Accelerators and Experimental Apparatuses

Abstract

The subject of the third chapter is the motion of charged particles induced by electromagnetic fields. The first section focuses on the kinematics of charged particles inside static fields and its application for particle tracking . The second section is dedicated to the physics of accelerators. The last section is devoted to the concept of luminosity and event rates at colliders.

Appendices

Appendix 1

The computer program below implements a Monte Carlo simulation of the experimental apparatus considered in Problem 3.10. The measured points $(y_0,y_1,y_2)$ are sampled from a Gaussian pdf centred around the true values $y_i=x_i^2/2R$ and with standard deviation equal to the detector resolution. The signed sagitta is computed from

$$\begin{aligned} s = \frac{y_2 + y_0}{2} - y_1, \end{aligned}$$

(3.201)

and a sign flip corresponds to the outcome $s<0$.

Appendix 2

The computer program below computes numerically the integral:

$$\begin{aligned} \sigma ^2_{\langle {p_\mathrm{T} \varDelta \phi }\rangle } \approx \left( \frac{N(\alpha -1)}{p_\mathrm{T}^\mathrm{L \; (1-\alpha )} - p_\mathrm{T}^\mathrm{H \; (1-\alpha )} } \int _{p_\mathrm{T}^\mathrm{L}}^{p_\mathrm{T}^\mathrm{H}} dp_\mathrm{T} \, \frac{p_\mathrm{T}^{-\alpha } }{c_2 + c_1 p_\mathrm{T}^2} \right) ^{-1} \end{aligned}$$

(3.202)

from Problem 3.12.