experimental studies and analysis of alfven eigenmodes in ......mina ac 0 min0 ()v () mnqt t qtr! !...

Porkolab/IAEA_Changdu/Cn_10.16.2006

M. Porkolab, E. Edlund, L. Lin, R. Parker, C. Rost, J.Sears, J. Snipes, S.J. Wukitch, PSFC, MIT, Cambridge,MA 02139 USA; B. Breizman, IFS, U Texas, Austin, TX 78712USA; N. Gorelenkov, G.J. Kramer, PPPL, Princeton, NJ08540 USA; A. Fasoli, CRPP-EPFL, CH-1015, Lausanne,Switzerland; H. Smith, Chalmers U., SE-41296, Goteborg,Sweden

Experimental Studies and Analysis ofAlfven Eigenmodes in Alcator C-Mod

IAEA_EX/P6-16


Experimental Studies and Analysis of AlfvénEigenmodes in Alcator C-Mod

Alfvén cascades (ACs) or equivalently, reverse shear Alfvén eigenmodes (RSAE) have been observed in

Alcator C-Mod during current ramp experiments in the presence of intense ICRF driven energetic minority

tails. These experiments were carried out at ITER relevant densities and magnetic field. Phase contrast

imaging (PCI) and magnetic pick-up coils have been used for detecting the Alfvén eigenmodes. The chirping

evolution (increasing in time) of the frequency spectrum has allowed us to deduce the temporal evolution of

the reversed shear q-profile. Numerical results from the latest version of the NOVA-K MHD code, including

finite pressure reproduces the experimental measurements, including the m inimum frequency. The

harmonic of the cascade frequency was also observed by the diagnost ics. In a different set of C-Mod

experiments a pair of active MHD antennas were used to excite ITER relevant intermediate toroidal mode

number (3 < n < 14) toroidal Alfvén eigenmodes (TAE), and their measured weak damping rates indicate

that such modes may be excited by alpha particles in ITER. We have also studied the feasibility of adding

PCI detection optics outside the ITER vessel that shares the CO2 laser interferometer port hardware.

Implementing PCI on ITER would greatly extend our capabilities to assess the importance of Alfvén mode

excitation on alpha particle confinement.

ABSTRACTABSTRACT


Overview

• Alfvén cascades (or RSAE) are being studied on Alcator C-Modduring the current ramp phase with intense ICRF, PRF > 2MW

• Cascades can be used as an equilibrium diagnostic because of theirgreat sensitivity to variations in the q profile

• Experimental data from the PCI system and magnetic pick-upcoils are compared to the MHD code NOVA and to recent theories

• Acoustic coupling terms can be dominant when m ≈ mqmin

• Harmonic of RSAE has been observed and motivated new theory

• PCI may be adopted to ITER using its 5 chord CO2 interferometer

• Actively launched TAE modes were used to measure the dampingrates (a few percent) of ITER relevant moderate n modes (3 to 12)

• The damping rates measured are in good agreement with theNOVA-K code but are sensitive to the precise plasma profiles


Alfven Cascades (Reversed Shear Alfven Eigenmodes, or RSAE) are Excited During Current Ramp with Intense

ICRF Minority Heating D(H)

Cascadesobserved

Alfven Wave Cascades (or RSAE) observedonly during the initial current ramp phasewhen RS (reversed shear) q profile is expected

0

0min )(2

1)( f

R

Vn

tq

mtf A

cascade

+!="

PCI Diagnostic


ICRF Driven Fast Ions Excite Alfvén EigenmodesTAEs disappear just after fast ion energy decays due to density rise

ICRF H minority fast ion energy reaches 300 keV (vH/vA ~ 0.7) due to 2 -4 MW RF power injected at densitiesnot exceeding 1x1020m-3 (Transp)


How Alfvén Cascades Become TAEsmin A

AC 0min 0

( ) v( )

( )

m nq tt

q t R! !

"= # +

ATAE

0

v

2qR! =

• Cascades require very low or reversed shear to widen theTAE gap to allow frequency chirping

• Cascades are excited at rational q values with qmin = m/n


AE Gap Width Indicates Frequency Evolution

At near integer q0 the wide n=1 gap allows the Alfvén cascadefrequency to sweep up to the TAE frequency

As q0 evolves to near a half integer value, the n=1 gap narrows tomeet the TAE frequency as the Alfvén cascade becomes a TAE

Alfvén Cascade TAE

n=1n=1

NOVA-K Code (PPPL)


Modeling Alfvén Cascades Provides q-evolution

The frequency evolution of Alfvén Cascades can be modeled byMISHKA or the Nova-K codes to determine the evolution ofthe minimum q value

The rapidly upward frequency chirping Alfvén Cascades evolve into slowly varying TAE modes

C Boswell


Alfvén Cascades Constrain the q Profile

The modeling indicates a flat or slightly reversed shear profilewith qmin = 3 at the start of the n=1 Alfvén Cascade (t = 0.12 s)

Then qmin falls from 3 to about 2.2 by the end of the cascades


AE Diagnostics: PCI + Magnetic Pick-up Coils

Magnetic pick-up coils:

65 poloidal field pick-up coils in poloidaland toroidal arrays

Can measure m < 14 and n < 75 2.5 MHz sampling rate

Phase-contrast imaging (PCI):

Measures line integrated electron densityfluctuations along 32 vertical chords

Sensitive to kR from 0.6 to 30 cm-1

10 MHz sampling rate


Principle of Phase Contrast Imaging (PCI)Zernike, PCI Microscope, 1930s, Nobel Prize

H. Weisen, first application to tokamak plasmas, 1980s, Lausanne


Core (PCI) and Global Alfvén Cascades (magnetic loops) May Differ

Alfvén cascade frequency sweeps up proportional to n

Core Alfvén Cascades on PCI have higher n numbers than global AC’s on the edge magnetic pickup coils

min AAC 0

min 0

( ) v( )

( )

m nq tt

q t R! !

"= # +


Recent Addition of Finite Pressure and Pressure Gradient intoNova-K Improves Modeling of the RSAE Modes

and Good Agreement Can Be Obtained with Experiment

The white curves show the Nova-Kmodeling without the finite pressureterm showing poor agreement at theminimum frequency

Inclusion of finite pressure and itsgradient in the upgraded Nova-Kassures matching of the minimumcascade frequency (175-200 kHz)

(q0=qmin+0.1)


22

2 2

2 2

0 min 0

2 71

( ) 4

A e iAC

i e

V m T Tn

R q t M R T! !"

# $# $= % + + +& '& '

( ) ( )

NOVA-K Code and Recent Analytic Theory Predict the Frequencyof Alfvén Cascades and are Compared with Experiment

• Alfvén Cascades that exist in reverse shearconditions are extremely sensitive to theminimum value of q

• Modeling with the ideal MHD code NOVAcan be used to diagnose the evolution of qminand more recently, the initial frequency

• The mode frequency is describedtheoretically as the Alfvénic term, thegeodesic acoustic term (geodesic acousticdeformation of the Alfvén continuum) andthe gradient terms (bulk and hot ion tail)(Breizman et al, Berk et al, Kramer et al,Zonka et al):

(1)

!

"#

2 $ %2

MR2rd

drTe +Ti( )%

"

m

eB

Mc

r

nplasma

d

drn fast (2)


• When m = nq the Alfvénic termvanishes in Eq. (1), the geodesic acousticcoupling term determines the minimumfrequency (for negligible gradients! )

•The acoustic term is then dominant andshould scale as Te

1/2 taking Ti α Te

• PCI data from four run days show astrong correlation with the predicted Te

1/2

scaling

• This data may be used to diagnose avalue of Ti/Te during the ramp-up phase

• The value of the gradient of the bulkplasma is small (1%); however, gradientof the fast ion term can be significant andnot well known; (not included in theNOVA modeling )

Initial Data on Minimum Frequency ShowsReasonable Scaling with Te

1/2

Alcator C-Mod data


• Candidate modes found in NOVA arecompared against PCI data forfrequency and structure.

• 2-D outputs are put through a“synthetic” PCI diagnostic (ie, PCIresponse is installed and integratedalong the beam line in NOVA-K )

• The calculations show that themultiply peaked structure measured byPCI is a result of phase cancellationfrom the line integration of the signal

The “Synthetic PCI” Diagnostic Has Been Developed toInterpret PCI Experimental Data on Mode Structure


NOVA Parameter Variation Determines Location of qmin

NOVA data is compared to PCI signals

* variation of qmin is used to match frequency * variation of radial location of the minimum can be used to match the peak spacing in mode structure (below) * variation of central shear seems to affect the relative magnitude of the peaks, however diagnostic uncertainties must first be accounted for to make this approach useful


2nd Harmonic Indicates Alfvén Cascades are Nonlinear

2nd harmonic AC’s on PCI with f2nd = 2 × f1st and A2nd = A1st/10 Not clearly visible on the magnetic pickup coils at the wall Indicates nonlinear excitation of ACs as expected by theory

2nd harmonic

2nd harmonic


Observation of Second Harmonic CascadesMotivated Recent Theory-May Determine δBω

• The harmonic amplitude increaseswith RF power and seems to bestronger for high field sideresonance• In principle, the ratio of the secondharmonic to fundamental amplitudecan be used to measure δBω (IFS-Chalmers collaboration, Smith et al,PoP 13, 042504 (2006))

!!"

#$$%

&'

00

0

0

2

B

B

r

Rmq

(

(

()

*

*

Use of this relation iscomplicated by the PCI’sline-integrated sensitivity

nonlinear stress (T2)

plasma displacement (Φ2)


Propose Tangential PCI on ITER Interferometer toDetect Alpha Particle and NBI Driven Alfvén Cascades

ITER Plans:5 chords of 2 cmCO2 beams

Add externaloptics to enablePCI operation


Summary-I

Ip ramp and intense ICRF minority heating provides target RS plasmas in C-Mod for Advanced Tokamak studiesRSAE (Alfven Cascades) have been identified with Phase Contrast Imagingand magnetic pickup coils and the temporal evolution of qmin has been deducedThe RSAE frequency evolution was modeled with the upgraded Nova-K codewhich now includes finite pressure, its gradient and appropriate acoustic modefiltering (but still missing energetic particle gradient terms)By retaining the geodesic acoustic deformation the code predicts fmin

of the cascades- a potential diagnostic of local pressure ( Te ) The role of fast particle gradients needs further assessment“Synthetic PCI” has been included in the NOVA Code and the spatial structure of the PCI signal has been interpreted satisfactorilyHarmonic of the RSAE has been observed and will be compared with recent theoretical predictions - diagnostic to measure δBω ?


Experimental Study of the Damping of Intermediate n (3-15)TAE Modes Using Actively Driven MHD Antennas

Two antennas above and below the outboard midplane Present amplifiers drive ~ 25 A each producing Br ~ 1 G at q=1.5 10 Hz < f < 1 MHz, broad toroidal spectrum |n| ~ 16 FWHM

~

Broad n spectrum is excited


Two Stable TAE Resonances with Sweeping TF

Two stable TAE resonancesas the toroidal field sweepsthe TAE frequency downand up at constant activeMHD frequency

Resonances occur at theTAE frequency for q=1.5


TAE Resonances with Sweeping Frequency

Multiple stable TAE resonanceswith sweeping Active MHDfrequency occur at factive~ 320 kHz

Fit gives damping rate γ/ω ~ 4.5%and n = 12


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 shearin contrast to low n ≤ 2 results on JET


Measured TAE Damping vs Triangularity

Average triangularity scanned from 0.3 < (δu + δl)/2 < 0.7

All these resonances have n = 6 Damping rate does not increase with

triangularity, in contrast to the result on JET for n=1

Indicates edge effects on moderate n TAE damping are not as strong as for low n modes


TAE Damping Rate Shows Weak Dependence on Ion ∇B Drift Direction

Reversed BT and Ip run with ion ∇B driftdirection upward

Measured TAE damping rate is perhaps slightly lower when ion ∇B drift directed away from the X point (LSN red points)

Contrasts JET result for n=1 where the measured TAE damping rate was 3 times higher when the ion ∇B drift was directed away from the X point


TAE Damping vs Dimensionless Parameters

Through density, toroidal field, and ICRF power scans the TAE damping rate was measured as a function of ν*e, ρ*i, and βN

The TAE damping rate appears to increase at very low collisionality

The TAE damping rate increases with ρ*I and βN

Note however that the n number may not be the same for all of these points and that changes in damping rate with n could mask these dependencies


• Damping rates decrease with triangularity and appear to be nearly independent of the ion ∇B drift direction in diverted plasmas

• Damping is not strongly affected by edge conditions(in contrast to low n TAE damping measured on JET)

• Damping rate is independent of ICRF power, possibly because the fastion toroidal precession was opposite to the TAE direction or that the fastion drive and the mode were localized at different radii

• The measured damping also appears to increase at very low ν* andincrease with ρ* and βN

• TAE damping rates depend sensitively on plasma parameters that aredifficult to measure accurately (q-profile, density profile, etc)

• It is possible that changes in these or other parameters, such as thetoroidal mode number, could obscure the parametric dependences

Summary II: Actively Launched Moderate-n TAE modes

experimental studies and analysis of alfven eigenmodes in ......mina ac 0 min0 ()v () mnqt t qtr! !...

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