Dependence of non-local effects on plasma parameters during cold-pulse experiments in Alcator C-Mod P. Rodriguez-Fernandez 1, N.M. Cao 1, A. Creely 1, M. Greenwald 1, S. Houshmandyar 2, N.T. Howard 1, A.E. Hubbard 1, J. Hughes 1, J. Irby 1, C. Petty 3, J.E. Rice 1, W.L. Rowan 2, A.E. White 1 1 Plasma Science and Fusion Center (MIT, MA) 2 Institute for Fusion Studies (University of Texas, TX) 3 General Atomics (San Diego, CA) 2016 US Transport Task Force Workshop March 29th - April 1st 2016 Denver, CO
Improved confinement needed for fusion Heat Transport and Energy Confinement Historical challenge... transport not fully understood... Is transport locally determined or could global parameters determine transport throughout the system? [Cardozo, 1995] Perturbative Trasport Analysis Transient response to a perturbation Sawtooth crashes, ECH, Impurity injection, etc Multi-pulse Laser Blow-Off System On C-Mod Laser ablation of CaF 2 slide Multiple injections, possible during single discharge
Typical Diffusive, Same Polarity Response Figure: T e (t) at different radial positions. ECE Raw data.
Non-Diffusive, Inverted Polarity Response Figure: T e (t) at different radial positions. ECE Raw data.
Non-Diffusive, Inverted Polarity Response What are we observing? Fast core T e response to an edge cold-pulse Inverse response: increase in core T e Why is this interesting? Challenges heat transport understanding Transient heat transport models Multichannel phenomena How are we going to study it? 1 Correlation with other phenomena 2 Cold-pulses parameterization 3 Perturbation and heat transport analysis Figure: T e (t) at different radii
Past Work on C-Mod [Rice J., NF, 2013] & [Gao C., NF, 2014] Unified model for multi-channel transport n e, ν non-local effects thresholds Figure: Figure 11 from [Rice J., NF, 2013]. Energy confinement time, core temperature perturbation amplitude and intrinsic rotation as functions of electron density. Shots at 0.8MA, ohmic. Figure: Figure 15 from [Rice J., NF, 2013]. Thresholds in density at different values of 1/q 95 for LOC/SOC transition, rotation reversal, and Te inversion and up-down asymmetry effects.
Old parameterization showed density threshold for different plasma currents The change in core temperature was recorded at a fixed time after LBO injection (10ms) to determine drop/rise Thresholds in density for all plasma currents Figure: Generation of points using old parameterization (Shot #1120216009)
This parameterization cannot capture combination of temperature rise and drop Example here shows a drop then a rise in temperature (but only drop is recorded) A rise would be non-diffusive: a linearized perturbation cannot change sign anywhere if described by a diffusive (parabolic) equation
Pulse shapes Fourier filter and B-Spline interpolation serves as qualitative estimate for pulse shapes Figure: Observed pulse shapes
To handle the combination of rise and drops, a new parameterization is needed: variable time, track maximum amplitude change Figure: Generation of points using new parameterization
MP793 used RF heating to separate core response from rotation reversal MP793 Shots I p = 0.8MA B t = 5.4T P rf = 0, 0.6, 1.2MW Preliminary Results from MP793 Non-local effects observed after rotation reversal Threshold in density increases with RF Figure: Shot #1150901023 (I p = 0.8MA, P rf = 0.6MW )
New parameterization allows to define dependency on density for MP793 and old Shots Figure: Compilation of core responses.
Interesting Data is Missing: New experiment in Last Experimental Campaign in C-Mod Goal: Separating Ip and RF roles Why? I p scan only available for ohmic shots RF scan only available for I p = 0.8MA Using new parameterization, high I p without threshold Goal: Separating RF and Spot-size roles Why? Suggested in the past ([Callen 97], [Gao 14]) RF observed to damp edge perturbation Core response strength and mixing effect depend on edge perturbation (and/or RF?)
Comprehensive Analysis is In-progress (I) Signal Processing: GSVD, Sawtooth events, B-Splines Objective: Characterize propagation time (is t prop < τ e?) Strong interaction with sawtooth GSVD not efficient So far: Fourier filter + B-Splines interpolation Generalized Singular Values Decomposition p 1 (t 1 )... p d (t 1 ) p(x, t) =.. p 1 (t N )... p d (t N ) u(x, t) = d k=1 α k a k (t) v k (x) T y(x, t) = d k=1 β k b k (t) v k (x) T
Comprehensive Analysis is In-progress (II) Power Balance (TRANSP) Two models were proposed in previous work ([Gao 14]): Pure Diffusive q e = n e χ e Te Pinch Model q e = n e χ e Te + n e V p T e Diffusive Model: Fast drop in core χ e to match exp. results Convective Model: Negative pinch velocity and χ e = const *Both models applied to shot #1120106020 (Ohmic, 0.8MA)
Categories of transport phenomena Ambiguous definition of τ crit Diffusive transport could, in principle, explain sudden temperature rises after cold-pulse injection Question to address: Can high stiffness of χ e be the key to explain non-local effects? Figure: Definitions for Transport Phenomena in the Literature
Future Work Correlating perturbative χ HP e with core temperature inversions χ HP e from partial sawtooth method [Creely A., NF, 2016] New multi-scale (ITG/TEM coupled with ETG) simulations match experimental χ HP e, [Howard N.T., PoP, 2014] Extending perturbative transport studies to DIII-D New LBO system will be designed and installed at DIII-D in coming years Opportunity to compare propagation of cold pulses with LBO to heat pulses with ECH Multi channel perturbative transport studies possible at both C-Mod and DIII-D using XICS (long term)
Preliminary Results (I): Threshold in χ e for appearance of non-local effects Figure: χ HP e from [Creely A., NF, 2016] as a function of amplitude of core response after cold-pulse injection in 1.2MW, 0.8MA plasmas. Both χ HP e and the core response are averaged for the entire shot (1 to 4 pulses). First correlation of non-local effects and χ HP e looks promising. Threshold in χ HP e for appearance of non-local effects is observed. Future study will include shots with different plasma currents, RF input power and electron densities.
Preliminary Results (II): Power balance shows localized drop in ohmic power around inversion radius Ohmic power spike also observed by [Cao N.M., TTF 2016]. Localized drop in current density can be identified. These effects are not observed in pure local cases.
Preliminary Results (III): Current density profile qualitatively different for non-local effect cases Localized drop in current density is observed when non-local effects appear. Future study will extend database to correlate amplitude of non-local effect with features of current profile.
Laser Blow-off (LBO) System at C-Mod Laser Details Pulsed Nd:YAG laser (λ = 1064 nm) 10 Hz and 0.68 J pulse energy Optics Details Diode laser for location of main beam Power density manipulation with mechanical iris and focal length [Howard N.T., RSI, 2011] Slide Details Spot sizes from 0.5 to 7 mm Li, CaF 2, M, W, Al, Fe, Nb... Normally: 100Å of Cr (laser absorption) and 2µm of desired material
Introduction Analysis Preliminary Results & Future Work DIII-D Collaboration References and Acknowledgments Hardware Plans for LBO on DIII-D Hardware from C-Mod LBO system Laser, Piezoelectric, Optical table, Digitizer Changes for DIII-D New vacuum interface Multiple-slide setup (rotating Figure: Picture of LBO vacuum interface ready for last campaign at C-Mod system, turbo pump) Target Time-line Installation in 2017 Full operation by end of 2017
Physics Plans for LBO on DIII-D Impurity Transport [Howard N.T., NF, 2012] Injections of trace amounts of non-intrinsic, non-recycling impurities. Non-perturbative (less than 10%) Brightness measurement for D, V coefficients Comparison with turbulence measurements. Additional constrain for gyrokinetic models validation Perturbative Transport Cold-pulse experiments Comparison with ECH heat pulses Turbulence measurements: CECE (low-k T e ), DBS (med-k ñ), BES (low-k ñ), PCI,...
Physics Plans at DIII-D in preparation for LBO Past ECH Heat Pulse Experiments Extend work by Craig Petty and Melinda Gildner Multichannel coupling effects ECH heat pulse and LBO cold pulse comparison Figure: Perturbed T e, T i during heat pulse (ECH) propagation. Better fit to data is achieved if ion-electron transport coupling is included [Gildner M., Private Communication, 2005] Summer Research, at DIII-D
References N.J. Lopes Cardozo, 1995 Plasma Phys. Control. Fusion 37 (1995) 799-852 J.E. Rice et al, Nucl. Fusion 53 (2013) 033004 C. Gao et al, Nucl. Fusion 54 (2014) 083025 J.D. Callen et al, Plasma Phys. Control. Fusion 39 (1997) B173B188 A. Creely et al, Nucl. Fusion 56 (2016) 036003 N.T. Howard et al, Physics of Plasmas 21 (2014) 112510 N.M. Cao, TTF 2016 (unpublished) N.T. Howard et al, Nucl. Fusion 52 (2012) 063002 M. Gildner, 2005 (private communication) Acknowledgments This work is supported by U.S. Department of Energy under contract numbers DE-FC02-99ER54512 (C-Mod) and DE-FC02-04ER54698 (DIII-D) and La Caixa Fellowship.