1. 1 Fast-ion D  (FIDA) Measurements of the Fast-ion Distribution Function Bill Heidbrink DIII-D Instruments Keith Burrell, Yadong Luo, Chris Muscatello, Brian Grierson NSTX Instruments Ron Bell, Mario Podestà Two-dimensional imaging Mike Van Zeeland, Jonathan Yu ASDEX Upgrade Instruments Benedijt Geiger Additional collaborators Deyong Liu, Emil Ruskov, Yubao Zhu, Clive Michael, David Pace, Mirko Salewski and many others Van Zeeland, PPCF 51(2009) 055001.

2. 2 Why Measure the Fast-ion Distribution Function? 1.The distribution function F(E,pitch,R,z) is a complicated function in phase space 2.Fast ions are major sources of heat and momentum.  needed to understand transport & stability 3.They drive instabilities that can expel fast ions and cause damage

3. 3 Outline 1.What is FIDA? How do we distinguish the FIDA light from all the other sources? 2.How does the FIDA signal relate to the fast-ion distribution function? Is our interpretation correct? 3.What are the applications? 4.What are the practical challenges? (New section) 5.How can we check the results? (New section) Slides in first three sections are from my 2010 HTPD invited talk: Rev. Sci. Instrum. 81 (2010) 10D727

4. 4 FIDA is an application of Charge Exchange Recombination Spectroscopy 1.The fast ion exchanges an electron with an injected neutral 2.Neutrals in the n=3 state relax to an equilibrium population; some radiate 3.The Doppler shift of the emitted photon depends on a component of the fast-ion velocity 3 cm

5. 5 FIDA is Charge Exchange Recombination Spectroscopy--with a twist The radiating atom is a neutral  no plume effect The fast ion distribution function is very complicated  need more than moments of the distribution The Doppler shift is large  low spectral resolution OK for FIDA feature but good resolution desirable anyway Many sources of bright interference  like a laser scattering measurement

6. 6 Bright interfering sources are a challenge D  light from injected, halo, and edge neutrals Visible bremsstrahlung Impurity lines Luo, RSI 78 (2007) 033505

7. 7 Background Subtraction Normally Determines the Signal:Noise T = F + F edge + V + I cx + I ncx + D cold + D inj + D halo (red only appears w/ beam) T = Total signal F = Active Fast-ion signal (the desired quantity) F edge = FIDA light from edge neutrals V = Visible bremsstrahlung I cx = Impurity charge-exchange lines I ncx = Impurity non-charge-exchange lines D cold = Scattered D  light from edge neutrals D inj = D  light from injected neutrals (beam emission) D halo = D  light from halo neutrals

8. 8 Must measure all other sources for an accurate FIDA measurement T = F + V + I cx + I ncx + D cold + D inj + D halo T = Total signal F = Fast-ion signal V = Visible bremsstrahlung I cx = Impurity CX (Fit to remove) I ncx = Impurity non-CX D cold = Cold D  (Measure attenuated cold line) D inj = Injected D  (Try to measure) Heidbrink, RSI 79 (2008) 10E520 Use “Beam-off” measurements to eliminate black terms

9. 9 Must extract the FIDA signal from the background 1.Used beam modulation for background subtraction 2.Can use a toroidally displaced view that misses the beam 3.Fit the entire spectrum (all sources) NSTX Background subtraction via beam modulation works in a temporally stationary plasma; an equivalent view that misses the beam works if the plasma is spatially uniform.

10. 10 Two main types of FIDA instruments: spectrometer or bandpass-filtered Tune to one side of the D  line

11. 11 Two main types of FIDA instruments: spectrometer or bandpass-filtered Measure full spectrum but block (attenuate) D  line Luo, RSI 78 (2007) 033505

12. 12 Two main types of FIDA instruments: spectrometer or bandpass-filtered Measure one side but attenuate D  line Heidbrink, RSI 79 (2008) 10E520

13. 13 Two main types of FIDA instruments: spectrometer or bandpass-filtered Bandpass filter one side of the spectrum Podestà, RSI 79 (2008) 10E521. or CCD

14. 14 Van Zeeland, PPCF 51(2009) 055001. “Imaging” neutral beam produces red- shifted light (filtered out) FIDA imaging: Put bandpass filter in front of a camera Oppositely directed fast ions from counter beam produces blue- shifted light (accepted by filter)

15. 15 Photograph of an ASDEX-U instrument grating (2000 l/mm) Princeton Instruments EMCCD camera 180mm lenses f2.8 Interference filter Geiger

16. 16 Outline 1.FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D  sources. 2.How does the FIDA signal relate to the fast-ion distribution function? Is our interpretation correct? 3.What are the applications? 4.What are the practical challenges? 5.How can we check the results?

17. 17 The “weight function” describes the portion of phase space measured by a diagnostic Heidbrink, PPCF 49 (2007) 1457 Define a “weight function” in phase space Like an “instrument function” for spectroscopy Doppler shift only determines one velocity component  energy & pitch not uniquely determined

18. 18 Different Toroidal Angles Weight Velocity Space Differently V2 R0 V2 In this case, get much more signal from a view with a toroidal component of 0.6.

19. 19 |v perp |, v ll are the best coordinates to use V2 Salewski, NF 51 (2011) 083014 10 o 45 o 80 o 100 o

20. 20 Ideal views give information about both |v perp | and v ll V2 R0 V2 Imagine a population at a single point in |v perp |, v ll space Shift gives information about v ll Spread gives information about v perp Ideal views are shifted by ~15 o from 0 o or 90 o Salewski, NF 51 (2011) 083014

21. 21 The “weight function” concept explains many results Changing T e changes NPA signal more than FIDA signal NPA measures a “point” in velocity space; FIDA averages More pitch-angle scattering at larger T e Luo, RSI 78 (2007) 033505

22. 22 Use Forward Modeling to Simulate the Signal V2 R0 V2 Forward modeling using a theory-based distribution function from TRANSP, …. Machine-specific subroutines for beam & detector geometry Data input: files with plasma parameters mapped onto flux coordinates Compute neutral densities of injected beam & halo Weighted Monte Carlo computes neutralization probability, collisional-radiative transitions, and spectra Heidbrink, Comm. Comp. Phys. (2010) FIDASIM code is available for download

23. 23 FIDASIM models FIDA, beam-emission, thermal, and VB features V2 R0 V2 Heidbrink, Comm. Comp. Phys. (2010) We plan to maintain a public version of Geiger’s Fortran90 FIDASIM

24. 24 Excellent Results were Obtained with the First Dedicated Instrument Studied quiet plasmas first where theoretical fast-ion distribution function is known Spectral shape & magnitude agree with theory Relative changes in spatial profile agree with theory Dependence on injection energy, injection angle, viewing angle, beam power, T e, & n e all make sense Consistent with neutrons & NPA Luo, Phys. Pl. 14 (2007) 112503.

25. 25 FIDA image agrees with theory One normalization in this comparison Van Zeeland, PPCF 51(2009) 055001.

26. 26 Outline 1.FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D  sources. 2.FIDA measures one velocity component of the fast-ion distribution function. Measurements in MHD-quiescent plasmas are consistent with theoretical predictions. 3.What are the applications? 4.What are the practical challenges? 5.How can we check the results?

27. 27 Type 1: Relative change in spectra Heidbrink, PPCF 49 (2007) 1457. Average over time windows of interest Discard time points with contaminated background This example: ion cyclotron acceleration of beam ions

28. 28 High-harmonic heating in a spherical tokamak produces a broader profile than in DIII-D Many resonance layers in NSTX Very large gyroradius Heidbrink, PPCF 49 (2007) 1457. Liu, PPCF 52 (2010) 025006.

29. 29 Type 2: Relative change in time evolution Van Zeeland, PPCF 50 (2008) 035009. Integrate over range of wavelengths Divide integrated signal by neutral density  “FIDA density” This example: Alfvén eigenmode activity is altered by Electron Cyclotron Heating (ECH); weaker modes  better confinement

30. 30 Severe Flattening of Fast-ion Profile Measured during Alfven Eigenmodes Heidbrink, PRL 99 (2007) 245002; NF 48 (2008) 084001. Corroborated by neutron, current profile, toroidal rotation, and pressure profile measurements Spectral shape hardly distorted

31. 31 TAE “Avalanches” in NSTX: Mode overlap & enhanced fast-ion transport Measure local drop in fast-ion density at MHD event using bandpass filter Fluctuations at mode frequency observed in sharp gradient region Podestà, Phys. Pl. 16 (2009) 056104. Magnetics

32. 32 View same radius from different angles to distinguish response of different orbit types V2 R0 V2 Vertical view most sensitive to “trapped” ions Tangential view most sensitive to “passing” ions “Sawtooth” crash rearranges field in plasma center Passing ions most affected, as predicted by theory Heidbrink RSI 79 (2008) 10E520. Muscatello, PPCF 54 (2012) 025006 Vertical Tangential Beams

33. 33 Type 3: Absolute Comparison with Theory Integrate over time window of interest Use calibration to get absolute radiance For profile, also integrate over wavelengths Compute theoretical spectra and profile This example: drift- wave turbulence in high temperature plasma causes large fast-ion transport Heidbrink PRL 103 (2009) 175001; PPCF 51 (2009) 125001

34. 34 Microturbulence causes fast-ion transport when E/T (energy/temperature) is small Small MHD or fast- ion driven modes Co-tangential off- axis injection Low power case in good agreement at small minor radius but discrepant at low Doppler shift (low energy) High power case discrepant everywhere Heidbrink PRL 103 (2009) 175001; PPCF 51 (2009) 125001

35. 35 More recent microturbulence data finds negligible transport Pace, PoP (2013) in preparation No MHD or fast-ion driven modes Well-diagnosed plasmas Spectra & profile consistent with classical predictions for several cases

36. 36 FIDA diagnostics are implemented worldwide TEXTOR Delabie RSI 79 (2008) 10E522. Michael (2010) private communication. MAST Osakabe, RSI 79 (2008) 10E519. LHD Beam emission FIDA emission Geiger (2010) private communication. ASDEX-U

37. 37 FIDA is a powerful diagnostic of the fast-ion distribution function Spectral information  one velocity coordinate Spatial resolution of a few centimeters By integrating light over the wing, get sub-millisecond temporal resolution With spectral integration, get two-dimensional images Radiance  absolute comparisons with theory Highlights of applications to date Confirm TRANSP predictions in MHD-quiescent plasmas Measure RF acceleration of fast ions Diagnose transport by Alfven eigenmodes Measure fast-ion transport by microturbulence

38. 38 Outline 1. FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D  sources. 2. FIDA measures one velocity component of the fast-ion distribution function. Measurements in MHD-quiescent plasmas are consistent with theoretical predictions. 3. FIDA measures transport by instabilities and acceleration by ICRH 4. What are the main practical challenges? 5. How can we check our results?

39. 39 Bright interfering sources present two challenges 1)Separate FIDA feature from other features 2)Large dynamic range of signal 60keV FIDA CII HeI Beam emission edge D-alpha 90keV Geiger, Plasma Phys. Cont. Fusion 53 (2011) 065010

40. 40 Initial (obsolete) approach: Avoid beam emission Filter or avoid the cold D  line Spectral intensity of injected neutral light is ~100 times brighter A vertical view works Heidbrink, PPCF 46 (2004) 1855

41. 41 Better approach: measure beam emission Grierson RSI (2012) 10D529 FIDA ~ n inj n f Infer n inj from beam emission  arrange viewing geometry to measure both

42. 42 Background Problem: Scattered D  Contaminates Signal & Changes in Time Normal data analysis Remove impurity lines Subtract background (from beam-off time) Average over pixels to obtain FIDA(t) Luo, RSI 78 (2007) 033505 (Careless) Normal Analysis says fast ions “bounce back” after sawtooth crash This is wrong! The problem: impurity and scattered D  light change!

43. 43 Four approaches to the very bright cold line Name Spectrometer Camera Cold D  NSTX vertical 1 Holospec Photonmax ND filter D3D vertical 2 Czerny-Turner Sarnoff blue-side only D3D oblique 3 Holospec Sarnoff blue-side w/ filter D3D main ion 4 Czerny-Turner Sarnoff mild saturation 1 Podestà, RSI 79 (2008) 10E521. 2 Luo, RSI 78 (2007) 033505. 3 Muscatello, RSI 81 (2010) 10D316. 4 Grierson, Phys. Pl. 19 (2012) 056107.

44. 44 Top view Vertical view NB line: B NSTX has both active and passive views

45. 45 Compare “beam-on” and “beam-off” spectra from adjacent time bins FIDA feature evident from magnetic axis to outer edge on active channels Spectra include impurity lines Raw data show FIDA feature

46. 46 Net spectra should go to zero at large Doppler shifts Should get same spectra from beam modulation (“beam on – beam off”) & reference view (“active view – passive view) Beam modulation spectra for reference view should be flat and ~ zero. Blue-shifted spectra meet criteria for this case Red-shifted spectra do not Example of successful & unsuccessful background subtraction

47. 47 Measure modulated spectra (“beam on – beam off”) in three bands: Large blue shift (above injection energy), cold D  line *, Large red shift Compile database for 11 times in 9 shots Strong correlations for all channels for both red and blue sides of spectra *includes some beam emission Amplitude Background offsets are caused by scattering of the bright central line

48. 48 Cold D  line causes problems Avoid views with large recycling Ideal detector solution: narrow notch filter that attenuates cold line Holospec transmission grating spectrometer has high throughput but more scattered light Want to measure full spectrum No filter (Grierson) causes detector saturation NSTX solution sees scattered light

49. 49 Collisions with edge neutrals produce FIDA light Existing FIDA diagnostics use active emission from an injected neutral beam Passive emission is observed when fast ions pass through the high- neutral density region at the plasma edge * For strong instabilities, the passive FIDA light is stronger than beam emission! DIII-D example during off-axis fishbones *Heidbrink, PPCF 53 (2011) 085007

50. 50 Outline 1. FIDA is charge-exchange recombination light that is Doppler-shifted away from other bright D  sources. 2. FIDA measures one velocity component of the fast-ion distribution function. Measurements in MHD-quiescent plasmas are consistent with theoretical predictions. 3. FIDA measures transport by instabilities and acceleration by ICRH 4. The cold D  line and varying backgrounds are major challenges 5. How can we check our results?

51. 51 Motivation for multiple calibration techniques Optical components change during tokamak operations Check validity of background subtraction Check validity of diagnostic modeling The standard in-vessel calibration procedure: 1.Backlight fibers & position integrating sphere 2.Reconnect fibers; measure # of counts  absolute intensity calibration

52. 52 Make low-power MHD-quiescent plasmas so beam ions are classical Compute the fast-ion distribution function with the TRANSP NUBEAM 1 module. Predict the FIDA spectra with the FIDASIM 2 synthetic diagnostic code. Measure spectra; subtract background; apply intensity calibration. 1 Pankin, Comp. Phys. Commun. 159 (2004) 157 2 Heidbrink, Comm. Comp. Phys. 10 (2011) 716 Plasma calibration procedure

53. 53 Holospec spectrometer, Sarnoff camera, blue-side only Cold D  line strongly filtered Low beam voltage to avoid instabilities Calculated VB > baseline Spectral shape in excellent agreement Satisfactory intensity agreement Plasma calibration procedure: sample data from DIII-D oblique view

54. 54 White plate and in-vessel source used to calibrate data Visible bremsstrahlung calculated from plasma parameters inside last-closed flux surface Background spectra should be > visible bremsstrahlung Low value of background suggests an intensity calibration error NSTX example of erroneous intensity calibration

55. 55 DIII-D “main-ion CER” system Good agreement for beam emission  correct modeling of injected neutrals Good agreement of baseline with VB  intensity calibration valid Discrepancy of both thermal line & FIDA  underestimate of halo neutral density? Fitting multiple features pinpoints possible sources of error

56. 56 Measurement errors Intensity calibration low-power beam shot, VB Background subtraction modulation/reference view, D  correlation Beam parameters Beam power, species mix, spatial profile BES Plasma parameters Density, temperature, equilibrium VB Modeling errors “Bugs” Deficiencies in model Thermal/FIDA comparison Cross-checks identify possible sources of error

57. 57 Low-power beam-heated plasmas provide a valuable check on FIDA measurements Multiple checks of background subtraction are desirable Measure other features such as visible bremsstrahlung, beam emission, and the thermal D  line to check the measurements & modeling Summary on calibration checks

58. 58 Backup slides

59. 59 A FIDA Measurement in ITER would give useful information Because the charge- exchange cross section peaks at low energies, the technique measures ions with The predicted signal is sensitive to anomalous losses Heidbrink, PPCF 46 (2004) 1855.

60. 60 Signal smaller; Background larger where n f Is the fast-ion density, (smaller) n n,I are the neutral densities (injected & halo) (smaller) is the reactivity to the n=3 atomic level (much larger)

61. 61 FIDA Measurements in ITER are very challenging FIDA technique favors low density plasmas Light from visible bremsstrahlung much brighter than predicted FIDA light (but measurements at few % level were successful in TFTR) How do you determine the background? Can imagine fitting the theoretical spectral shape for improved sensitivity but our recent data show “anomalous processes” alter the spectral shape! Perhaps can still calculate a reduced chi-square & say whether the data are consistent with neoclassical transport

62. 62 Integrated modeling that fits all features FIDA ~ n inj n f Infer n inj from beam emission  arrange viewing geometry to measure both Heidbrink, NF 52 (2012)