放射線検出器の基礎 - 2 飯嶋徹
電離によるエネルギー損失 2 2 de 2 Z 1 2mc 2 2 ln e β δ = Kz β (1 2 dx A β I β ) 2 K = 4π N r m c = 0.3071 MeV cm / gr 2 2 2 0 0 e I Mean ioniza9on energy I 7 = 12 + ev Z Z Z < 13 I 1.19 = 9.76 + 58.8 Z ev Z Z 13 物質のZ/Aに比例 Z/A~1/2, β~1 1.5MeV/(g cm 2 ) 入射粒子の速度 (β) に依存粒子識別が可能低速では1/β 2 高速ではβ 2 /(1- β 2 ) で上昇
Propor9onal Counter - + - + - + - + 1 V ln( / ) 0 E = r b a Propor9onal region Electrons gain enough energies to further create an electron- ion pair Avalanche (cascade) Output propor9onal to the primary electron- ion pairs.
Mul9plica9on in gas
MWPC (Mul9 Wire Propor9onal Counter)
チェレンコフ輻射 荷電粒子が媒質を媒質中での光速より速く進む時 チェレンコフ光が放射される c Δ t n vδt 1 β > n cosθ c = 1 nβ n: refractive index of the medium θc: Emission angle of the Cherenkov radiation
Let s look at it! 14 2009/3/14
Refractive index and P th P th = n m 2 1 Material n P th (GeV/c) Quartz (sol.) π K 1.47 0.13 0.46 C 5 F 12 (liq.) 1.24 0.19 0.67 Aerogel 1.03 0.57 2.00 C 4 F 10 (gas) 1.0014 2.64 9.33 Aerogel fill the gap between liquid and gas. widely used now. 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 15
Threshold Cherenkov Counter n Threshold momentum for Cherenkov emission p th > n m 2 1 n=1.01~1.05ぐらいの物質があれば数 GeV/cのπ/K 識別が可能 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 16
Two Classes of Cherenkov Counters n Threshold Cherenkov Counter Judge only whether or not Cherenkov lights are produced, and therefore the particle velocity exceed 1/n. n Ring Imaging CHerenkov counter (RICH) Image the Cherenkov ring using a position sensitive photodetector, and measure the Cherenkov angle θ c. Threshold-type RICH-type Radiator Position-sensitive photodetector 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 17
Photodetectors What are happening inside? 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 18
Three Steps for Photodetection n Generation of a primary photoelectron or electron-hole (e-h) pair [ photoelectric / photoconductive effect ]. Quantum efficiency (QE), Collection efficiency (CE) n Amplification of the photoelectron signal by one or more multiplicative steps (à secondary electrons). Gain (G), Multiplication factor (δ), Excess noise factor (ENF) n Collection of the secondary electrons to form the electric signals. Electric noise Transit time spread (TTS) 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 19
Photomultiplier Tube Focusing electrode Collection efficiency (C.E.) 1 st dynode #secondary electrons -- δ 1 Pulse height resolution Glass window cut-off λ MgF 2 115nm Sapphire 145nm Fused Silica 160nm UV-glass 190nm Photocathode Borosilicate See next 270nm page 2009/3/14 Dynodes Multiplicative amplification G = δ1 δ2 δ3 δn k δ i = a E k = 0.7 0.8 G= ( a E ) = AV k n k n Lectire on PID by Toru Iijima @ TIPP09 20
Quantum Efficiency Fiugure provided by Hamamatsu Photonics 100 10 Cs-Te Bi-alkali 各種光電面の量子効率 (QE) GaAsP GaAs Multialkali (S-20) Extended Red Multialkali (S-25) QE (%) InP/InGaAs 1 (S-1) 0.1 2009/3/14 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 170 Wavelength (nm) Lectire on PID by Toru Iijima @ TIPP09 21
Magnetic Field Effects Electron motion in B field = Helix motion n n n n Radius Pitch R = Photoelectron ~ 0.5eV Secondary electron ~ 6eV v ω c c 2π πe d = vp ω B Conventional PMT does not work. 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 22
Dynode Structure Line focus Metal channel Conventional, wide usage Good resolution, high gain Cannot be used in B field. Fine-mesh Position sensitive Up to ~100 Gauss Micro-channel-plate Up to 1.5 Tesla 2009/3/14 Very fast Up to 1.5 Tesla Lectire on PID by Toru Iijima @ TIPP09 23
Backup 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 24
Noble gas + Quencher DriT velocity: 5-10 cm/ms OTen used gas mixture; P10: Ar(90%) + CH 4 (10%) Chamber gas Magic gas: Ar(75%)+Isobutane(24.5%)+freon(0.5%) Drift velocity Diffusion
電子と物質の相互作用 電離損失 放射損失 ( 制動放射 Bremsstrahlung) 2 2 de 4NZr 0 0 1/3 1 = E ln(183 Z ) + dx 137A 18 X rad 4NZr = ln(183 ) 137A 2 2 1 0 0 1/3 0 Z 放射長 (radia9on length) de dx de rad E = X 0 dx rad X 0 0 = E exp x 臨界エネルギー (cri9cal energy) de de = dx dx ion rad EC ; 800 Z + 1.2 ( MeV)
光子と物質の相互作用 光電効果 (photo- electric effect) 7 4 5 2 K Z 0 mc e h 2 2 25 2 0 = 8 re / 3 = 6.651 10 cm ; = 1/137 σ = 4α 2 φ ( / ν) φ π α コンプトン散乱 2 3 mc e 2k σc = ln + 0.5 2 σt 8 k mec 8π 2 25 2 σ T = r0 = 6.65 10 cm 3 対生成 (pair produc9on) σ λ pair pair 7 A 1 9 N X 0 0 9 = X 0 Pair production に対する 7 mean free path
T(X0) 通過後 電磁カスケードシャワー Nt () = 2 t e E()/ t particle = E 2 プロセスは Et () < EC まで続く Ionization, compton, Shower maximum t = max 0 [ ] ln / E0 E C ln 2 γ t e e e + γ e e 1 2 3 4 N max max γ = exp( t ln 2) = E E 0 C t( X0) クーロン散乱による横方向の広がり ( モリエール半径, Moliere radius) R M ; X 21MeV E 半径 R M 内に全シャワーエネルギーの 90% が集中 0 C
EM Calorimeter γ n Development of cascade shower N(t) = 2 t E(t)/particle = E 0 x 2 -t n Process continues until E(t) < E c T max = ln(e 0 /E c )/ln2 N total max t= 0 n Moliere radius t = = = t tmax + tmax 2 2 1 2 2 2 E E 1 0 21MeV RM = X g cm E c t in radiation length c 2 0 [ / ]
Frank- Tamm の公式 単位長さ (X)x 単位波長 (l) 当たりに放射される光子の数 (N) 2 dn = dxdλ 2πα 2 λ 2 sin θc( λ) α: 微細構造定数 λ: フォトン波長 dn dedx α z 2 = sin θc( E) E: フォトンエネルギー h c 2 2 = 370sin ( ) 2 θ 1 1 c E ev cm
Energy (Pulse Height) Resolution n Energy resolution; 2 2 fenf Ne = + pe.. σ E E N S f N ENF e N = n QE CE pe.. γ S = G n QE CE - If Low noise or high gain (ex. conventional PMT); σ E E f ENF = f N ENF pe.. N pe.. eff. S = N eff. p.. e = N pe.. σ S 2 γ Excess noise factor Electric noise charge Number of photoelectrons Signal charge ENF determined by amplification statistics, often dominated by number of secondary electrons (e-h pairs) at the 1 st stage of amplification. 2009/3/14 Lectire on PID by Toru Iijima @ TIPP09 31