Realistic characterization of chirping instabilities in tokamaks Vinícius Duarte 1,2 Nikolai Gorelenkov 2 , Herb Berk 3 , Mario Podestà 2 , Mike Van Zeeland 4 , David Pace 4 , Bill Heidbrink 5 1 University of São Paulo, Brazil 2 Princeton Plasma Physics Laboratory 3 University of Texas, Austin 4 General Atomics 5 University of California, Irvine PPPL Theory Seminar, March 31, 2016 1
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Realistic characterization of chirping instabilities in ...
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Assumptions:• Perturbative procedurefor• Truncation at third order due to closeness to marginalstability• Bump-on-tail modalproblem,uniformmode structureCubic equation:lowest-order nonlinear correction to the evolution of mode amplitudeA:
Berk,Breizman and Pekker,PRL1996Lilley,Breizman and Sharapov,PRL2009 6
Assumptions:• Perturbative procedurefor• Truncation at third order due to closeness to marginalstability• Bump-on-tail modalproblem,uniformmode structureCubic equation:lowest-order nonlinear correction to the evolution of mode amplitudeA:
Berk,Breizman and Pekker,PRL1996Lilley,Breizman and Sharapov,PRL2009
Assumptions:• Perturbative procedurefor• Truncation at third order due to closeness to marginalstability• Bump-on-tail modalproblem,uniformmode structureCubic equation:lowest-order nonlinear correction to the evolution of mode amplitudeA:
• If nonlinearity is weak:linearstability,solution saturates at alow level and fmerely flattens(systemnot allowed to further evolvenonlinearly).
• If solution of cubic equation explodes:systementers astrong nonlinear phase with largemode amplitudeand can be driven unstable (precursorof chirping modes).
Berk,Breizman and Pekker,PRL1996Lilley,Breizman and Sharapov,PRL2009
• NOVAcode:finds linear,idealmode structures• Itskinetic postprocessor NOVA-Kcomputesresonance surfaces and provides damping and
lineargrowth rates.Phase space and bounce averages arenecessary to calculate effectivecollisional coefficients
• NOVA’s mode structures arecomparedwith NSTXreflectometer measurements (fluiddisplacement timesthe localdensity gradient is equivalent to the density fluctuation).InDIII-DECEis used
8Podestà etal,NF2012
Chirping interms of effective collisional coefficients forrealistic resonances and mode structures
Pitch-angle scattering:leadsto loss of correlation(loss of phase information from one bounce toanother)Drag (slowing down):coherently movesstructuresdowninvelocity
Bump-on-tailmodeling is not enough toresolvethe regions incollisionalspace thatallows forchirping modes
Missing physics inthe simplified theoreticalprediction:mode structure, (multiple)resonancesurfaces and phase-space and bounce averages
Experimentalobservations:Red diamonds:chirping was observedGreendots:nochirping observed
9
Follow from cubicequation
Outline
• Introduction to frequency chirping• Berk-Breizmanmodel:cubic equation formode amplitudeevolution at
early times• Bump-on-tail modeling• Generalization tomulti-dimensional resonances inspace and
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them
16
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them• Proper modeling needs to account for(multiple) resonance surfaces and mode
structures
16
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them• Proper modeling needs to account for(multiple) resonance surfaces and mode
structures• If microturbulence is included, the generalized Berk-Breizman model reproduces
well experimentalobservation
16
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them• Proper modeling needs to account for(multiple) resonance surfaces and mode
structures• If microturbulence is included, the generalized Berk-Breizman model reproduces
well experimentalobservation• Other stochastic contributions may be due to ripples and mode overlap
16
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them• Proper modeling needs to account for(multiple) resonance surfaces and mode
structures• If microturbulence is included, the generalized Berk-Breizman model reproduces
well experimentalobservation• Other stochastic contributions may be due to ripples and mode overlap• InDIII-D,chirping has been identified to be linked with L->Hmode transition.
Possibility of chirping control viarotation shear
16
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them• Proper modeling needs to account for(multiple) resonance surfaces and mode
structures• If microturbulence is included, the generalized Berk-Breizman model reproduces
well experimentalobservation• Other stochastic contributions may be due to ripples and mode overlap• InDIII-D,chirping has been identified to be linked with L->Hmode transition.
Possibility of chirping control viarotation shear
Ongoing work
16
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them• Proper modeling needs to account for(multiple) resonance surfaces and mode
structures• If microturbulence is included, the generalized Berk-Breizman model reproduces
well experimentalobservation• Other stochastic contributions may be due to ripples and mode overlap• InDIII-D,chirping has been identified to be linked with L->Hmode transition.
Possibility of chirping control viarotation shear
Ongoing work• Refinement of turbulence contribution using Beam Emisson Spectroscopy
16
Conclusions• Diffusive effects suppress chirping structures while slowing down enhances them• Proper modeling needs to account for(multiple) resonance surfaces and mode
structures• If microturbulence is included, the generalized Berk-Breizman model reproduces
well experimentalobservation• Other stochastic contributions may be due to ripples and mode overlap• InDIII-D,chirping has been identified to be linked with L->Hmode transition.
Possibility of chirping control viarotation shear
Ongoing work• Refinement of turbulence contribution using Beam Emisson Spectroscopy• Development of aline-broadened quasilinear diffusion solvercoupled with NOVA
and NOVA-K:chirping criterion is important foridentification of parameter space forquasilinear validity 16