MWPC, Charged Particle Trajectory Tracking System 20160383 Jaewhan - - PowerPoint PPT Presentation
Introduction Theory Design & Considerable Factors MWPC, Charged Particle Trajectory Tracking System 20160383 Jaewhan Oh December 3, 2017 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System Introduction Theory Design
Introduction Theory Design & Considerable Factors
20160383 Jaewhan Oh December 3, 2017
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
1 Introduction 2 Theory 3 Design & Considerable Factors
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
MWPC developed by Georges Charpak at 1968. The Nobel Prize in Physics 1992 was awarded to Georges Charpak for his invention and development of multiwire proportional chamber
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Good time resolution Good position accuracy Self-triggered operation
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Multi-wire proportional chamber gives positional information
Consists of two cathode plates, and a set of thin parallel anode wires. (r=30 µm Au)
Figure: Schematic view of MWPC
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
When high energy particle pass through the MWPC, it makes ion-electron pair. It called as primary ionization. Free electron accelerated by electric field that caused by anode wires. It collide with other gas molecule and make another ionization pair. It called as secondary ionization. Ratio between number of event of primary ionization and secondary ionization is called as a gas gain.
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Secondary ionization process amplifies the number of electrons and it called as Townsend avalanche.
Figure: Townsend avalanche
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Mean stopping power for high energy charged particle can expressed as
− < dE dx >= a(E) + b(E)E
(2.1) a(E) means eletronic term and b(E) means radiation term
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
In 1930, H.Bethe introduced generalized oscillator strength which related to form-factor. Bethe-Bloch Formula Let Eloss is energy loss of charged particle and I means mean excitation energy of medium. In high energy region we have
Eloss = K
2 z2 Z
A
1
β2 [ln 2mec2β2γ2Kmax I2 − β2].
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Ioniztion energy of various gases Gas
ρ(g/cm3) I0 Wi(eV) dE/dx(Mevg−1cm2) H2
8.38 ·105 15.4 37 4.03 He 1.66 ·10−4 24.6 41 1.94
N2
1.17·10−3 15.5 35 1.68 Ne 8.39 ·10−4 21.6 36 1.68 Ar 1.66 ·10−3 15.8 26 1.47 Kr 3.49 ·10−3 14.0 24 1.32 Xe 5.49 ·10−3 12.1 22 1.23
CO2
1.86 ·10−3 13.7 33 2.21
CH4
6.70 ·10−4 10.8 23 1.86
Table: Density, Ionization potential, Energy required to produce an ionization pair and Mean energy loss of charged particles in various gases
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Electric Potential When V(c)=0 and applied potential on anode wires are V0, electric potential in MWPC is
V(x, y) = CV0
4πǫ0
[2πL d − ln(4(sin2 πx d + sinh2 πy d ))]
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Electric Field When V(c)=0 and applied potential on anode wires are V0, electric field in MWPC is
E(x, y) = CV0
2ǫ0d(1 + tan2 πx
s tanh πy s )
1 2 (tan2 πx
d + tanh2 πy d )− 1
2
Figure: Electric field and potential
in MWPC
Figure: More detail view
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Use Ar 75% and CO2 25% mixture Value of applied voltage is 1.55kV, and gap size is 3.2mm.
Figure: Gas gain verse wire-wire distance
Expectation value of gas gain is 104. Choose the distance between wire as 0.75cm
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Expectation value of signal size is around 50mV. Amplification rate have to be 1012. Also, integration time is around 100ns.
Figure: Design of wire plate Figure: Real material
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Townsend avalanche multiplication can easily occur in noble gas. Financial problem. Xenon and Krypton are expansive. Therefore we usually use Argon gas Photoelectric effect.
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
Capacitance of wire When V(c)=0 and applied potential on anode wires are V0, capacitance per unit length of wire is
C =
2πǫ0
πL d − ln(2πa s )
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
We have to consider electrostatic force between anode wires. Electrostatic Force When r is distance between anode wires and C is capacitance per unit lenght then electrostatic force between wires is,
F(r) = (CV0)2
2πǫ0 1
r
Anode wire Benting or attachment! Give critical damage to Circuit elements. Cannot know the exact trajectory of charged particle
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
We can solve this problem just apply some tension on anode wires. The value of applied tension is depend on applied voltage and wire distance. If we have a lot of wires we have to consider the yield strength
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
When T is the mechanical tension of wire and δ is displacement of wire along its length then Restoring force of wire is
R = T dx2 d2δ
(3.2) For equilibrium, this have to be same as electrostatic force between
δ(x) = δ0 sin(CV0
2s
π ǫ0T x)
(3.3)
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
From boundary condition, δ(L) = δ(0)= 0 Tc is given and if applied tension is bigger than critical tension, no solution is possible other than δ(x) = 0
T > Tc =
1 4πǫ0
(CV0L s )2
(3.4)
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System
Introduction Theory Design & Considerable Factors
20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System