1. Measurement and Simulation of Dα Emission from First-Orbit Fast Ions and the Application to General Fast-Ion Loss Detection in the DIII-D Tokamak
Nathan G. Bolte
William Heidbrink, Michael Van Zeeland, David Pace, Xi Chen
IAEA’s
14th Technical Meeting on Energetic Particles in Magnetic Confinement Systems
Vienna, Austria, 1-4 September 2015

2. A New Fast-Ion Loss Detection Method is Found
Sawtooth-Loss Spectrum
Intensity
Wavelength (Ang)
First-Orbit Spectrum
Intensity
Wavelength (Ang)
Sawtooth ejects 6x more fast ions than prompt losses
+ New simulation: Sawtooth ejects ~1% of fast ion pop.
(Also, found a novel way to infer the neutral density)

3. Talk Outline Introduction Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Experimental Data – First-Orbit Losses
Experimental Data – Sawtooth Losses
Passive FIDA Simulation (P-FIDAsim)
Absolute Sawtooth Losses
Neutral Density
Conclusion

4. Talk Outline Introduction Existing fast-ion loss diagnostics
Motivation for novel fast-ion loss diagnostic
Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Experimental Data – First-Orbit Losses
Experimental Data – Sawtooth Losses
Passive FIDA Simulation (P-FIDAsim)
Absolute Sawtooth Losses
Neutral Density
Conclusion

5. Existing Fast-Ion Loss Diagnostics are Not Sufficient
Currently several techniques
Many methods will not work in future devices
Even using all of them, more phase-space coverage needed
Difficult to truly quantify losses
BES & FIDA pick up edge light when active beam is off
Possible new method: Calibrate an edge-light system w/ prompt losses
Large spatial & velocity coverage
measure losses absolutely
scalable to reactor conditions
W.W. Heidbrink, et al., PPCF 53, (2011).

6. Prompt Losses Confirm: Edge Light During Fast-Ion Losses
BILD
Prompt-losses on beam ion loss detector
Edge-light on BES system
BES
W.W. Heidbrink, et al., PPCF 53, (2011).
Idea born  measure and simulate spectra of first-orbit fast ions.

7. Talk Outline Introduction Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Concept
Experimental design
Experimental Data – First-Orbit Losses
Experimental Data – Sawtooth Losses
Passive FIDA Simulation (P-FIDAsim)
Absolute Sawtooth Losses
Neutral Density
Conclusion

8. First-Orbit Ions CX to Produce Doppler-Shifted Light
Fast Ion D-Alpha (FIDA) radiation from recently neutralized deuterium.
n: 3 → 2 (656.1 nm)
Ionization
Fast Ion Orbit
Neutral Beam Injection
Edge Neutral
(Excitation)
Radiates
Fast Neutral
Photon
Collection Lens
Charge Exchange
(to excited state)
Charge Exchange & Radiation
Active FIDA Lines of Sight (probe confined ions)
Tokamak
Plan View
Passive FIDA Lines of Sight (probe lost ions)
Collection Lens & Fiber Optics
To Spectrometer

9. Experimental Methods for First-Orbit Spectra
Calculate ion orbits or run a simulation to choose:
Views, Beam, Ip, BT
Chords must not view an active beam
Modulate ion source for background subtraction
Ramp Ip (if necessary)
Run tokamak in L-mode to avoid ELMs for this proof of principle (expected to also work in H- mode)

10. Talk Outline Introduction Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Experimental Data – First-Orbit Losses
Extraction of first-orbit signal
Experimental Data – Sawtooth Losses
Passive FIDA Simulation (P-FIDAsim)
Absolute Sawtooth Losses
Neutral Density
Conclusion

11. Edge Spectra Have Recognizable Features
Wavelength (Ang)
Intensity (a.u.)
Time (s)
4.5
4.0
3.5
Wavelength (Ang)
Intensity (a.u.)
Shot
Beam 30LT
Chord P6

12. Blue-Shifted Region Modulated by Beam
Wavelength (Ang)
Intensity (a.u.)
Time (s)
4.5
4.0
3.5
Lineout at 6530 Ang
Intensity (a.u.)
Beam Power (MW)
Time (ms)
Time (ms)
Shot
Beam 30LT
Chord P6

13. Conditional Averaging Using Beam Modulation Times Gives “First-Orbit Spectra”
Wavelength (Ang)
Intensity (a.u.)
Time (s)
4.5
4.0
3.5
Intensity (a.u.)
400
300
200
100 15 10 5
Wavelength (Ang)
Uncertainty
Shot
Beam 30LT
Chord P6

14. Talk Outline Introduction Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Experimental Data – First-Orbit Losses
Experimental Data - Sawtooth Losses
Extraction of Sawtooth Spectra
Check with TRANSP/FIDAsim
vs. location & strength
Passing ions more affected
Passive FIDA Simulation (P-FIDAsim)
Absolute Sawtooth Losses
Neutral Density
Conclusion

15. Conditional Averaging Using Sawtooth Crash Times Gives “Sawtooth-Loss Spectra”
First-Orbit Spectrum
Beam Power
Time (s)
Intensity
Time (ms)
Conditional Averaging
Wavelength (Ang)
Wavelength (Ang)
ECE Power
Time (ms)
Sawtooth-Loss Spectrum
Shot ms
Chord P4
Intensity
Wavelength (Ang) 20 40 60 80
Conditional Averaging

16. TRANSP + FIDAsim Agrees with Experiment
Ffi just inside LCFS (TRANSP)
1.8e12/cc
1.0
W = FIDAsim weight function
0.5
𝑺= 𝑭𝑾𝒅𝑬𝒅𝒑
Pitch
0.0
-0.5
-1.0
0.0
Sawtooth-Loss Spectrum
Energy (keV) 80
Beams inject co-going
Co-going losses should be blue shifted
Experiment shows greater blue shift
Rough calculation confirms blue shift predominate 60
Shot ms
Chord P4
Intensity 40 20
Wavelength (Ang)
Edge fast-ion density goes up during sawtooth crash

17. Sawtooth Intensity (∆Te/Te) Sawtooth Location (ρinversion)
Sawtooth Losses Quantified Relative to First-Orbit Losses; And Show the Expected Trends
Blue FIDA Region
ST Light / FO Light 6 4 2
Sawtooth Intensity (∆Te/Te)
Blue FIDA Region
ST Light / FO Light 6 4 2
Sawtooth Location (ρinversion)
Stronger crash (greater core Te drop)  Greater losses
Crash further out (greater ρinversion)  Greater losses

18. Passing Ions Suffer More Losses than Trapped Ions
Oblique views (passing)  more blue-shifted
Vertical views (trapped)  more evenly distributed
TRANSP/FIDAsim spectra reaffirm the trend
Passing ion losses > trapped ion losses
Consistent with Muscatello et al that core fast-ion density goes down during sawtooth crash; passing ions more than trapped *
Spectral Values
Equidistance from Cold Dα
Mean Spectrum (blue region) (a.u.)
Mean Spectrum (red region) (a.u.)
* C.M. Muscatello, PPCF 54 (2012)

19. Talk Outline Introduction Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Experimental Data – First-Orbit Losses
Experimental Data – Sawtooth Losses
Passive FIDA Simulation (P-FIDAsim)
Code structure
Verification by FIDAsim
Comparison with Experimental Spectra
Absolute Sawtooth Losses
Neutral Density
Conclusion

20. Chord Geometry & B Fields
Simulation Concept
Inputs
Chord Geometry & B Fields
Equilibrium
Profiles
Beam Geometry
Chord Geometry
Fast-Ion Density
Inside Chord? N Y
Calculate Ion Orbit
Beam Model
Save Orbit Steps
Neutral Density Model
nn(ρ) (with free scaling factor)
Local Values
CR Model
Profiles & Fields
Electron Impact Rates
Edge-Neutral Atomic Level Populations
Doppler &
Stark shift
Dα Emission Rates
Bin & Scale
Synthetic Diagnostic
Scale Up
Solid Angle
Chord Volume
Instrumental Broadening & Response Function
Final Spectra

21. P-FIDAsim Spectra Verified by FIDAsim
Chord P9a. 17% Difference
P-FIDAsim
FIDAsim
Spectral Radiance
x1013 ph/s-m-sr-A
Very Different Codes
Chord P9b. 5% Difference
FIDAsim
P-FIDAsim
Ffi (tor. symmetric)
Orbit Tracking (3D)
Beam Neutrals (MC)
Neutral Profile
3D Grid Along Beam
Captured Ion Loc.
P-FIDAsim
FIDAsim
Spectral Radiance
x1013 ph/s-m-sr-A
6 Chords (P9a-P10c). Avg. 13.6% Difference
1.4
1.2
P-FIDAsim/FIDAsim
1.0
0.8
0.6
Wavelength (Ang)

22. Comparison of Simulated Spectra with Data Shows Signals are from First-Orbit Ions
Simulation
Triangular Equil. R=0.75
Experiment
Chord P8
Shot
3300−4992 ms
Chord P4
Shot ms
Chord P6
Shot ms
Chord V1
Shot ms
Experiment
Simulation
Long Int. Time. R=0.70
Wavelength (Ang)
Wavelength (Ang)
Experiment
Simulation
Large Exp. Signal. R=0.72
Chords P6 & P8. R=0.71
86 cases
6 NB, 13 views, Ip, Bt, ne, equil. shape, no. x-points
Simulation reproduces many features
Correlation range: 41-80%
Average correlation: 58%
Experiment

23. Talk Outline Introduction Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Experimental Data – First-Orbit Losses
Experimental Data – Sawtooth Losses
Passive FIDA Simulation (P-FIDAsim)
Absolute Sawtooth Losses
Neutral Density
Conclusion

24. Sawtooth Losses Estimated by “Calibrating” with First-Orbit Measurements
Same shot  Same profiles, same vol.  𝑳 𝑺𝑻 𝑳 𝑭𝑶 ≈ 𝒏 𝑺𝑻 𝒏 𝑭𝑶
Example: Shot , ms, chord P4
LST/LFO = 6.1, 𝒏 𝑭𝑶 = 6.5x109 cm-3  𝒏 𝑺𝑻 = 4.0x1010 cm-3
Toroidally symmetric loss volume: 𝑽 𝒍𝒐𝒔𝒔 =(𝟐𝝅𝑹)( 𝝅 𝟒 𝜿𝒂)∆ 𝒓 𝒏 ∆ 𝒓 𝒏 is edge neutral decay length (21 cm)
𝒏 𝑺𝑻 𝑽 𝒍𝒐𝒔𝒔 = 7.4x1016 fast ions lost (1.2% of TRANSP inventory)
TRANSP Kadomtsev sawtooth model  1.7%

25. Talk Outline Introduction Passive Fast-Ion D-Alpha (FIDA) Diagnostic
Experimental Data – First-Orbit Losses
Experimental Data – Sawtooth Losses
Passive FIDA Simulation (P-FIDAsim)
Absolute Sawtooth Losses
Neutral Density
Motivation to measure
Inversion Method
Results
Conclusion

26. Motivation to Find Neutral Density
Not regularly measured at DIII-D (or other facilities)
Free parameter in P-FIDAsim
Validation of P-FIDAsim
Knowledge improves quantification of losses
Affect confinement and heat flux to the walls

27. Inversion Method: 𝒏 𝒏 (𝝆)  𝒏 𝒏 (𝑹,𝒛)
𝜶 𝒛 = 𝒏 𝒏 (𝒛;𝒂𝒕 𝒘𝒂𝒍𝒍)
𝑬=𝑺𝜶
using non-negative least-squares solver
𝜶= 𝑺 −𝟏 𝑬
6 chords used to scale nn model

28. Inferred Neutral Density Consistent with Previous Measurements×
|z| (m)
α(z)
α Extrapolation
♦♦♦ α from Inversion
nn Scaling Factor
(x1010 cm-3) 2 4 6 8
𝒏 𝒏 (𝝆)
nn(R,z) = ρ
P-FIDAsim†
𝒏 𝒏 𝒄 𝒎 −𝟑
1011
1010
109
108
Poloidally Averaged
r/rs
Measured*
* B.A. Carreras. PoP, 5(7), 1998.
† Shot ms

29. Inferred Neutral Density Consistent with Previous Measurements and Simulations
1011
Neutral Flux into Core
(cm-2s-1)
1017
1016
1015
1014
1013
Double Null
P-FIDAsim
Shot
Double Null
1010
109
nn at LCFS
(cm-3)
108
107
P-FIDAsim
Shot
x-point
106
105
Poloidal Angle (deg)
Poloidal Angle (deg)
Neutral Flux into Core
(cm-2s-1)
1017
1016
1015
1014
1013
Modeled by DEGAS†
1011
Measured*
1010
1010
109
109
nn at LCFS
(cm-3)
108
108
x-point
107
107
106
106
Single Null
Single Null
105
105
Poloidal Angle (deg)
Poloidal Angle (deg)
* B.A. Carreras. Phys. of Plasmas, 5(7), 1998.
† M. Groth. J. Nucl. Materials, : , 2005.

30. Conclusion First-orbit & sawtooth loss spectra measured
P-FIDAsim consistent with measurements
Neutral density inferred: similar to simulations & measurements (8x109cm-3 at LCFS, 1x1011cm-3 at wall)
Fast ions expelled by sawtooth measured: consistent with TRANSP (6x first-orbit losses, ~1% of fast-ion inventory)
New method developed to quantify losses/transport !

31. Future Work Improve simulation run time (GC orbit, Fortran, etc.)
Confirm application in H-mode
Compare neutral density with other techniques
Measure losses from other instabilities
Tomography for better resolution of losses
Spectroscopic measurements of alpha losses in ITER

32. Thank You