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 & Considerable Factors 1 Introduction 2 Theory 3 Design & Considerable Factors 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors History 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 Advantages Good time resolution Good position accuracy Self-triggered operation 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors MWPC Multi-wire proportional chamber gives positional information of charged particle trajectory Consists of two cathode plates, and a set of thin parallel anode wires. (r=30 µ m Au) Figure: Schematic view of MWPC 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors MWPC 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 Townsend avalanche 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 Bethe-Bloch formula Mean stopping power for high energy charged particle can expressed as − < dE (2.1) dx > = a ( E ) + b ( E ) E 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 Bethe-Bloch fomula In 1930, H.Bethe introduced generalized oscillator strength which related to form-factor. Bethe-Bloch Formula Let E loss is energy loss of charged particle and I means mean excitation energy of medium. In high energy region we have β 2 [ ln 2 m e c 2 β 2 γ 2 K max 1 E loss = K 2 z 2 Z − β 2 ] . I 2 A 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Bethe-Bloch fomula Ioniztion energy of various gases ρ ( g/cm 3 ) dE/dx ( Mevg − 1 cm 2 ) Gas I 0 W i ( eV ) 8.38 · 10 5 H 2 15.4 37 4.03 1.66 · 10 − 4 He 24.6 41 1.94 1.17 · 10 − 3 N 2 15.5 35 1.68 8.39 · 10 − 4 Ne 21.6 36 1.68 1.66 · 10 − 3 Ar 15.8 26 1.47 3.49 · 10 − 3 Kr 14.0 24 1.32 5.49 · 10 − 3 Xe 12.1 22 1.23 1.86 · 10 − 3 13.7 33 2.21 CO 2 6.70 · 10 − 4 10.8 23 1.86 CH 4 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 Design Electric Potential When V ( c ) =0 and applied potential on anode wires are V 0 , electric potential in MWPC is [ 2 πL V ( x , y ) = CV 0 − ln ( 4 ( sin 2 πx d + sinh 2 πy d ))] 4 πǫ 0 d 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Design Electric Field When V ( c ) =0 and applied potential on anode wires are V 0 , electric field in MWPC is E ( x , y ) = CV 0 2 ǫ 0 d ( 1 + tan 2 πx s tanh πy 2 ( tan 2 πx d + tanh 2 πy 1 d ) − 1 s ) 2 Figure: Electric field and potential Figure: More detail view in MWPC 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Design 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Design of Geometrical factor Use Ar 75% and CO 2 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 10 4 . Choose the distance between wire as 0.75cm 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Design for wire plates Expectation value of signal size is around 50mV. Amplification rate have to be 10 12 . Also, integration time is around 100ns. Figure: Design of wire plate Figure: Real material Used 1pF capacitors & 100k Ω resistors 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Gas Mixture 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 Wire tension Capacitance of wire When V ( c ) =0 and applied potential on anode wires are V 0 , capacitance per unit length of wire is 2 πǫ 0 C = πL d − ln ( 2 πa s ) 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Wire tension 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 ) = ( CV 0 ) 2 1 2 πǫ 0 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 Wire tension 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 of wire plate. 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Wire tension 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 dx 2 (3.2) d 2 δ For equilibrium, this have to be same as electrostatic force between wires. Then solution δ ( x ) is � π δ ( x ) = δ 0 sin ( CV 0 ǫ 0 T x ) (3.3) 2 s 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Wire tension From boundary condition, δ ( L ) = δ ( 0 ) = 0 T c is given and if applied tension is bigger than critical tension, no solution is possible other than δ ( x ) = 0 1 ( CV 0 L ) 2 (3.4) T > T c = 4 πǫ 0 s 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System

Introduction Theory Design & Considerable Factors Thank you for your attention! 20160383 Jaewhan Oh MWPC, Charged Particle Trajectory Tracking System