1. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 TAE Damping Rates on Alcator C-Mod Compared with Nova-K J A Snipes *, N N Gorelenkov ‡, J Sears * * MIT Plasma Science and Fusion Center, Cambridge, MA USA ‡ Princeton Plasma Physics Laboratory, Princeton, NJ USA

2. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 First Evidence of Really Large Scale TAE Transport Presented at a Plasma Physics Meeting  Far exceeds any TAE transport ever presented on JET  Far exceeds any TAE transport ever presented on TFTR  Appears to be relevant to accretion disks in astrophysical plasmas

3. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Introduction  Moderate n ~ 5 – 10 Alfvén Eigenmodes (AEs) are expected to be unstable in ITER and could affect the fast  population  Understanding and control of AEs could improve fusion burn control and lead to improved confinement  Unstable AEs are excited in C-Mod at ITER B T and n e with T e  T i and up to 300 keV fast hydrogen ion tails generated by ICRH  Stable AEs are excited in C-Mod with a pair of active MHD antennas that drive moderate |n| < 16 modes  Damping rates of these moderate n stable AEs have been compared with MHD calculations with the Nova-K code including continuum, radiative, collisional and Landau damping

4. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Active MHD Antennas Excite Broad n Spectrum  Two antennas above and below the outboard midplane  Two amplifiers drive ~ 25 A each producing B r ~ 1 G at q=1.5  10 Hz < f < 1 MHz, broad toroidal spectrum |n| ~ 16 FWHM ~

5. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Stable TAE Resonances at Constant Frequency  Three stable AE resonances as the toroidal field and density sweep the plasma TAE frequency through the constant active MHD frequency  Resonances occur near the center of the TAE frequency gap for q=1.5

6. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 TAE Resonances with Sweeping Frequency  Multiple stable TAE resonances with sweeping active MHD frequency, gives a damping rate  /  ~ -1.2% and n = -9

7. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Limited vs Diverted Plasma Outer Gap Scan Active TAE resonances were only observed with moderate outer gaps in inner wall limited plasmas or  with small outer gaps in diverted plasmas Damping rates are in the same range as those found in JET limited plasmas but are lower than in JET diverted plasmas where |  /  | > 5% Compare limited and diverted plasmas to assess the role of high edge shear on  / 

8. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 TAE Damping Rate Independent of Edge Shear  Elongation scan varied edge magnetic shear by a factor of 2  Resonant TAE mode numbers from 4  n < 14  For moderate n modes, no clear dependence on edge magnetic shear in contrast to low n  2 results on JET

9. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Nova-K Damping Rate Calculations  Nova-K was used without fast particles to calculate the total damping rate of Alfvén eigenmodes in the same frequency range as the experiment including plasma rotation  Both inner wall limited and lower single null diverted plasmas were modeled  Measured damping rates from 0.76 % < |  /  | < 3.0 % and measured modes from 3  n  9 were modeled  Calculated q profiles from TRANSP and EFIT were compared  Sensitivity of the damping rate to q was calculated by scaling the q profile with 0.9, 1.0, and 1.1 times the EFIT q profile

10. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Inner Wall Limited n=4 Mode  Constant active MHD frequency ramping TF through the TAE resonance  f TAE = 420 kHz, n=4,  /  ~ -3% inner wall limited case

11. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Nova-K Agrees Better with EFIT q Profile  Plasma rotation typically < 5 kHz  frequency uncertainty ~ ±20 kHz  Closest mode in Nova-K: 423 kHz,  /  = -0.35% a factor of 10 lower Shot 1021003013

12. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Nova-K Indicates Broad Mode Structure  Closest mode found by Nova-K without strong continuum interaction  Broad radial eigenmode structure with large edge component Shot 1021003013 423 kHz, n=4 Radial Eigenmode Structure Perpendicular Field Perturbation

13. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Lower Single Null n=3 Mode  Constant active MHD frequency ramping TF through the TAE resonance  f TAE = 436 kHz, n=4,  /  ~ -0.76% lower single null case

14. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Nova-K Agrees Better with TRANSP q Profile  Plasma rotation -4 to -8 kHz  f plasma =f meas +12 to 24 kHz=448 – 460 kHz  Closest mode in Nova-K: 452.4 kHz,  /  = -0.77% in good agreement Shot 1030520026 Flat q profile y exponent = 4, q0 = 0.95 1030520026 only strong continuum interaction

15. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Nova-K Indicates Broad Mode Structure  Closest mode found by Nova-K without strong continuum interaction  Broad radial eigenmode structure with large edge component  Calculated  /  = -0.77% in good agreement with the measured  /  = -0.76% Shot 1030520026 Radial Eigenmode Structure 452.4 kHz, n=3

16. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Near Double Null Inner Wall Limited n=9 Mode  Sweeping active MHD frequency through several TAE resonances  f TAE = 487 kHz, n=9,  /  ~ -1.2% near double null inner wall limited resonance

17. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Nova-K Agrees Better with EFIT q Profile  Plasma rotation -2 to -5 kHz  f plasma =f meas +18 to 45 kHz=505 – 532 kHz  Closest mode in Nova-K: 513 kHz,  /  = -0.88% close to measured -1.2%  10% changes in q can change the calculated damping by a factor of 4 – 10 Shot 1050615011

18. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Nova-K Indicates Broad Mode Structure  Closest mode found by Nova-K without strong continuum interaction  Broad radial eigenmode structure with large edge component Shot 1050615011 513 kHz, n=9 Radial Eigenmode Structure Perpendicular Field Perturbation

19. J A Snipes, 6 th ITPA MHD Topical Group Meeting, Tarragona, Spain 4 – 6 July 2005 Conclusions  Moderate n stable TAEs are easily excited in C-Mod with a pair of active MHD antennas driving total perturbations ~ 1 G radial field  TAE damping rates can be measured with synchronous detection of edge magnetic pick-up coil signals  Damping rates of 4 < n < 14 stable TAEs in the range of 0.5 < |  /  | < 4.5% similar to what is found on JET for low n TAE damping rates  The damping rate appears to be sensitive to the edge magnetic configuration  But, there is no clear dependence of moderate n stable TAE damping rates on edge magnetic shear in C-Mod through an elongation scan  Calculations of moderate n TAE damping rates with Nova-K are sensitive to changes in q(r) with order of magnitude changes in  /  for 10% changes in q  Good agreement between measured and calculated damping rates can be obtained in some cases for reasonable q profiles calculated from EFIT