27th IAEA Fusion Energy Conference Ahmedabad, India. October 22 27, PDF Free Download

Advances in Runaway Electron Control and Model Validation for ITER by C. Paz-Soldan1 with contributions from: N. Eidietis,1 E. Hollmann,2 A. Lvovskiy,3 C. Cooper,3 J. Herfindal,4 R. Moyer,2 D. Shiraki,4 K. Thome,1 P. Aleynikov,5 D. Brennan,6 L. Carbajal,4 D. del-castillo-negrete,4 O. Embreus,7 T. Fulop,7 M. Hoppe,7 C. Liu,6 P. Parks,1 D. Spong,4 General Atomics University of California, San Diego 3 Oak Ridge Associated Universities 4 Oak Ridge National Laboratory 5 Max-Planck Institute, Greifswald 6 Princeton Plasma Physics Laboratory 7 Chalmers University 27 18 1 63 2 62 1 Presented at 10 27th IAEA Fusion Energy Conference Ahmedabad, India October 22 27, 2018 1

Runaway Electron (RE) Control is an Existential Concern for Fusion-Grade Tokamaks REs are formed after a disruption and can damage the first wall RE Strike on JET C. Reux et al 2

Runaway Electron (RE) Control is an Existential Concern for Fusion-Grade Tokamaks REs are formed after a disruption and can damage the first wall Talk presents experiment and modeling advances for the: 1. Formation Phase: Avoidance 2. Plateau Phase: Mitigation Limited opportunity for empirical tuning of RE mitigation 6 Validated predictive modeling of RE control is essential RE Avoidance RE Mitigation

RE Formation Phase Offers the Opportunity to Completely Avoid RE Issues 1. Can we predict the initial (seed) RE current? 2. Do we have options to avoid the RE plateau phase? 7 RE Seed Current RE Avoidance

Experimental RE Seed Current of ~ 1 ka Estimated Far Away from Hot-Tail Theory Predictions Hot-Tail mechanism 1 expected to dominate RE seed production in ITER 1 Smith et al, PoP 2008 8

Experimental RE Seed Current of ~ 1 ka Estimated Far Away from Hot-Tail Theory Predictions Hot-Tail mechanism 1 expected to dominate RE seed production in ITER Early theory 1 exceeds experimental estimates from pellet ablation light 2 10 7 10 5 10 3 RE seed current (A) Experiment Smith 1 10 1 0 1 2 9 1 Smith et al, PoP 2008 2 E. Hollmann et al, NF 2017

Experimental RE Seed Current of ~ 1 ka Estimated Far Away from Hot-Tail Theory Predictions Hot-Tail mechanism 1 expected to dominate RE seed production in ITER Early theory 1 exceeds experimental estimates from pellet ablation light 2 Recent theory 3 self-consistently treats plasma cooling with RE seed formation but now under-predicts RE seed Open area for improvements Pellet interaction missing 10 7 10 5 10 3 10 1 RE seed current (A) Experiment Smith 1 Aleynikov & Briezman 3 0 1 2 10 3 P. Aleynikov, B. Breizman, NF 2017 1 Smith et al, PoP 2008 2 E. Hollmann et al, NF 2017

DIII-D Sometimes Experiences Unreliable RE Formation Threshold Behavior Observed RE formation in DIII-D can be unreliable Corollary: RE plateaus avoidable Ip [MA] 1.2 0.8 Primary Ar 0.4 0 #177028: 50 torr l Ar #177030: 130 torr l Ar Yes plateau No plateau 0 2 4 6 8 10 12 t-t dis (ms) Threshold for RE avoidance seen in primary Argon quantity and Ip Ip [MA] 1.2 0.8 2x 2x 2x threshold 2x No plateau RE plateau 2x 11 0 50 100 150 Primary Ar Argon quantity Quantity [torr l] [torr-l]

Intense Alfvenic Instabilities (~ MHz range) Observed During RE Plateau Formation, Correlates with Avoidance Avoided RE plateaus correlate with intense & coherent MHz-frequency modes 12 Candidate: compressional Alfven wave driven by REs Ip [MA] Freq [MHz] Freq [MHz] 1.2 0.8 Primary Ar 0.4 0 4 3 2 1 0 4 3 2 1 0 #177028: 50 torr l Ar #177030: 130 torr l Ar Yes plateau No plateau #177028 - No Plateau #177030 - Yes Plateau 0 2 4 6 8 10 12 t-t dis (ms) -100-150 -200-100 -150-200 Power/frequency (db/hz) Power/frequency (db/hz) A. Lvovskiy et al, PPCF (in press)

Intense Alfvenic Instabilities (~ MHz range) Observed During RE Plateau Formation, Correlates with Avoidance Avoided RE plateaus correlate with intense & coherent MHz-frequency modes 13 Candidate: compressional Alfven wave driven by REs Hard x-ray spectrometry indicates critical RE energy for mode Ip [MA] Freq [MHz] Freq [MHz] 1.2 0.8 Primary Ar 0.4 0 4 3 2 1 0 4 3 2 1 0 #177028: 50 torr l Ar #177030: 130 torr l Ar modes appear modes appear max E RE Yes plateau No plateau max E RE #177028 - No Plateau 2.5 MeV #177030 - Yes Plateau 2.5 MeV 0 2 4 6 8 10 12 t-t dis (ms) -100-150 -200-100 -150-200 Power/frequency (db/hz) Power/frequency (db/hz) A. Lvovskiy et al, PPCF (in press)

Intense Alfvenic Instabilities (~ MHz range) Observed During RE Plateau Formation, Correlates with Avoidance Avoided RE plateaus correlate with intense & coherent MHz-frequency modes 14 Candidate: compressional Alfven wave driven by REs Hard x-ray spectrometry indicates critical RE energy for mode Modes causal to hard x-ray bursts indicating some RE loss Can this explain avoided plateau? Ip [MA] Freq [MHz] Freq [MHz] 1.2 0.8 Primary Ar 0.4 0 4 3 2 1 0 4 3 2 1 0 #177028: 50 torr l Ar #177030: 130 torr l Ar #177028 - No Plateau #177030 - Yes Plateau RE losses/5 Yes plateau RE losses No plateau 0 2 4 6 8 10 12 t-t dis (ms) -100-150 -200-100 -150-200 Power/frequency (db/hz) Power/frequency (db/hz) A. Lvovskiy et al, PPCF (in press)

Excitation of Alfvenic Instabilities May Explain Critical Argon Quantity and Ip Dependence for RE Avoidance Increasing Argon reduces highenergy REs & suppresses modes Ø RE plateau forms 1 No plateau RE plateau Increasing I P increases highenergy RE & enhances modes Ø RE plateau avoided Surprising result challenges assumptions about instability Is neglect of instabilities justified? Instability Power [a.u.] More Ar Higher I P 0 4 5 6 7 8 9 max RE Energy [MeV] 15 A. Lvovskiy et al, PPCF (in press)

Secondary Injection (of High-Z Material) during Plateau Phase is Main Defense for ITER 1. Do we understand RE distribution function and dissipation rate? 2. How can the dissipation rate be increased? RE Mitigation 16

Resolving Anomalous RE Dissipation is a Key Issue Seen in Multiple Experiments and Regimes 5x Critical E-field 10x Critical E-field R. Granetz et al, Phys Plasmas 2014 Ohmic Flat-top E. Hollmann et al, Nucl Fusion 2011 Post-Disruption 17

Direct Comparison of Experimental and Theoretical RE Distribution Functions Confirm Non-Monotonicity RE distribution obtained from: HXR spectroscopy (experiment) 0-D Fokker-Planck (model) Both peak at similar energies High-energy falls off faster in experiment Increasing collisional damping reduces RE energy in both 1-D RE distribution via Bremsstrahlung 0 log 10 f(e e ) -1 (a.u.) -2-3 -4 0-1 Experiment Model Peak 165826 165824 log 10 f(e e ) 0-30 o 20 1.5 10 19 m -3 1.0 10 19 m -3-2 0 5 10 15 20 E (MeV) C. Paz-Soldan et al, PRL 2017

Direct Comparison of Experimental and Theoretical RE Distribution Functions Confirm Non-Monotonicity RE distribution obtained from: HXR spectroscopy (experiment) 0-D Fokker-Planck (model) Both peak at similar energies High-energy falls off faster in experiment Increasing collisional damping reduces RE energy in both 1-D RE distribution via Bremsstrahlung 0 log 10 f(e e ) -1 (a.u.) -2-3 -4 0-1 Experiment Model Peak 165826 165824 log 10 f(e e ) 0-30 o 21 Synchrotron-based RE validation to be discussed later this session 1.5 10 19 m -3 1.0 10 19 m -3-2 0 5 10 15 20 Synchrotron: del-castillo-negrete, TH/4-3 E (MeV) C. Paz-Soldan et al, PRL 2017

High Frequency Antenna Reveals Kinetic Instabilities at ~100 MHz in Ohmic Flat-top RE Experiments Instability intensity proportional to RE population size Identified as whistler wave by varying dispersion relation terms f [MHz] 150 140 130 120 110 Antenna Signal De-stabilized (in part) by non-monotonic distribution function features ~ 100 MHz modes predicted (and observed) ~ GHz modes also predicted (no diagnostic) 171087 100 5. 000 5. 025 5. 050 5. 075 5. 100 5. 130 Time [s] Whistler Structure Antenna 22 D. Spong, TH/P8-17 & K. Thome, EX/P6-29 D. Spong et al, PRL 2018

Inclusion of Kinetic Instability Recovers Anomalous Dissipation and Improves Distribution Agreement Experiment identified dissipation rate and distribution function anomalies Quasi-linear diffusion model w/ instability reproduces elevated E/E crit threshold Possible resolution to reported discrepancy Growth Decay Much better match of RE distribution slope with kinetic instability included Kinetic instabilities essential to understand Ohmic flat-top regime dynamics 25 C. Liu, TH/P8-16 C. Liu et al, PRL 2018

Are Instabilities an Alternate Path to Dissipate the RE Plateau? Secondary injection expected to be high- Z material (Argon) Can kinetic instabilities offer an alternate path to control? Plan A: High-Z Injection Plan B: Instabilities? (natural or driven) 26

Exploitation of Kinetic Instability Easiest in Collisionless Plasmas Stability diagram calculated 1 for high-freq kinetic instabilities Quiescent Ohmic Flat-top Experiments Natural Post-Disruption Normalized Instability Growth Rate (10 5 /s) Kinetic Instability Growth - Collision Rate (105 s-1) 1 P. Aleynikov, B. Breizman, NF 2015 27

Exploitation of Kinetic Instability Easiest in Collisionless Plasmas Stability diagram calculated 1 for high-freq kinetic instabilities Quiescent Ohmic Flat-top Experiments High-Z (Ar) injection likely to suppress instabilities via collisional damping However - counter example already shown: ~ 1 MHz modes Stability analysis 1 needs to be amended for Alfvenic modes Natural Post-Disruption Inject Ar Normalized Instability Growth Rate (10 5 /s) Kinetic Instability Growth - Collision Rate (105 s-1) 1 P. Aleynikov, B. Breizman, NF 2015 28

Exploitation of Kinetic Instability Easiest in Collisionless Plasmas Achievable by Injecting Deuterium Stability diagram calculated 1 for high-freq kinetic instabilities Quiescent Ohmic Flat-top Experiments High-Z (Ar) injection likely to suppress instabilities via collisional damping However - counter example already shown: ~ 1 MHz modes Stability analysis 1 needs to be amended for Alfvenic modes Inject D2 Natural Post-Disruption Inject Ar Normalized Instability Growth Rate (10 5 /s) Kinetic Instability Growth - Collision Rate (105 s-1) Low-Z (D 2 ) injection reduces density 2 and thus damping 29 1 P. Aleynikov, B. Breizman, NF 2015 2 D. Shiraki et al, NF 2018

D 2 Injection Enables Observation of Natural Kinetic Instability in Few-eV Post-Disruption RE Plateau Natural instability observed in post-d 2 RE plateau, but so far only with large applied electric fields Indicates natural RE distribution function is stable in DIII-D Area for future work, alongside RF antennas for active launch Antenna Signal Active and passive methods under study 30

Dissipation via Secondary Injection Must Happen Faster than Vertical Instability Loss Rate ITER RE beam will be vertically unstable Finite time to dissipate RE finite time to act 31 K. Aleynikova et al, Plasma Phys. Rep. 2016

Dissipation via Secondary Injection Must Happen Faster than Vertical Instability Loss Rate finite time to act ITER RE beam will be vertically unstable Finite time to dissipate RE DIII-D has developed vertically unstable RE beams to address key physics questions RE Current (ka) Final Loss 32

RE Current at Final Loss Can Be Reduced with High-Z Reduced RE current at final loss achieved by increasing Argon quantity RE Current (ka) 270 & 400 33

RE Current at Final Loss Can Be Reduced with High-Z but Saturation of Dissipation Observed Reduced RE current at final loss achieved by increasing Argon quantity RE dissipation saturates at given Ar quantity Upper bound on assimilation Universal observation 1,2,3 RE Current (ka) (torr-l) 0 180 270 & 400 Possible show-stopper for high-z dissipation 34 1 C. Reux et al, NF 2015, 2 G. Papp, IAEA 2016 3 Z.Y. Chen, ITPA 2017

Saturation of Dissipation Linked to Ionization Power Balance: Temperature Effects Can Slow High-Z Diffusion Ionization of large Ar quantities causes significant T e drop Less Ionization Lower temperature and higher Ar density reduces diffusion coefficient Classical diffusion goes like T / n Slower Diffusion Vertical loss happens faster than Ar can diffuse: not enough time Observed dissipation saturates RE dissipation depends on ionization power balance Less Assimilation 35 E. Hollmann et al, NF (in prep)

Important Advances in RE Experiments and Modeling are Improving Predictive Capability for ITER DMS Design RE Avoidance: Modeling does not yet predict RE seed Kinetic instability may explain threshold dependence on I P and Ar quantity Instability Power [a.u.] 1 No plateau RE plateau More Ar Higher Ip RE Mitigation: Including kinetic instability in modeling reproduces elevated E/E crit threshold Application to disruption under study High-Z dissipation saturation linked to ionization power balance 0 4 5 6 7 8 9 max RE Energy [MeV] 36

Bonus Slides 37

Model Validation Using Synchrotron Emission Images Explores Pitch-Angle and Spatial RE Dynamics Agreement with experiment seen in multiple simulations Experiment a) b) Model Pitch-angle distribution is not what 0-D Fokker-Planck models would predict 0.6 0.4 165826 25 MeV (Mono-energy) c) d) See later talk for more information 0.2 0.0-0.2-0.4 165826 1.2 1.4 1.6 1.8 2 2.2 Energy from GRI 1.2 1.4 1.6 1.8 2 2.2 38 D. Del-Castillo Negrete, TH/4-3 M. Hoppe et al, NF 2018 L. Carbajal et al, PoP 2018

Dynamics of Final Loss Phase Sets Ultimate Requirement for RE Mitigation What final RE current is tolerable? Can we predict the heating of the first-wall? 39

Joule Heating of First-Wall from RE Strike Can Be Predicted as well as its Z-dependence 0-D circuit model 1 developed to predict Joule heating of wall from RE strike 10 2 Joule Heating (kj) 0D Model 40 RE loss time required input, measured in DIII-D Model successfully captures total heating and Z-dependence 0-D Model Successful Local Estimates are Future Work 10 1 Measured Measured + Loss Terms 10 0 0 2 4 6 8 10 Z 1 R. Martin-Solis, NF 2017 E.M. Hollmann et al, NF 2017

27th IAEA Fusion Energy Conference Ahmedabad, India. October 22 27, 2018