Putting it all together

Putting it all together- Particle Detectors Writeup for 3rd section: http://yeti.phy.bris.ac.uk/Level3/phys30800/CourseMaterials/Part_3.pdf

Measurements • Destructive • Initial particle absorbed or significantly scattered • Detection generally by energy deposited by charged particles produced • Can detect neutral particles • Non-Destructive • Particle only minimally perturbed • Generally involves electrically charged particles depositing energy through many soft scatters • Aim for low mass detector

Types of Measurement Position (tracking) Timing Time of flight Event separation Velocity Cerenkov/Transition radiation Energy Total energy dE/dx

Position measurement • All detectors give some indication of particle position • ( even if it is only that the particle passed through the detector ) • Most detectors have better resolution in one (or two) directions than the other two (or three). • Hodoscope ~ cm (2D) • Silicon strip detector ~5mm (1D) • Silicon pixel detector ~5mm (2D) • Photographic emulsion ~1mm (3D)

Position Measurement - Tracking • Measuring two (or more) points along the path of a particle allows its direction as well as is position to be measured. • Measuring a number of points along the path of a particle allows any curvature to be measured.  Radius of curvature in a magnetic field gives the momentum

Position Measurement – Tracking Pattern recognition can be tricky….

Timing Measurement • The time at which a particle passed through a detector can be measured to better than 1ns (10-9s) • Scintillator tends to be good ( 100ps ) • Can measure velocity of particle • “time-of-flight” (ToF ) from interaction to detector. • Measuring b and p or E gives particle mass ( E=bm, p=bgm) and hence (usually) identity • ToF only useful for fairly low energy particles ( “slightly relativistic” ) since highly relativistic particles all have b=1 within the bounds of error.

Timing Measurement • Distinguish particles from different “events” • The interval between interactions generating the particles being measured is is often short. Need good timing resolution to separate tracks from different events. • Measure start time for drift chambers. • … and other devices that rely on measuring signal propagation times.

Timing Measurement – Particle ID

Timing Measurement – Particle ID • Hermes experiment uses TOF as one means of particle identification. • Bunches of electrons hit fixed target. • Measure time between collision and particles reaching scintillation detectors. • m2 = (1/2 – 1) p2

Dead Time • Most detectors take a finite time to produce a signal and recover before they can detect another. This is the dead-time • Dead time varies with detector e.g. Si-strip detector ~ ns , Geiger-Muller tube ~ ms • If the dead-time is Tdand particles arrive at a mean rate of r per unit-time then probability that the detector is “dead” is ~ rTd • I.e. efficiency is e = e0(1 – rTd )

Timing Coincidence • Where a detector has a high background it is common to use two or more detectors in coincidence • Output from combined detector only if all parts detect a particle. ( or 3 of 4, ….. etc.) • If two detectors have a background rate of B1, B2 and a signal is produced if both detectors “fire” within the coincidence time,Dt then the background rate from the combined detector is B = B1 B2 Dt

Energy Measurement Rate of energy loss – dE/dx Total energy - Calorimetry

Energy Measurement – dE/dx • Measure the rate of energy loss of a charged particle through detector by ionization - dE/dx • dE/dx Depends on bg • ( particles with same bg but different masses give ~ same dE/dx ) • Measuring bg and one of E,p, gives particle mass.

dE/dx Data dE/dx (keV/cm) p K p e • Data from gaseous track detector. • Each point from a single particle • Several energy loss samples for each point • “Averaged” to get energy loss • Fluctuations easily seen m p (GeV/c)

Energy Measurement – Calorimetry • Measure total energy of a particle by stopping the particle in a medium and arranging for the energy to produce a detectable signal. This process is called calorimetry • Detector needs to be thick enough to stop the particle • Can measure energy of neutral particles using calorimetry

Energy Measurement – Regions of Applicability

Measuring Velocity • Use a process such as Cerenkov radiation or transition radiation where the threshold/intensity of the radiation depends on the velocity of the particle • Cerenkov radiation: angle and intensity are functions of b • Transition radiation: intensity is a function of g (useful for highly relativistic particles) • dE/dx by ionization ( already mentioned)

Sources of measurement error • Fluctuations of underlying physical processes • “Statistical” fluctuations of numbers of quanta or interactions • Variation in the gain process • Noise from electronics etc.

Fluctuation in dE/dx by Ionization

Fluctuation in dE/dx by Ionization • Up to now we have discussed the mean energy lost by a charged particle due to ionization. • The actual energy lost by a particular particle will not in general be the same as the mean. • dE/dx due to a large number of random interactions • Distribution is not Gaussian.

Fluctuation in dE/dx by Ionization • Distribution of dE/dx usually called the “Landau Distribution”

Fluctuation in dE/dx – Gaussian Peak • Most interactions involve little energy exchange and there are many of them. • The total energy loss from these interactions is a Gaussian (central limit theorem)

Fluctuation in dE/dx – Gaussian Peak • For a Gaussian distribution resulting from N random events the ratio of the width/mean  1/N • Increasing the thickness of the detector decreases the relative width of the Gaussian peak: • (from Bethe)

Fluctuation in dE/dx – High Energy Tail • The probability of a interaction that involves a significant fraction of the particles energy is low. However such interactions produce a large signal in the medium.

Fluctuation in dE/dx – High Energy Tail • Energy loss is in the form of “d-rays” –scattered electrons with appreciable energy. • Energy deposited in a thin detector can be different from the energy lost by the particle – the d-electron can have enough energy to leave the detector. • Depending on the thickness of the detector there may not be any d-electrons produced.

dE/dx – High Energy Tail • Because of the high energy tail increasing the thickness of the detector does not improve the dE/dx resolution much. • Relative width of Gaussian peak reduces, so would expect to get better estimate of mean dE/dx, but…. • Probability of high energy interaction rises, so tail gets bigger. • Usual method of measuring dE/dx is to take several samples and fit distribution (or just discard values far from Gaussian peak)

Multiple Scattering Deflection of a charged particle by large numbers of small angle scatters.

Multiple Scattering • Looking at dE/dx from ionization, ignore nuclei. • Energy transfer small compared to scattering from (lighter) electrons. • However, scattering from nuclei does change the direction of the particles momentum, if not its magnitude. • Deflection of particle’s path limits the accuracy with which the curvature in a magnetic field can be determined, and hence the momentum measured.

“Single Scattering” • Deflections are in random directions • “Drunkards Walk” • Total deflection from N collisions  N • The angular deflection caused by a single collision is well modelled by the Rutherford Scattering formula: ds/dW  1/q4  ds/dq  1/q3 Most probable scatter is at small angle

Multiple Scattering • RMS angular deflection, projected onto some plane: • RMS deflection  x • Length scale is the radiation length X0

Multiple Scattering – Probability Distribution • Small scattering angles - many small scatters. Gaussian • Large scattering angles from single large scatters. Probability  1/q3

Quantum Fluctuations • A signal consists of a finite number of quanta (electrons, photons,….) • If at some stage in detection chain the number of quanta drops to N then the relative fluctuation in the signal will be: • NB. Any subsequent amplification of the signal will not reduce this relative fluctuation

Quantum Fluctuations – Poisson Distribution • If the number of quanta is small then the probability of producing m quanta when the average is n is: • Probability of producing no signal: Efficiency of detector reduced by (1- e-n)

Quantum Fluctuations –Fano Factor • If the energy deposited by a particle is distributed between many different modes, only a small fraction of which give a detectable signal then the Poisson distribution is applicable. • E.g. scintillation detector: small fraction of deposited energy goes into photons. Only few photons reach light detector.

Quantum Fluctuations: Fano Factor • If most of deposited energy goes into the signal then Poisson statistics are not applicable. • E.g. Silicon detector – energy can either cause an electron-hole pair (signal detection and most likely process) or phonons. • In this case the fractional standard deviation: • F is the “Fano factor” (F ~ 0.12 for Si detector)

Electronic Noise • Most modern detectors produce and electrical signal, which is then recorded. • Electronic circuits produce noise – with careful design this can be minimized. • Consider different sources of intrinsic noise: • Johnson noise • Shot noise • Excess noise.

Johnson Noise • Appears across and resistor due to random thermal motion of charge carriers. • k : Boltzmanns constant • T : Temperature above absolute zero • B : Bandwidth ( range of frequency considered) • White noise spectrum (same noise power per root Hz at all frequencies)

Shot Noise • Fluctuation in the density of charge carriers ( “rain on a tin roof” ) • White noise spectrum

Excess Noise • Anything other than Johnson and shot noise. • Depends on details of electronic devices (e.g. transistors) • Often has a 1/f spectrum ( same power per decade of frequency )

“Typical” Detector Front-End Equivalent Circuit:

Noise: Dependence on Amplifier Capacitance. • The input resistance and capacitance of a detector “front end” form a low-pass filter which filters the Johnson noise from the input resistance:

Noise: Dependence on Amplifier Capacitance. • “Filtered” noise: • Noise spectrum : • Integrate over all frequencies to get total noise energy:

Noise: Dependence on Amplifier Capacitance. • Amplifier noise often expressed in terms of the number of electrons, DN, that would generate the same output. • Q = CV = e DN • Hence: • Johnson noise increases with the input capacitance of the pre-amplifier.

Overall Statistical Error • Depends on detector and the quantity measured, but… • For quantity like dE/dx which is estimated from the signal size: • S = A E • S=measured signal • E=primary signal , A=amplification

Overall Statistical Error • First term is fluctuation in production of interaction process ( e.g. Landau distribution of –dE/dx) .

Overall Statistical Error • Signal is made up of a number of quanta ( electrons, photons, ions, … ). • Second terms comes from the fluctuation in the number of quanta, ns , ( F is the Fano factor) .

Overall Statistical Error • In general, not all the quanta in the signal are collected – there is a “statistical bottle-neck” where the number of quanta, nh , is a minimum. • The contribution to the error due from this bottleneck is approximated by the third term: .

Overall Statistical Error • Many detectors have an amplification stage (e.g. drift chambers have gain due to avalanche near the anode wire) • The gain process will have some fluctuation, represented by the fourth term • Each quanta produces on average A quanta after amplification. .

Putting it all together - Particle Detectors