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J A Snipes, 6th 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
J A Snipes, 6th 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
J A Snipes, 6th 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 BT and ne with TeTi 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
J A Snipes, 6th 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 Br ~ 1 G at q=1.5
10 Hz < f < 1 MHz, broad toroidal spectrum |n| ~ 16 FWHM
~
J A Snipes, 6th 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
v( 1.5)
3A
TAE qR
J A Snipes, 6th 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
J A Snipes, 6th 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 /
J A Snipes, 6th 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
J A Snipes, 6th 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
J A Snipes, 6th 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
fTAE = 420 kHz, n=4, / ~ -3% inner wall limited case
J A Snipes, 6th 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
J A Snipes, 6th 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
J A Snipes, 6th 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
fTAE = 436 kHz, n=4, / ~ -0.76% lower single null case
J A Snipes, 6th 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 fplasma=fmeas+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
J A Snipes, 6th 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 1030520026Radial Eigenmode Structure
452.4 kHz, n=3
J A Snipes, 6th 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
fTAE = 487 kHz, n=9, / ~ -1.2% near double null inner wall limited
resonance
J A Snipes, 6th 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 fplasma=fmeas+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
EFIT q profile * 0.9, q0 = 0.9, 1050615011, 0.83 - 0.88 sFreq (kHz) e-collisions thermal e D C continuum Total
509 -1.86E-09 -6.79E-06 -4.58E-04 -8.69E-06 -9.73E-03 -1.02538 -2.20E-09 -7.34E-06 -5.72E-04 -9.45E-06 -1.31E-03 -0.19
EFIT q profile * 1.1, q0 = 1.1, 1050615011, 0.83 - 0.88 sFreq (kHz) e-collisions thermal e D C continuum Total
508 -1.89E-09 -3.49E-06 -5.61E-04 -1.69E-05 -4.52E-05 -0.06512 -1.00E-09 -6.85E-06 -1.35E-03 -2.12E-05 -8.00E-04 -0.22
Peaked TRANSP q profile, q0 = 0.54, 1050615011, 0.83 - 0.88 sFreq (kHz) e-collisions thermal e D C continuum Total
507.9 -5.83E-07 -0.0007805 -0.09588 -0.001539 -1.143874 -1.24519.2 -3.188E-07 -0.0005219 -0.07085 -0.001544 -0.427648 -0.50537.7 -4.962E-07 -0.0008748 -0.08044 -0.001346 -0.507674 -0.59
J A Snipes, 6th 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
J A Snipes, 6th 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