6 (1999) p.3102bounce frequency b (VA

2/R0)1/2 (4 S n Br/B0)1/2

Berk et al., Phys. Fluids, 5 (1993) p.1506

Detailed studies of hole-clump modes on MASTDetailed studies of hole-clump modes on MAST

Comparison of theory prediction with experiment gives reasonable agreement:

64 66 68 70 720

1

2

Am

plitu

de, a

.u.

Time, ms

up, theory down, theory up, exp. down, exp

from these we can estimate Br/B0:

for #5568 at t = 64.4ms: f ~ 110kHz, f ~ 18kHz, t ~ 0.8ms, Br/B0 4 10-4

64 66 68 70 72 ms

f, 140kHz 120

100

80


MAST

Modelling MAST #5568 with the HAGIS Code

(a) - Fourier spectrogram of outboard midplane Mirnov coil signal, MAST, shot 5568

(b) - theory prediction (Berg)

(c) - HAGIS simulations for full details of HAGIS simulations see S Pinches, this meeting

(a) (b) (c)

HAGIS simulations, MAST, shot 5568

Modes with m = 3,4,5 were found in experiment, #5568


MAST

Energetic Particle Driven MHD in STsEnergetic Particle Driven MHD in STs

mediummedium- regime

• As increases, Alfvén eigenmodes don't exist anymore if dt/dr

exceeds a critical value:

- R q2 dt/dr > r/R + 2 ` + S2

G.Y.Fu, Phys.Plasmas 2, (1995) p.1029H.L.Berk et al., Phys. Plasmas 2, (1995) p.3401

• In these regimes, there are no TAEs because of the high-, but chirping modes can still exist entirely due to the beam.

Liu Chen, Phys. Plasmas 1, (1994) p.1519

• Fishbones may also exist


MAST

Experimental results, chirping modes on START, Experimental results, chirping modes on START, t > 5 %

- disappear at high density, ne > 1020m-3

- the starting frequency scales with Bt ne-0.5 t

-0.75

- relatively benign, reduce energy content by < 3% in a single burst (reversibly)

- n = 1 - dominant, mainly m = 3 in this shot

- observed close to q = 3 surface (SXR)

Note, that TAE modes do not exist in these plasmas due to high details: Gryaznevich, Sharapov NF 40, (2000), 907

START #35159

SXR image of a chirping burst

Mirnov coil spectrogram


MAST

Humpbacked n = 2 fishbones on MAST, t ~ 5 - 10%

• Found only when fishbone coincides with sawtooth (during flat-top)

• Have lower frequency compared with hole-clump and chirping-down modes, but higher than ordinary m/n = 1/1 fishbones

• Typically observed at higher NB power and higher density, t > 5 %

f, kHz 40

30

20

10

0240 250 260 t,ms

dB/dt

n = 2

n = 1

240 250 260 t,ms

MAST, #9002MAST, #9002


MAST

Fishbones during sawtoothing flat-top, MAST ##9003-05, PNBI ~2.3MW, ENBI ~40keV, t ~ 8 %

Ip

PNBI

SXR

efit

Bt

MHD

R0

tefit

ne8a_


MAST

Humpbacked fishbones on MAST

f, kHz 100

50

0 200 220 240 260 280 300 t,ms

MAST #9005f, kHz 100

50

0100 120 140 160 180 t,ms

start of sawteeth

• fishbones seen prior to sawteeth

• humpbacked fishbones start with sawteeth


MAST

MAST #9003f, kHz 100

50

0100 120 140 160 180 200 t,ms

230 250 270 290 310 330 t,ms

f, kHz 100

50

0

Humpbacked fishbones on MAST

start of sawteeth


MAST

• at high pol, typically ~ 0.5 - 0.6 chirping mode can trigger an n = 1 mode

• sometimes, with higher NB power, density and higher mode amplitude, this happens at lower pol

• these modes cause degradation of performance; they also often lock and restrict MAST operating space

Chirping modes on MAST can trigger long-lasting tearing modes

f, kHz 200

100

0 150 170 190 210 230 250 t,ms

high pol, #2967 low pol, #9005

f, kHz 100

50

0 135 145 155 t,ms

MAST, #9110, t ~ 7 %


MAST

• However, damping of these instabilities is determined by the sign of the bracket in

- (1- /) exp{-(VTi/VA)2}

Mikhailovskii, Sharapov, Plasma Phys. Reports 25, (1999) p.803F.Zonca et al., Plasma Physics Control Fusion 38, (1996) p.2011

which depends on plasma profiles. This sign was found to be positive

for high- START plasmas, since no such activity was detected,

confirming good damping of modes on thermal plasma when t(0) ~ 1

^ *i

High-beta,High-beta, Next Step ST relevant regime Next Step ST relevant regime

• high- (t(0) ~ 1) regime implies VT < VD VA(0) << V << VTe,

as VT,D/VA ~ i1/2 ~ 1

• so thermal ions are in primary resonance with Alfvén velocity, but not

fast -particles. Drift thermal ion instabilities become possible.


MAST

High-beta,High-beta, Next Step ST relevant regime Next Step ST relevant regime

• At high beta, alpha-driven instabilities are likely to be due to higher-

frequency (cyclotron range of frequencies) instabilities caused by

energy-gradient sources (e.g. bump-on-tail or temperature anisotropy).- compressional Alfvén modes, NSTX

• no TAE modes have been found in simulations at t > 5 %

• no EPD MHD activity has been observed in high- regimes on START

• chirping modes on MAST disappear at t > 12 %

• fishbones should be stable in high-t ST due to magnetic well effect

Kolesnichenko et al, Ph.Rev.Let 82 (1999) 3260


MAST

Regime EPD modes observed impact on thermal plasma

impact on fast particles

low-(< 5%)

TAE, EAE;

multi-n chirping modes (up, down and both);

fishbones, n=1; ICE

not observed no correlation found on START and MAST up to date (but see NSTX)

higher-(5 - 15%)

chirping modes (down);

fishbones, n=1,2,3

small reversible loss of Wtot;

indirect effect through EPD-triggered long-lasting modes

correlated loss with chirping modes

high- (>15%)

not observed on START not observed on START

not observed on START

Impact of EPD MHD on START and MAST plasmasImpact of EPD MHD on START and MAST plasmas


MAST

EPD MHD. Impact on the route to the burning EPD MHD. Impact on the route to the burning plasma (low and medium plasma (low and medium ))

• Plasmas in the burning ST device with low central shear and high edge pressure gradients may be affected by different types of EPD MHD activity due to smaller shear and longer resonant interaction between waves and energetic ions during current ramp-up and heating phases. Small shear also affects the threshold for stochastic diffusion

• NTMs may be triggered by EPD MHD modes and cause

performance degradation

• More activity has been seen on MAST and NSTX compared to START (long-lasting TAE modes, multi-n chirping modes and fishbones). These modes may cause significant fast ion losses (NSTX).


MAST

EPD MHD. Impact on burning plasmasEPD MHD. Impact on burning plasmas

• There is no theoretical prediction or experimental evidence up to date that EPD MHD modes may strongly affect the performance of burning ST plasmas

• No EPD MHD activity has been observed in high- regimes on

START, EPD MHD activity on MAST reduces with increase in -value

• The main problem with EPD MHD modes during the burning phase may be connected with -particle losses that may damage the first wall

More data needed on:More data needed on:

• Fast particle losses due to EPD MHD, IRE and sawteeth in the high- burning plasma relevant regimes with low magnetic shear

• Energy losses due to EPD MHD activity in high- high performance regimes

• EPD MHD modes in collisionless high-bootstrap plasmas


MAST

CONCLUSIONSCONCLUSIONS

• Good experimental data on EPD MHD modes in STs has Good experimental data on EPD MHD modes in STs has already been obtainedalready been obtained

• Experimental study of these modes in STs provides an opportunity to test theoretical models, which could then be applied to -particle physics predictions in ITER and beyond.

• Recent progress both in theory and diagnostics of energetic particle driven modes in STs gives a new boost for cross machine comparison and verification of the theory.

MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA Energetic Particle Driven MHD in Spherical Tokamaks. M Gryaznevich.

Documents

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