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Simulation of Acceptance for conical parameters of Lightguide

Simulation of Acceptance for conical parameters of Lightguide. S. B. A. R. 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!]

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Simulation of Acceptance for conical parameters of Lightguide

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  1. Simulation of Acceptance for conical parameters ofLightguide John Fry NA62_UK 20-05-2011

  2. S B A R 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) = (y0tanβ, 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 (α+3β) β (α+β) Q C D N α P John Fry NA62_UK 20-05-2011

  3. 20 mm cone length Optimum outer diameter <21 mm. John Fry NA62_UK 20-05-2011

  4. Optimum outer diameter <19mm. John Fry NA62_UK 20-05-2011

  5. 10 mm cone length Optimum outer diameter <17mm. Not acceptable for DOuter= 18 mm John Fry NA62_UK 20-05-2011

  6. The conical angle, β, increases with DOuter . The angle of incidence Increases with 2nβ for n reflections. Transmission decreases rapidly. John Fry NA62_UK 20-05-2011

  7. Cone length 15 mm Half-angle = 18.4o [71.6o for comparison with above] John Fry NA62_UK 20-05-2011

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