1. Photon propagation and ice properties Bootcamp 2012 @ UW Madison Dmitry Chirkin, UW Madison r air bubble photon

2. Scattering and Absorption of Light Source is blurred Source is dimmer scattering absorption a = inverse absorption length (1/λ abs ) b = inverse scattering length (1/λ sca )

3. Mie scattering theory Continuity in E, H: boundary conditions in Maxwell equations e -ikr+i  t e -i|k||r| r

4. Mie scattering theory Analytical solution! However: Solved for spherical particles Need to know the properties of dust particles: refractive index (Re and Im) radii distributions

5. Mie scattering theory Dust concentrations have been measured elsewhere in Antarctica: the “dust core” data

6. Mie scattering - General case for scattering off particles Scattering function: approximation

7. A better approximation to Mie scattering f SL Simplified Liu: Henyey-Greenstein: Mie: Describes scattering on acid, mineral, salt, and soot with concentrations and radii at SP

8. Properties of photon propagation Locally at x,y,z and for a given wavelength: group refractive index  propagation speed phase refractive index  Cherenkov angle absorption coefficient scattering coefficient scattering function ice properties defined everywhere for any wavelength

9. Photon spectrum Flasher 405 nm For muons: folded with Cherenkov spectrum

10. Angular profile of photons from muons

12. Propagating photons in IceCube Photonics: 2000 – up to now Photon propagation code PPC: 2009 - now

13. Photonics: conventional on CPU First, run photonics to fill space with photons, tabulate the result Create such tables for nominal light sources: cascade and uniform half-muon Simulate photon propagation by looking up photon density in tabulated distributions  Table generation is slow  Simulation suffers from a wide range of binning artifacts  Simulation is also slow! (most time is spent loading the tables)

14. Direct photon tracking with PPC propagate photons directly when needed photon propagation code insert photon length to absorptiondistance to next scatter propagate to next scatter scatter check for intersection with OMs Check for distance to absorption hitlost

15. IceCube simulation with PPC on GPUs photon propagation code graphics processing unit

16. PPC simulation on GPU graphics processing unit execution threads propagation steps (between scatterings) photon absorbed new photon created (taken from the pool) threads complete their execution (no more photons) Running on an NVidia GTX 295 CUDA-capable card, ppc is configured with: 448 threads in 30 blocks (total of 13440 threads) average of ~ 1024 photons per thread (total of 1.38. 10 7 photons per call)

17. Photon Propagation Code: PPC There are 5 versions of the ppc: original c++ "fast" c++ in Assembly for CUDA GPU C++ with OpenCL All versions verified to produce identical results comparison with i3mcml http://icecube.wisc.edu/~dima/work/WISC/ppc/

18. Also compare to clsim CLaudio SIMulator developed by Claudio Kopper Written in C++ with OpenCL

19. GPU scaling Original:1/2.081/2.70 CPU c++:1.001.00 Assembly:1.251.37 GTX 295:147157 GTX/Ori:307424 C1060: 104112 C2050: 157150 GTX 480:210204 On GTX 295: 1.296 GHz Running on 30 MPs x 448 threads Kernel uses: l=0 r=35 s=8176 c=62400 On GTX 480: 1.401 GHz Running on 15 MPs x 768 threads Kernel uses: l=0 r=40 s=3960 c=62400 On C1060: 1.296 GHz Running on 30 MPs x 448 threads Kernel uses: l=0 r=35 s=3992 c=62400 On C2050: 1.147 GHz Running on 14 MPs x 768 threads Kernel uses: l=0 r=41 s=3960 c=62400 Uses cudaGetDeviceProperties() to get the number of multiprocessors, Uses cudaFuncGetAttributes() to get the maximum number of threads

20. Cudatest: lean and mean ice fitting machine cudatest: Found 6 devices, driver 2030, runtime 2030 0(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32) l1 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1) 1(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32) l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1) 2(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32) l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1) 3(1.3): GeForce GTX 295 1.296 GHz G(938803200) S(16384) C(65536) R(16384) W(32) l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1) 4(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32) l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1) 5(1.3): GeForce GTX 295 1.296 GHz G(939261952) S(16384) C(65536) R(16384) W(32) l0 o1 c0 h1 i0 m30 a256 M(262144) T(512: 512,512,64) G(65535,65535,1) 3 GTX 295 cards, each with 2 GPUs PSU 0 and 1 4 and 5 2 and 3 nvidia-smi -lsa GPU 0: Product Name: GeForce GTX 295 Serial: 1803836293359 PCI ID: 5eb10de Temperature: 87 C GPU 1: Product Name: GeForce GTX 295 Serial: 2497590956570 PCI ID: 5eb10de Temperature: 90 C GPU 2: Product Name: GeForce GTX 295 Serial: 1247671583504 PCI ID: 5eb10de Temperature: 100 C GPU 3: Product Name: GeForce GTX 295 Serial: 2353575330598 PCI ID: 5eb10de Temperature: 105 C GPU 4: Product Name: GeForce GTX 295 Serial: 1939228426794 PCI ID: 5eb10de Temperature: 100 C GPU 5: Product Name: GeForce GTX 295 Serial: 2347233542940 PCI ID: 5eb10de Temperature: 103 C As fast as 900 CPU cores

21. Measuring the ice properties

22. scattered absorbed Measuring Scattering & Absorption Install light sources in the ice Use light sensors to: - Measure how long it takes for light to travel through ice - Measure how much light is delayed - Measure how much light does not arrive Use different wavelengths Do above at many different depths

23. Experimental setup (SPICE)

24. Flasher dataset

25. Ice layer parametrization 10 m In each 10-meter layer define: scattering absorption

26. SPICE: South Pole Ice model Start with the bulk ice of reasonable scattering and absorption At each step of the minimizer compare the simulation of all flasher events at all depths to the available data set do this for many ice models, varying the properties of one layer at a time  select the best one at each step converge to a solution!

27. Likelihood description of data: SPICE Mie Find expectations for data and simulation by minimizing –log of Regularization terms: Measured in simulation: s and in data: d; n s and n d : number of simulated and data flasher events Sum over emitters, receivers, time bins in receiver

28. Statistical description There is an obvious constraint which can be derived, e.g., from the normalization condition Suppose we repeat the measurement in data n d times and in simulation n s times. The  s and  d are the expectation mean values of counts per measurement in simulation and in data. With the total count in the combined set of simulation and data is s + d, the conditional probability distribution function of observing s simulation and d data counts is

29. Two hypotheses: If data data and simulation are unrelated and completely independent from each other, then we can maximize the likelihood for  s and  d independently, which with the above constraint yields On the other hand, we can assume that data and simulation come from the same process, i.e., We can compare the two hypotheses by forming a likelihood ratio

30. Derivation for multiple bins

31. Example: exp(-x/5)/5 To enhance the differences between the two likelihood approaches, consider that the amount of simulation is only 1/10 th of that of data 200 2000

32. Using full range of the data and simulationSimulated exp(-x/5.0) with mean of 5.0

33. Optimal binning is determined by desire to: capture the changes in the rate maximize the combined statistical power of the bins The conditional probability (given the total count D) is if the bins are considered independently  i =d i. if the rate is constant across all bins,  =  i =D/L. The likelihood ratio is This never exceeds 1!  so we use 1/L! or 8. Bin size

34. Limiting case of near-constant rate Small bin description Single large bin of length L: We prefer a single large bin if:

35. Optimal binning typical

36. Optimal binning: flasher data -log(8) log(L!)

38. Initial fit to sca ~ abs Starting with homogeneous “bulk ice” properties iterate until converged  minimize  q 2 1 simulated event/flasher 4 ev/fl10 ev/fl

39. Fit to scaling coefficients  sca and  abs Both  q 2 and  t 2 have same minimum!

40. Absolute calibration of average flasher is obtained “for free”  no need to know absolute flasher light output beforehand  no need to know absolute DOM sensitivity 1  statistical fluctuations Minima in p y, t off, f SL

41. Dust logger: tilt of the ice layers

42. Dust logger

43. IceCube in-ice calibration devices 3 Standard candles 56880 Flashers 7 dust logs

44. Ice tilt in ppc Measured with dust loggers (Ryan Bay)

45. Correlation with dust logger data effective scattering coefficient (from Ryan Bay) Scaling to the location of hole 50 fitted detector region

46. Ice anisotropy?

47. Geometry around string 63

48. Evidence in flasher data 62 54 55 64 71 70 53 45 56 72 77 69

49. Dependence with distance

50. What is Ice anisotropy Direction of more scattering Direction of less scattering Naïve approximation: multiply the scattering coefficient by a function of photon direction, e.g., by 1 +  ( cos 2  - 1/3 ) However, this is unphysical:  (n in,n out ) =  (-n out,-n in ) (time-reversal symmetry)  (n in,n out ) =  (-n in,-n out ) (symmetry of ice)   (n in,n out ) =  (n out,n in )

51. A possible parameterization The scattering function we use is f(cos  ), a combination of HG and SL. How about this extension: f(cos  )= f(n in. n out )  f(An in. An out )  0 0 A = 0  0 in the basis of the 2 scattering axes and z (  are, e.g., 1.05). 0 0 1/  However, function f(cos  ) is well-defined for only cos  between -1 and 1. A possible modification is n in  An in /| An in |  n out  A -1 n out /| A -1 n out |. This introduces two extra parameters:  (in addition to the direction of scattering preference). The geometric scattering coefficient is constant with azimuth. However, the effective scattering coefficient receives azimuthal dependence as:

52. Scattering example (5% anisotropy)

53. Fitting for the anisotropy coefficients  1 =0.040,  2 =-0.082

54. Effect of anisotropy on simulation  =1.0  =1.04,  =0.92

55. How important is anisotropy? from SPICE paper threshold: > 0, 1, 10, 100, 400 p.e. 30% 21% so-so awesome ! threshold: > 10 p.e.

56. Can we resolve ice anisotropy? 8% more scattering 36 o NW N E Ice flow direction 41 o NW C130-Skyway

57. History of SPICE model evolution 11/19/09 SPICE (also known as SPICE1): first version seeded with AHA as initial solution AHA is used for extrapolation above and below the detector relies on AHA for correlation relation between be(400) and adust(400). 02/01/10 SPICE2: fixed the hdh bug (see ppc readme file) seeded with bulk ice as initial solution dust logger and EDML data is used for extrapolation dust logger data is used to extend in x and y, taking into account layer tilt. 02/17/10 SPICE2+: fixed the "x*y" option hit counting in ppc be(400) vs. adust(400) relation is determined with a global fit to arrival time distributions. 04/28/10 SPICE2x: improved charge extraction in data: improved merging of the FADC and ATWD charges implemented saturation correction fixed the alternating ATWD bug updated DOM radius 17.8 --> 16.51 cm (cosmetic change: modifies only the meaning of py) fixed the DOM angular sensitivity curve (removed upturn at cos(theta)=-1). 06/09/10 SPICE2y: Fixed code determining the closest DOMs to the current layer (when using tilted ice) Iterations (after timing fits) are combined (improving description in the dust layer) Randomized the simulation based on system time (with us resolution). 07/23/10 SPICEMie: Much improved treatment of oversized DOMs in ppc Fits scattering function to a linear combination of HG and SAM functions, using higher g=0.9 Perform a global fit for py, overall time offset, scattering and absorption correlation coefficients Tilt map is estimated with respect to (0, 0) in IceCube coordinates (simplifies use with photonics). 04/16/12 SPICE Lea: Improved data processing with the new feature extraction Improved likelihood description and optimized binning Introduced and fitted ice anisotropy effect SPICE 1 : Relies on AHA as a first guess, and for correlation between b e and a dust. SPICE 2 : Adds extrapolation with dust logger and EDML, ice tilt map from Ryan SPICE 2+ : Use full arrival time distributions, full fit for both b e and a dust. SPICE Mie: Fit for t off and shape of the scattering function SPICE e -a: New NNLS-based feature extraction. Fitted ice anisotropy

58. Older ice models: AHA, WHAM

59. Embedded light sources in AMANDA 45° isotropic source (YAG laser) cos  source (N 2 lasers, blue LEDs) tilted cos  source (UV flashers)

60. Timing fits to pulsed data Fit paraboloid to  2 grid ►Scattering: e ±  e ►Absorption: a ±  a ►Correlation:  ►Fit quality:  2 min Make MC timing distributions at grid points in e - a space At each grid point, calculate  2 of comparison between data and MC timing distribution (allow for arbitrary t shift )

61. Fluence fits to DC data d1d1 d2d2 DC source In diffusive regime: N(d)  1/d exp(-d/ prop )  prop = sqrt( a e /3) c = 1/ prop d log(Nd) slope = c c1c1 c2c2 c1c1 dust No Monte Carlo!

62. Light scattering in the ice bubbles shrinking with depth dusty bands

63. Wavelength dependence of scattering

64. Light absorption in the ice LGM

65. 3-component model of absorption Ice extremely transparent between 200 nm and 500 nm Absorption determined by dust concentration in this range Wavelength dependence of dust absorption follows power law

66. A 6-parameter Plug-n-Play Ice Model b e (,d ) a(,d ) scattering absorption b e ( ,d ) Power law: -  3-component model: CM dust -  + Ae - B / T(d )T(d ) Linear correlation with dust: CM dust = D·b e (400) + E A = 6954 ± 973 B = 6618 ± 71 D = 71.4± 12.2 E = 2.57 ± 0.58  = 0.90 ± 0.03  = 1.08 ± 0.01 Temperature correction:  a = 0.01a  T id=301 id=302 id=303

67. AHA model Additionally Heterogeneous Absorption: deconvolve the smearing effect

69. Ice models vs. flasher data

70. Describing the data Ice model must describe the data to which it was fit, Ice model is built using the calibration in-situ light flasher data  ice model must describe the flasher data. Here I quantify the (dis)agreement with a width of the distribution of the charge ratio q simulation /q data for all pairs of emitters and receivers in a flasher data set.

71. SPICE 1 threshold: > 0, 1, 10, 100, 400 p.e. 29.2%

72. SPICE Mie threshold: > 0, 1, 10, 100, 400 p.e. 27.7%

73. SPICE e -a threshold: > 0, 1, 10, 100, 400 p.e. 20.0%

74. AHA (fixed ppc table) threshold: > 0, 1, 10, 100, 400 p.e. 55.2%

75. WHAM threshold: > 0, 1, 10, 100, 400 p.e. 42.4%

76. Remarks on comparison Ice model error in description of the light deposition in the range of 125-250 meters away from the emitters: SPICE 1:29.2% SPICE Mie:27.7% SPICE Lea:20.0% AHA:55.2% WHAM:42.4%

77. Well, what about timing? See full collection of plots at http://icecube.wisc.edu/~dima/work/IceCube-ftp/ppc/lea/.http://icecube.wisc.edu/~dima/work/IceCube-ftp/ppc/lea/

78. lea vs. wham: 63,5 flashing

79. lea vs. wham: 63,15 flashing

80. lea vs. wham: 63,25 flashing

81. lea vs. wham: 63,35 flashing

82. lea vs. wham: 63,45 flashing

83. lea vs. wham: 63,55 flashing

85. Direct Hole Ice simulation Hole radius = ½ nominal DOM radius Hole effective scattering ~ 50 cm Hole absorption ~ 100 m Do we need more detailed DOM simulation, including info about both the direction and point on the DOM surface? Perhaps not, if the scattering length in the hole is not much shorter than the hole radius (speculation).

86. Traditional “hole ice” angular sensitivity

87. DOM 20,20  20,19: n z =cos . nominal direct hole ice

88. DOM 20,20  20,21: n z =cos .

89. DOM 20,20  20,19: xz Ratio direct hole ice/nominal nominal hole ice deficit enhancement

90. DOM 20,20  20,21: xz enhancementdeficit nominal hole ice

91. Remarks on the hole ice Effect of the hole ice is quite subtle: The number of photons is reduced on the side facing the emitter, and enhanced in the direction away from the emitter. The traditional “hole ice” implementation via the angular sensitivity modification reduces the number of photons in the direction into the PMT, and enhances the number of photons arriving into the back of the PMT. If the emitter is inside the hole ice, the enhancement of photons received on the same string is dramatic. Either effect is much smaller when receiver is on the different string  can decouple measurement of bulk ice properties from the hole ice