Measurement of momentum for charged particles Detector Basic - PowerPoint PPT Presentation

Measurement of momentum for charged particles Detector Basic 18/07/18 M2 Yosuke Kobayashi

Measurement of momentum • Charged particle traveling in a magnetic field is acted on Lorentz force. 𝑟 : charge 𝑔 = 𝑟𝒘 × 𝑪 𝐶 : magnetic field strength 𝑤 : velocity • If the strength of the magnetic field and the radius are known, the momentum can be measured. B e + 𝑛𝑤 𝑞 𝑠 = 𝑟𝐶 = 𝑟𝐶 r 𝑛 : mass of particle 𝑞 [𝐻𝑓𝑊/𝑑] = 0.3 𝑠 𝑛 𝐶[𝑈] 2

Measurement method • Tracks are reconstructed by each detector. - The momentum is determined from the radius and the charge is obtained from the direction of bending. • Track reconstruction detectors - Gas multiplication detector - Position resolution : 50 ~ 300 μm - Scintillation counter - Position resolution : Different by scintillator… - Semiconductor detector - Position resolution : Different by pixel size… 3

Real application • The measured track is close a straight line in real application. • sagitta s is calculated. 2 𝑠 2 = (𝑠 − 𝑡) 2 + 𝑀 s 2 L r-s 𝑠 2 − 𝑀 2 r 𝑡 = 𝑠 − 4 B 2 + 𝑀 2 8𝑡 ≈ 𝑀 2 𝑠 = 𝑡 8𝑡 (𝑡 ≪ 𝑀) The relation between radius and momentum 𝑟𝐶 ⟹ 𝑡 = 𝑟𝐶𝑀 2 𝑠 = 𝑞 𝑞 4

• Reference • http://summerstudents.desy.de/e69118/e177730/e2 02573/Detectors_Summer2015_part4.pdf 5

Appendix 𝑞 = 𝑛𝑤 = 𝑠𝑟𝐶 [kg ・ m/s] 𝑠 : radius [m] 𝑟 : charge 𝑞𝑑 = 𝑠𝑟𝐶𝑑 [J] 𝐶 : magnetic field strength [T] 𝑠𝑟𝐶𝑑 1.6×10 −19 [eV] 𝑞𝑑 = 𝑞𝑑 = 𝑠𝐶𝑑 [eV] 𝑞𝑑 = 𝑠𝐶 ∙ 3.0 × 10 8 [eV] 𝑞 = 0.3𝑠𝐶 [GeV/c] 6