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