Active and Fast Particle Driven Alfvén Eigenmodes in Alcator C-Mod

Active and Fast Particle Driven Alfvén Eigenmodes in Alcator C-Mod JUST DID IT. J A Snipes, N Basse, C Boswell, E Edlund, A Fasoli #, N N Gorelenkov, R S Granetz, L Lin, Y Lin, R Parker, M Porkolab, J Sears, S Sharapov *, V Tang, S Wukitch MIT Plasma Science and Fusion Center, Cambridge, MA USA # CRPP, Association Euratom Confederation Suisse, EPFL Lausanne, Switzerland Princeton Plasma Physics Laboratory, Princeton, NJ USA * Euratom/UKAEA Fusion Association, Abingdon, UK

Outline Motivation and overview of Alfvén eigenmode physics AE diagnostics on C-Mod Active MHD experiments stable AEs Unstable flattop AEs during sawtooth stabilization Unstable current rise AEs Alfvén Cascades, TAEs, EAEs Conclusions

Fast α Particles Pass Through Alfvén Resonances AEs can transport α s out of the plasma and quench the fusion burn Validate physics models and diagnostics: fast particles and q(r)

Alfvén Waves in Toroidal Plasmas Alfvén continuum: 2 2 2 = A ω () r k ()v r () r In a cylinder provides strong damping to global modes In a torus, coupling of poloidal harmonics m and m+1 produces Gaps in the continuum spectrum Weakly damped eigenmodes, e.g., Toroidal AE s, Elliptical AE s, etc ω = v (0)/( qr) A A a 0 B /( qr nm) T a 0 i i

AE Drive and Damping Mechanisms γ TAE growth rate: ω fast particle drive ω * = 2 H nqv 2ω rβ c H d β dr H q 2 β * H ω γ ( 1) f d res ω ω fraction of resonant particles e.g., precession magnetic drift resonance: v H 1 v 2qk θ ρ A H damping Multiple damping mechanisms: Continuum damping Radiative damping Collisional damping Landau damping

Outline Motivation and overview of Alfvén eigenmode physics AE diagnostics on C-Mod

Active MHD Antennas Excite Broad n Spectrum Two antennas above and below the outboard midplane ~ Present 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

AE Diagnostics: PCI + Magnetic Pick-up Coils Phase-contrast imaging (PCI): Measures line integrated electron density fluctuations along 32 vertical chords Sensitive to k R from 0.6 to 17 cm -1 10 MHz sampling rate Magnetic pick-up coils: 65 poloidal field pick-up coils in poloidal and toroidal arrays Can measure m < 14 and n < 75 2.5 MHz sampling rate

Outline Motivation and overview of Alfvén eigenmode physics AE diagnostics on C-Mod Active MHD experiments stable AEs

Two Stable TAE Resonances with Sweeping TF Two stable TAE resonances as the toroidal field sweeps the TAE frequency down and up at constant active MHD frequency Resonances occur at the TAE frequency for q=1.5

TAE Resonances with Sweeping Frequency Multiple stable TAE resonances with sweeping Active MHD frequency occur at f active ~ 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 shear in contrast to low n 2 results on JET

Outline Motivation and overview of Alfvén eigenmode physics AE diagnostics on C-Mod Active MHD experiments stable AEs Unstable flattop AEs during sawtooth stabilization

Energetic Particle Modes During Sawteeth EPM s and Alfvén Eigenmodes during sawteeth can help to: Test theoretical models Determine the q profile evolution Measure the effects of fast particles on sawtooth stabilization Provide a qualitative measure of the fast particle evolution

Modes Coalesce During Monster Sawteeth n spectrum n = 4 10 modes decrease in frequency from 750 650 khz during sawtooth stabilization matching the TAE frequency at q=1 Multiple frequency modes decrease in frequency and coalesce to a single frequency just before the sawtooth collapse v ω q A TAE ( = 1) = 2R

Outline Motivation and overview of Alfvén eigenmode physics AE diagnostics on C-Mod Active MHD experiments stable AEs Unstable flattop AEs during sawtooth stabilization Unstable current rise AEs Alfvén Cascades, TAEs, EAEs

How Alfvén Cascades Become TAEs ω m nq () t v min A AC() t = + ω0 qmin() t R0 ω = TAE va 2qR 0 Cascades require very low or reversed shear to widen the TAE gap to allow frequency chirping Cascades are excited at rational q values with q min = m/n

Core and Global Alfvén Cascades Differ ωac (t ) = m nqmin (t ) v A + ω0 qmin (t ) R0 ¾ Alfvén cascade frequency sweeps up proportional to n ¾ Core Alfvén Cascades on PCI have higher n numbers than global AC s on the edge magnetic pickup coils J A Snipes, 46th APS Division of Plasma Physics Meeting, Savannah, GA 18 November 2004

Modeling Alfvén Cascades Provides q Evolution The frequency evolution of Alfvén Cascades can be modeled by the MISHKA code to determine the evolution of the minimum q value The rapidly upward frequency chirping Alfvén Cascades develop into slowly varying TAE modes as the frequency peaks C Boswell

AE Gap Width Indicates Frequency Evolution Alfvén Cascade TAE n=1 n=1 At near integer q 0 the wide n=1 gap allows the Alfvén cascade frequency to sweep up to the TAE frequency As q 0 evolves to near a half integer value, the n=1 gap narrows to meet the TAE frequency as the Alfvén cascade becomes a TAE

Alfvén Cascades Constrain the q Profile The modeling indicates a flat or slightly reversed shear profile with q min = 3 at the start of the n=1 Alfvén Cascade (t = 0.12 s) Then q min falls from 3 to about 2.2 by the end of the cascades

ICRF Driven Fast Ions Excite Alfvén Eigenmodes ICRF H minority fast ion energy reaches 300 kev v H /v A ~ 0.7 TAE s disappear just after the fast ion energy drops

Modes Match AE Center of the Gap Frequency at q=2 EAE Nova-K RF beat wave TAEs ACs Downward sweeping AE from 1 MHz to 900 khz matches f EAE (q=2) Alfvén Cascades start below the q=2 TAE frequency and sweep up to it

2 nd Harmonic Indicates Alfvén Cascades are Nonlinear 2 nd harmonic 2 nd harmonic 2 nd harmonic AC s on PCI with f 2nd = 2 f 1st and A 2nd = A 1st /10 Not clearly visible on the magnetic pickup coils at the wall Indicates nonlinear excitation of ACs as expected by theory

Inboard RF Resonance Alfvén Cascades are More Stable inboard RF resonance central RF resonance outboard RF resonance R/R res = 0.9 R/R res = 1.0 R/R res = 1.1

Theory Predicts RF Resonance Effect on AEs Theory predicts the AE growth rate to scale as γ ω ~ dh F(v) dv where ω is the precession drift frequency, ω ω ω dh dh which slows down as the RF resonance is moved inboard An MHD code, Nova-K, including fast particles, finite orbit width and finite Larmor radius effects was used to model RF resonance changes The central RF resonance case was scanned over pitch angle keeping all other parameters fixed at t = 0.122 s at the top of a cascade Kinetic profiles were taken from TRANSP/FPPRF/TORIC which indicated a peak T H = 160 kev The q profile was assumed to have slightly reversed shear with q 0 = 2.11 and q min = 2.06 at r/a = 0.4

Broad TAE Structure is Found for Central RF Resonance Broad n=1 radial mode structure f = 342 khz close to measured frequency of 360 khz Dominant m=2, 3 harmonics Long wavelength broad mode structure consistent with being observed on edge magnetic coils and not observed on core PCI

Fast Ion Temperature Affects AE Growth Rate Maxwellian and pitch angle distribution in Nova-K: f E R 2 2 exp[ ( res dr p ) /( ) ] T R R H axis axis where E = ½mv 2, T H is the fast ion temperature, p=µb axis /E, and µ is the magnetic moment µ 1 2 = v / 2 m B AE growth rate peaks at 160 kev while finite Larmor radius effects reduce the growth rate at high tail temperatures

AE Growth Rate is Lower for Inboard RF Resonance Scanning the RF resonance radius in Nova-K indicates outboard growth rate is somewhat larger than inboard Qualitatively agrees with the experimental observation of weaker inboard modes Quantitative agreement would require measurements of the distribution function Toroidal precession drift frequency slowing on the inboard side also explains frequency downshift of AEs for the inboard resonance

Conclusions Damping rates of 4 < n < 14 stable TAEs are 0.5 < γ/ω < 4.5% No clear dependence of moderate n TAE damping rates on edge magnetic shear in C-Mod through an elongation scan Core Alfvén Cascades from PCI have higher n than global AC s from magnetic pickup coils indicate a flat or slightly reversed shear q profile TRANSP/FPPRF calculated ICRF driven fast ion energies exceed 300 kev AEs are more stable with an inboard ICRF resonance location in qualitative agreement with Nova-K calculations Slowing of the toroidal precession drift may also explain downward frequency chirping of Alfvén eigenmodes with an inboard resonance Moderate n = 4 10 unstable TAE s during monster sawteeth decrease in frequency and mode number and coalesce just before the sawtooth collapse