Post on 15-Feb-2016
description
John Fry NA62_UK 20-05-2011 1
Simulation of Acceptance for conical parameters of Lightguide
John Fry NA62_UK 20-05-2011 2
A B
CD N
S
Q
P
R
α
β
(α+β)
(α+3β)Definitions:2a = AB = 8 mm [fixed by choice of PMT]2b = CD = variable [> 18 mm; fixed by space constraints]c = DN = (b-a) [fixed by a and b, but convenient!]L = AN [free to vary, but as small as possible] L tanβ = c [β is constrained by a, b, and L]
Coordinates and geometry:D (0, 0); A ((b-a), L); B ((b+a), L); C (2b, 0)Q is the photon impact point (x0, y0) = (y0 tanβ, y0) [for y0 < L]Any photon impacting the cone at Q will reach the PMT in one reflection provided y0 lies between L and the following value:
P is at the centre of curvature on the radius vector bisecting AB
John Fry NA62_UK 20-05-2011 3
17 19 21 23 25 27 29 310
100
200
300
400
500
600
700
800
900
1000
Effective Area versus Cone Diameter Collection Efficiency versus Cone Diameter
Cone Diameter (mm)
20 mm cone length
Optimum outer diameter <21 mm.
John Fry NA62_UK 20-05-2011 4
15 16 17 18 19 20 21 22 23 24 250
100
200
300
400
500
600
700
800
900
1000
Effective Area versus Cone Diameter Collection Efficiency versus Cone Diameter
Cone Diameter (mm)
15 mm cone length
Optimum outer diameter <19 mm.
John Fry NA62_UK 20-05-2011 5
15 16 17 18 19 20 21 22 23 24 250
100
200
300
400
500
600
700
800
900
1000
Effective Area versus Cone Diameter Collection Efficiency versus Cone Diameter
Cone Diameter (mm)
10 mm cone length
Optimum outer diameter <17 mm. Not acceptable for DOuter = 18 mm
John Fry NA62_UK 20-05-2011 6
0 10 20 30 40 50 60 70 80 90 1000.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
Fraction of reflected light versus angle
Angle of incidence (degrees)
Frac
tion
of li
ght r
eflec
ted
The conical angle, β, increases with DOuter . The angle of incidenceIncreases with 2nβ for n reflections. Transmission decreases rapidly.
John Fry NA62_UK 20-05-2011 7
1.9 2.4 2.9 3.4 3.9 4.4 4.9 5.4 5.950
55
60
65
70
75
80
85
90
95
100
Comparision of Al MgF2 deposits for NA62
Glass Al MgF2 30° simulationGlass Al MgF2 68° simulationGlass Al MgF2 77° simulationGlass Al MgF2 31nm 30° measurementGlass Al MgF2 31nm 68° measurement
Energie in EV
Refle
ction
in %
Cone length 15 mmHalf-angle = 18.4o
[71.6o for comparison with above]