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TITLE F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 RADIATION DETECTION AND MEASUREMENT Prof. Glenn Knoll, organizer Short Courses November 10-11 2002 IEEE NSS/MIC Norfolk, November 10-16, 2002 1 INTRODUCTION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 GASEOUS DETECTORS’ FAMILY TREE TIME PROJECTION CHAMBER CHERENKOV RING IMAGING MULTIWIRE PROPORTIONAL CHAMBER STREAMER TUBES TRANSITION RADIATION TRACKER DRIFT CHAMBERS COMPTEUR A TROUS STRAWS PROPORTIONAL COUNTER GAS ELECTRON MULTIPLIER MICROWELL MICROMEGAS MICROSTRIP CHAMBERS MICROGAP PARALLEL PLATE COUTER AVALANCHE CHAMBERS PESTOV COUNTER RESISTIVE PLATE CHAMBERS 2 PART 1 F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 IONIZATION DRIFT AND DIFFUSION CAPTURE LOSSES AVALANCHE MULTIPLICATION 3 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 COULOMB INTERACTIONS OF CHARGED PARTICLES WITH MOLECULES PRIMARY IONIZATION: ELECTRON-ION PAIRS Minimum ionizing particles: Helium Argon GAS (STP) dE/ dx (keV/ cm) n (ion pairs/ cm) 0.32 2.4 6 25 Xenon 6.7 44 CH 4 DME 1.5 16 3.9 55 Statistics of primary ionization: Poisson: k -n n = P e k! n k n: average k: actual number (Maximum) detection efficiency: e = 1- e -n thickness e Helium 1 mm 2 mm 45 70 Argon 1 mm 2 mm 91.8 99.3 GAS (STP) 4 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 SECONDARY AND TOTAL IONIZATION CLUSTERS AND DELTA ELECTRONS: GAS (STP) n (ion pairs/cm) cm) N (ion pairs/cm) Helium Argon Xenon CH 4 DME 6 25 44 16 55 8 90 300 53 160 N: total ion-electron pairs n _ ~3 N CLUSTER SIZE DISTRIBUTION: P (m) ~ W m2 H. Fischle et al, Nucl. Instr. and Meth. A301(1991)202 5 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 CONSEQUENCES OF ENERGY LOSS STATISTICS LANDAU DISTRIBUTION OF ENERGY LOSS: Counts 4 cm Ar-CH4 (95-5) 5 bars 6000 PARTICLE IDENTIFICATION Requires statistical analysis of hundreds of samples N = 460 i.p. 4000 FWHM~250 i.p. Counts 15 GeV/c 6000 protons 2000 electrons 4000 0 0 500 1000 N (i.p.) 2000 For a Gaussian distribution: sN ~ 21 i.p. FWHM ~ 50 i.p. 0 0 500 1000 N (i.p) I. Lehraus et al, Phys. Scripta 23(1981)727 6 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 LOCALIZATION ACCURACY IN DRIFT CHAMBERS WORSENED BY LONG-RANGE ELECTRONS: Drift Time 5% of events! F. Sauli, Nucl. Instr. and Meth. 156(1978)147 7 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 CENTER OF GRAVITY OF INDUCED CHARGE READOUT STRONG ANGULAR DEPENDENCE OF POSITION ACCURACY Position accuracy as a function of the track angle to the normal to the chamber: G. Charpak et al, Nucl. Instr. and Meth. 167 (1979) 455 8 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 ANGULAR DEPENDENCE OF POSITION ACCURACY IN MICRO-STRIP CHAMBERS: F. Van den Berg et al, Nucl. Instr. and Meth. A349 (1994) 438 9 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 DECLUSTERING EFFECT IN TIME PROJECTION CHAMBERS: B=1.5 T B offset Drift Data: D. Decamp et al, Nucl. Instr. and Meth. A269(1990)121 Simulation: A. Sharma, CERN 10 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 LIMITED TIME RESOLUTION OF WIRE AND MICROPATTERN CHAMBERS: Space distribution of the cluster closer to an electrode: A1n (x) = ne -n x Time distribution of the cluster closer to an electrode: A1n (t) = ne -n w t w: drift velocity 50 w = 5 cm/µs A1n(t) 40 30 20 6 ns 3 ns 25 ip/cm 10 0 0 50 ip/cm 5 10 20 15 Time (ns) 11 IONIZATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 PARALLEL PLATE CHAMBERS: SUB-NANOSECOND RESOLUTION FAST SIGNAL INDUCTION DURING AVALANCHE DEVELOPMENT: Useful gap R. Arnaldi et al, Nucl. Phys. B 78(1999)84 12 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 DRIFT AND DIFFUSION OF CHARGES IN GASES ELECTRIC FIELD E = 0: THERMAL DIFFUSION ELECTRIC FIELD E > 0: CHARGE TRANSPORT AND DIFFUSION IONS ELECTRONS E 13 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 DRIFT AND DIFFUSION OF IONS (CLASSIC KINETIC THEORY OF GASES) Ions remain thermal up to very high fields Maxwell energy distribution: - F(e ) = C e e e KT Average (thermal) energy: eT = KT 0.025 eV Diffusion equation Fraction of ions at distance x after time t: dN 1 = e N 4 Dt x2 4 Dt dx D: diffusion coefficient RMS of linear diffusion: s x = 2Dt Molecules diffuse rapidly in the available volume (leaks!) 14 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 IONS DRIFT VELOCITY (Almost) linear function of field Mobility: = w E ~ constant for a given gas (at fixed P and T) GAS Ar CH4 Ar-CH4 80-20 ION Ar+ CH4+ CH4+ µ+ (cm2 V-1 s-1) @STP 1.51 2.26 1.61 MWPC: 1 cm gap, Ar-CH4, 5 kV/cm Total ions drift time T+ ~ 120 µs TPC: 1 m drift, Ar-CH4, 200 V/cm Total ions drift time T+ ~ 300 ms IONS DIFFUSION (Einstein’s law): D KT s x = 2Dt e 2KT x Same for all ions! sx = e E = E. McDaniel and E. Mason The mobility and diffusion of ions in gases (Wiley 1973) 15 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 DRIFT AND DIFFUSION OF ELECTRONS IN GASES Electric Field Electron Swarm Drift Ds, Dt s Drift velocity: w= Ds Dt Space diffusion rms: s = 2Dt = 2D s w sx = s1 x Townsend expression: w= e E 2m : mean collision time E w = w Drift velocity and diffusion are gas and field dependent: P 1 E E s = F D = g P P P P : pressure 16 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 LARGE RANGE OF DRIFT VELOCITIES AND DIFFUSIONS DRIFT VELOCITY: DIFFUSION: 17 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 ELECTRON TRANSPORT THEORY BALANCE BETWEEN ENERGY ACQUIRED FROM THE FIELD AND COLLISION LOSSES Energy distribution probability: F0 (e ) = C e e le (e ) = - 3e (e ) de e E le (e ) 2 1 (e ) Drift velocity: w= Mean free path between collisions N s (e ) 2 e E e le (e ) 3m s: electron-molecule cross section) Fractional energy loss in collisions F0 (e ) e de v= 2e m Diffusion coefficient: D= le (e ) v F0 (e ) de 3 Frost and Phelps, Phys. Rev. 127(1962)1621 V. Palladino and B. Sadoulet, Nucl. Instr. and Meth. 128(1975)323 G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413 S. Biagi, Nucl. Instr. and Meth. A283(1989)716 18 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 CHARGE TRANSPORT DETERMINED BY ELECTRON-MOLECULE CROSS SECTION: MAGBOLTZ S. Biagi, Nucl. Instr. and Meth. A421 (1999) 234 http://consult.cern.ch/writeup/magboltz/cross/ http://cpa94.ups-tlse.fr/operations/operation_03/POSTERS/BOLSIG/ 19 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 COMPUTED DRIFT VELOCITY IN MIXTURES http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec 20 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 LONGITUDINAL DIFFUSION (// E) E Field LONGITUDINAL DIFFUSION: sL Drift TRANSVERSE DIFFUSION: Transverse diffusion ( µm for 1 cm drift) Longitudinal diffusion ( µm for 1 cm drift) SMALLER THAN TRANSVERSE DIFFUSION: sT http://consult.cern.ch/writeup/garfield/examples/gas/Welcome.html 21 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 DRIFT TIME ACCURACY: DEPENDS ON IONIZATION DENSITY Anode Wire Drift sL Single electron Several electrons Many electrons Detection threshold Error on first electron electron: s1 ~ 2 3 ln N sL N=100 s1~ 0.4 sL RESOLUTION LIMITS OF DRIFT TUBES: G. Scherberger et al, Nucl. Instr. and Meth. A424(1999)495 W. Riegler et al, Nucl. Instr. and Meth. A443(2000)156 22 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 EFFECTS OF MAGNETIC FIELD THE SWARM IS ROTATED BY AN ANGLE B IN THE PLANE PERPENDICULAR TO E AND B THE MAGNETIC DRIFT VELOCITY IS wB w0 THE TRANSVERSE DIFFUSION IS REDUCED B E E^B tan B = B wB = E wB wB E B 1 2 2 : mean collision time = eB /m E // B sT E sL r B wB Larmor frequency wB = w0 sL = s 0 sT = s0 1 2 2 23 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 DRIFT IN MAGNETIC FIELD: SIMPLE MODEL: = 0 0 = 2mw0 eE 24 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 TRANSVERSE DIFFUSION IN SEVERAL GASES transv diff gases bis 1000 DRIFT MULTIPLICATION Ar 600 Ar-CH 90-10 REDUCTION IN MAGNETIC FIELD // E 4 400 2 200 Ar-CO 70-30 2 CO 2 0 102 103 P10 diffusion vs mag field log bis 800 Ar-CO 90-10 104 E (V/cm) 105 Diffusion for 1 cm (µm) s for 1 cm (µm) T 800 Argon-Methane 90-10 700 DRIFT MULTIPLICATION 600 sT (B=0) 500 400 sL 300 sT (B=2.5 T) 200 sT (B=5 T) 100 0 102 103 104 105 E (V/cm) 25 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 COMPUTED FROM TRANSPORT THEORY (MAGBOLTZ) 26 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 MAGNETIC FIELD EFFECTS: DISTORSIONS IN DRIFT CHAMBERS W. de Boer et al, Nucl. Instr. and Meth. 156(1978)249 27 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 MAGNETIC FIELD EFFECT: COORDINATE DISTORSIONS IN MICRO-STRIP CHAMBERS F. Angelini et al, Nucl. Instr. and Meth. A347(1994)441 28 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 TRANSVERSE DIFFUSION: SUBSTANTIALLY REDUCED IN SOME GASES TIME PROJECTION CHAMBER: Center-of-gravity of cathode signal B=0 E // B B>0 D. Nygren, TPC proposal (PEP4, 1976) 29 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 STABILITY OF OPERATION VOLTAGE AND PRESSURE THE DRIFT VELOCITY IS A FUNCTION OF REDUCED FIELD E/P E w = f P DRIFT VELOCITY SATURATION: INSENSITIVE TO VARIATIONS OF E AND P E P 30 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 STABILITY OF OPERATION TEMPERATURE Dw DT 3.4 10 -3 = w T C AT LOW FIELDS (THERMAL ELECTRONS): At high fields, the thermal coefficient in some gases decreases and even becomes negative: Dw/w/ºC CO2 4 Methylal 3 2 C4H10 A-C4H10-Methylal 66-30-4 A 1 0 CH4 -1 100 500 1000 2000 E (V/cm) G. Shultz and J. Gresser, Nucl. Instr. and Meth. 151(1978)413 31 CAPTURE F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 ELECTRON CAPTURE LOSSES ON ELECTRONEGATIVE GASES Attachmant coefficient of oxygen: Electrons surviving after 20 cm drift (E = 200 V/cm): The attachment cross section is energy-dependent, therefore strongly depends on the gas composition and electric field 32 CAPTURE F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 ELECTRON CAPTURE - VERY SENSITIVITE TO GAS MIXTURE Energy resolution of a proportional counter with two gas fillings (and some leaks!): 5.9 keV X-rays “Hot” gas ARGON-ETHANE 50-50 “Cold” gas DIMETHYLETHER R. Openshaw, TRIUMF (private, 2000) 33 DRIFT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 USE OF CF4 AS QUENCHER REPLACING CH4 IN TPCs - FAST DRIFT VELOCITY - SMALL DIFFUSION - NO HYDROGEN (REDUCED NEUTRON SENSITIVITY) - NON-FLAMMABLE L. G. Christophorou et al, Nucl. Instr. and Meth.163(1979)141 34 CAPTURE F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 ELECTRON CROSS SECTIONS IN CF4 http://consult.cern.ch/writeup/magboltz/cross/ 35 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 INCREASING THE FIELD TOWARDS CHARGE MULTIPLICATION Electrons energy distribution at increasing fields: Excitation Ionization 10.5 eV 15.5 eV 0.2 kV/cm IONIZATION 15.7 eV 5 kV/ cm EXCITATION 11.6 eV 1 kV/ cm 0 5 10 15 20 25 30 Electron energy (eV) 36 MULTIPLICATION IONIZATION CROSS SECTION AND TOWNSEND COEFFICIENT F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 Mean free path for ionization = 1 Ns N: molecules/cm3 Townsend coefficient = 1 Ionizing collisions/cm S.C. Brown, basic data of plasma physics (MIT press, 1959) 37 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 AVALANCHE MULTIPLICATION IN UNIFORM FIELD Combined cloud chamber-avalanche chamber: E x Ions dn = n dx n(x) = n0e x Multiplication factor or Gain n M(x) = = e x n0 Electrons H. Raether Electron avalanches and breakdown in gases (Butterworth 1964) 38 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 MEASUREMENT OF THE TOWNSEND COEFFICIENT Current vs voltage for constant charge injection in a parallel plate counter: Radiation M V 1 s I = ln M s 39 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 TOWNSEND COEFFICIENT IN GAS MIXTURES ARGON-CH4: in Argon A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)420 40 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 SIGNAL DEVELOPMENT PARALLEL PLATE COUNTERS: -Q -Q +Q +Q -Q -Q A charge +Q between two conductors induces two negative charge profiles (image charge) Moving the charge modifies the induced charge profile on the conductors and generates detectable signals +Q towards an electrode: positive induced signal Induced signals are equal and opposite on anode and cathode 41 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE COLLECTION ONLY) Single charge +Q: CATHODE Charge induced on each electrode by +Q moving through the difference of potential dV: V= -V0 dq = Q s s0 +Q dV ds =Q V0 s0 Integrating over s (or time t): ANODE q(s) = V=0 Q s s0 q(t ) = Q wt s0 w: drift velocity Electrons- ion pair (-Q and +Q) released at the same distance s from the cathode : w -t w t q(t ) = Q 0 t T s s0 0 s - s w t 0 q(t ) = Q T t T s s0 0 q(t ) Q w- (w+ ) : electron (ion) drift velocity T- (T+ ) : total electron (ion) drift time Total signal: q(T ) = Q Q s0 - s s0 (+Q on cathode , -Q on anode) T- T t 42 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION) -V0 During the avalanche development, the increase in the number of charges after a path ds is: s n = n0e s s0 and the total after a path s: dn = nds 0 The incremental charge induction due to electrons after a path s: dq- = -en0es Integrating over s: ds s0 en0 s en0 s en0 w-t q (s) = (e -1) e = e s0 s0 s0 - and the corresponding current : dq- en0w- w-t en0 w-t i (t ) = = e = -e dt s0 T - The current signal iduced by the ions is instead given by: en0 w-t w*t 0 t T i (t ) = e -e T en0 s w* t T t T i (t ) = e - e T 1 w* = 1 1 w w- 43 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 PARALLEL PLATE COUNTERS: SIGNAL DEVELOPMENT (CHARGE MULTIPLICATION) Fas electron signal Slow ion tail 44 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 SIGNAL DEVELOPMENT WIRE PROPORTIONAL COUNTERS: Thin anode wire coaxial with cathode Cathode radius b Electric field: CV0 1 E(r) = 2e 0 r C= 2e 0 lnb a Anode radius a Avalanche development around a thin wire: + + + + + + + + + 45 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 PROPORTIONAL COUNTERS: GAIN CHARACTERISTICS ln M Streamer Saturation Breakdown Multiplication Collection Attachment n1 n2 IONIZATION CHAMBER PROPORTIONAL COUNTER Voltage 46 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 PROPORTIONAL COUNTERS: SIGNAL DEVELOPMENT Incremental charge induced by Q moving through dV: dQ = Q Q dV dV = dr V0 V0 dr Assuming that the total charge of the avalanche Q is produced at a (small) distance from the anode, the electron and ion contributions to the induced charge are: q- = Q a dV QC a dr = ln V0 a dr 2e 0 a Q b dV QC b q = dr = ln V0 a dr 2e 0 a and QC b ln = -Q on the anode 2e0 a q- ln(a ) - ln a = The ratio of electron and ion contributions: lnb - ln(a ) q The total induced signal is q = q- q = - For a counter with a=10µm, b=10 m: q-/q+ ~1% ( Q on the cathode) The electron-induced signal is negligible Neglecting electrons, and assuming all ions leave from the wire surface: t QC r(t) q(t ) = q (t ) = - dq = ln 2 e a 0 0 dr CV0 1 = E = dt 2e0 r QC CV0 QC t q(t ) = ln 1 t =ln1 2 2e 0 2 e 2e0a 0 t 0 Total ions drift time: e0 (b2 - a2 ) T = CV0 i(t ) = - CV0 r(t) = a t 2 e 0 2 QC 1 2e0 t0 t q(T ) = -Q 47 MULTIPLICATION F. Sauli-Short Courses-IEEE-NSS 2002-PART 1 CHARGE SIGNAL: q(t) q(t) Q 0 0.2 0.4 0.6 0.8 1.0 t (µs) 0 100 200 300 400 500 t (µs) T+ AMPLIFIER TIME CONSTANT; 50 ns q(t) CURRENT SIGNAL: i(t) 100 ns 300 ns 0 20 40 60 80 100 t (ns) 0 100 200 300 400 500 t (ns) 48