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.

• If the strength of the magnetic field and the

radius are known, the momentum can be measured.

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𝑠 =

𝑛𝑤 𝑟𝐶 = 𝑞 𝑟𝐶

𝑔 = 𝑟𝒘 × 𝑪

𝑟 : charge 𝐶 : magnetic field strength 𝑤 : velocity e+ r B 𝑛 : mass of particle

𝑞 [𝐻𝑓𝑊/𝑑] = 0.3 𝑠 𝑛 𝐶[𝑈]

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…

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Real application

• The measured track is close a straight line in

real application.

• sagitta s is calculated.

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s r r-s L

𝑡 = 𝑠 − 𝑠2 − 𝑀2 4

B

𝑠 = 𝑡 2 + 𝑀2 8𝑡 ≈ 𝑀2 8𝑡 (𝑡 ≪ 𝑀) The relation between radius and momentum

𝑠 = 𝑞 𝑟𝐶 ⟹ 𝑡 = 𝑟𝐶𝑀2 𝑞

𝑠2 = (𝑠 − 𝑡)2+ 𝑀 2

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• Reference
• http://summerstudents.desy.de/e69118/e177730/e2

02573/Detectors_Summer2015_part4.pdf

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Appendix

𝑞 = 𝑛𝑤 = 𝑠𝑟𝐶 [kg・m/s] 𝑞𝑑 = 𝑠𝑟𝐶𝑑 [J] 𝑞𝑑 =

𝑠𝑟𝐶𝑑 1.6×10−19 [eV]

𝑞𝑑 = 𝑠𝐶𝑑 [eV] 𝑞𝑑 = 𝑠𝐶 ∙ 3.0 × 108 [eV] 𝑞 = 0.3𝑠𝐶[GeV/c]

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𝑠 : radius [m] 𝑟 : charge 𝐶 : magnetic field strength [T]