1. 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 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.

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

3. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA  - particle physics constraints for burning plasmas: 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

4. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA 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 v beam = v A resonance) To prevent first orbit losses of  -particles in burning ST the plasma current should be I p > 5.4 (R/a) -1/2 (k 2 +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  N 2 (  B/B) 2, where N - number of eigenmodes,  B - field perturbation  - particle physics constraints for burning ST plasmas:

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

6. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA 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 simulations Sharapov, STW 1996 q(r) n(r)/n(0) 210210 0 r/a 1 Im( ) =  R 0 /c A (0) TAE EAE NAE m=1 m=2 m=3,4,5... r/a Alfvén eigenmodesin STs. Low Alfvén eigenmodes in STs. Low-  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

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

8. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA Multiple modes within the TAE gap frequency range, f A = c A /4  qR 0 ~ 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 Power, a.u. Frequency, kHz (a) (b) P NBI ~ 0.5 - 0.3 MW, E 0 ~ 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. Low Experimental results, EPD modes. Low-  regime on START

9. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA f, kHz 200 150 100 50 0 20 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, n e ~ 2.5 10 19 m -3 P NBI ~ 0.65MW, E 0 = 28keV,  t < 5 % Experimental results, EPD modes. Low Experimental results, EPD modes. Low-  regime on MAST

10. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA 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 Experimental results, EPD modes. Low Experimental results, EPD modes. Low-  regime on MAST 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)

11. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA 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), 2852 f, kHz 400 200 0 20 40 50 60 70 80 90 100 120 130 140 150 t,ms Experimental results, EPD modes. Low Experimental results, EPD modes. Low-  regime on MAST

12. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA 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 0 140 150 160 170 t,ms Experimental results, EPD modes. Low Experimental results, EPD modes. Low-  regime on MAST

13. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA MAST shot #5547. NBI D to D; ~ 1.2MW during current ramp. B t ~ 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 0 70 74 78 t,ms 54 58 62 t,ms f, kHz 400 200 0 dB  /dt n = 2 n = 1 n = 3 59.0 60.0 t,ms70.0 72.0 74.0 t,ms New features of chirping modes on MAST

14. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA New 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 I p ramp-up at 4MA/s. Modes chirp up and down in frequency  t < 2.5 % MAST #9109, 1.2MW, 40 keV NBI at I p flat-top. Typical chirping modes - frequency chirps down,  t < 3 % NBI f, kHz 200 100 0 100 110 120 130 t,ms NBI f, kHz 200 100 0 60 70 80 t,ms

15. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA MAST #5568, NBH during I p ramp at 7MA/s in DND regime, P NBI ~1MW, E NBI ~40keV, B t =0.52T, n e ~1.5  10 19 m -3, no sawteeth, q(0) efit > 2, l i efit ~ 0.5 - 0.7,  t < 3% New features of chirping modes on MAST IpIp P NBI SXR q(0) l i efit BtBt MHD n e  8a _

16. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA spectrogram of bursts with simultaneous chirping-down and chirping-up frequency (MAST, NBH shot #5568 ) New features of chirping modes on MAST 64 66 68 70 72 ms f, 140 kHz 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

17. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA - 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 New features of chirping modes on MAST

18. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA 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 t 1/2, C  1 for a single resonance Berk et al., Phys. Plasmas, 6 (1999) p.3102 bounce frequency  b  (V A 2 /  R 0 ) 1/2  (4 S n  B r /B 0 ) 1/2 Berk et al., Phys. Fluids, 5 (1993) p.1506 Detailed studies of hole-clump modes on MAST Comparison of theory prediction with experiment gives reasonable agreement: from these we can estimate  B r /B 0 : for #5568 at t = 64.4ms: f ~ 110kHz,  f ~ 18kHz,  t ~ 0.8ms,  B r /B 0  4  10 -4 64 66 6870 72 ms f, 140 kHz 120 100 80

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

20. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA Energetic Particle Driven MHD in STs medium medium-  regime As  increases, Alfvén eigenmodes don't exist anymore if d  t /dr exceeds a critical value: - R  q 2  d  t /dr > r/R + 2   ` + S 2 G.Y.Fu, Phys.Plasmas 2, (1995) p.1029 H.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

21. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA Experimental results, chirping modes on START, Experimental results, chirping modes on START,  t > 5 % - disappear at high density, n e > 10 20 m -3 - the starting frequency scales with B t n e -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

22. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA 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 0 240 250 260 t,ms dB  /dt n = 2 n = 1 240 250 260 t,ms MAST, #9002

23. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA Fishbones during sawtoothing flat-top, MAST ##9003-05, P NBI ~2.3MW, E NBI ~40keV,  t ~ 8 % IpIp P NBI SXR  efit BtBt MHD R0R0  t efit n e  8a _

24. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA Humpbacked fishbones on MAST f, kHz 100 50 0 200 220 240 260 280 300 t,ms MAST #9005 f, kHz 100 50 0 100 120 140 160 180 t,ms start of sawteeth fishbones seen prior to sawteeth humpbacked fishbones start with sawteeth

25. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA MAST #9003 f, kHz 100 50 0 100 120 140 160 180 200 t,ms 230 250 270 290 310 330 t,ms f, kHz 100 50 0 Humpbacked fishbones on MAST start of sawteeth

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

27. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA However, damping of these instabilities is determined by the sign of the bracket in   - ( 1 - /  ) exp {-( V T i / V A ) 2 } Mikhailovskii, Sharapov, Plasma Phys. Reports 25, (1999) p.803 F.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^*i High-beta, Next Step ST relevant regime high-  (  t (0) ~ 1) regime implies V T < V D  V A (0) << V  << V Te, as V T,D /V A ~  i 1/2 ~ 1 so thermal ions are in primary resonance with Alfvén velocity, but not fast  -particles. Drift thermal ion instabilities become possible.

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

29. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA RegimeEPD modes observedimpact on thermal plasma impact on fast particles low-  (< 5%) TAE, EAE; multi-n chirping modes (up, down and both); fishbones, n=1; ICE not observedno 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 W tot ; indirect effect through EPD- triggered long- lasting modes correlated loss with chirping modes high-  (>15%) not observed on START Impact of EPD MHD on START and MAST plasmas

30. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA EPD MHD. Impact on the route to the burning 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).

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

32. MAST M Gryaznevich. EPD MHD in STs. 8th IAEA TM on EP. 6-8 Oct. 2003, San Diego, USA CONCLUSIONS Good experimental data on EPD MHD modes in STs has already been obtained Good experimental data on EPD MHD modes in STs has already 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.