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Photon propagation and ice properties

Bootcamp 2010 @ UW Madison

photon

r

air bubble

Dmitry Chirkin, UW Madison

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

Mie scattering theory

Dust concentrations have been measured elsewhere in Antarctica: the “dust core” data

Scattering function: approximation

- Mie scattering
- - General case for scattering off particles

Scattering and Absorption of Light

Source is

blurred

scattering

absorption

Source is

dimmer

a = inverse absorption length (1/λabs)

b = inverse scattering length (1/λsca)

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

scattered

absorbed

Embedded light sourcesin AMANDA

isotropic source

(YAG laser)

cosq source

(N2 lasers, blue LEDs)

tilted cosqsource

(UV flashers)

45°

Timing fits to pulsed data

Make MC timing distributions

at grid points in le-la space

At each grid point, calculate

c2 of comparison between

data and MC timing distribution

(allow for arbitrary tshift)

Fit paraboloid to c2 grid

►Scattering: le±se

►Absorption: la±sa

►Correlation: r

►Fit quality: c2min

Fluence fits to DC data

- In diffusive regime:
- N(d) 1/dexp(-d/lprop)
- lprop = sqrt(lale/3)
- c = 1/lprop

dust

d1

d2

No Monte Carlo!

DC source

log(Nd)

c1

slope = c

c2

c1

d

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

A 6-parameter Plug-n-Play Ice Model

scattering

id=301

Power law:

l-a

be(l,d)

be(400,d)

id=302

A = 6954 ±973

B = 6618 ±71

D = 71.4±12.2

E = 2.57 ±0.58

a = 0.90 ±0.03

k = 1.08 ± 0.01

Linear correlation with dust:

CMdust= D·be(400) + E

absorption

3-component model:

CMdustl-k+ Ae-B/l

a(l,d)

T(d)

id=303

Temperature correction:

Da = 0.01a DT

AHA model

Additionally Heterogeneous Absorption: deconvolve the smearing effect

Is this model perfect?

Individually fitted for each pair: best possible fit

Points at same depth not consistent with each other!

Fits systematically off

Is this model perfect?

When replaced with the average, the data/simulation agreement will not be as good

From ice paper

Averaged scattering and absorption

Measured properties not consistent with the average!

Deconvolving procedure is unaware of this and is using the averages as input

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!

Correlation with dust logger data

(from Ryan Bay)

effective scattering coefficient

Scaling to the location of hole 50

fitted detector region

Improvement in simulation

by Anne Schukraft

by Sean Grullon

Downward-going CORSIKA simulation

Up-going muon neutrino simulation

Photon tracking with tables

- 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)

PTD

Photons propagated through ice with homogeneous prop.

Uses average scattering

No intrinsic layering: each OM sees homogeneous ice, different OMs may see different ice

Fewer tables

Faster

Approximations

Photonics

Photons propagated through ice with varying properties

All wavelength dependencies included

Layering of ice itself: each OM sees real ice layers

More tables

Slower

Detailed

Light propagation codes: two approaches (2000)Bulk PTD

Layered PTD

photonics

2

3

2

1

2

3

2

1

2

3

2

average ice

type 1 type 2 type 3

“real” ice

Direct photon tracking with PPC

photon propagation code

- simulates all photons without the need of parameterization tables
- using Henyey-Greenstein scattering function with <cos q>=0.8
- using tabulated (in 10 m depth slices) layered ice structure
- employing 6-parameter ice model to extrapolate in wavelength
- transparent folding of acceptance and efficiencies
- Slow execution on a CPU: needs to insert and propagate all photons
- Quite fast on a GPU (graphics processing unit): is used to build the SPICE model and is possible to simulate detector response in real time.

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