CERN Summer Student Lectures 2004 Detectors Particle interaction

CERN Summer Student Lectures 2004 Detectors ® Particle interaction with matter and magnetic fields ® Tracking detectors ® Calorimeters ® Particle Identification Olav Ullaland / PH department / CERN

These lectures in Detectors are based upon: John David Jackson Classical Electrodynamics John Wiley & Sons; ISBN: 047130932 X Dan Green The Physics of Particle Detectors Cambridge Univ Pr (Short); ISBN: 0521662265 Fabio Sauli Principles of Operation of Multiwire Proportional and Drift Chambers CERN 77 -09 Christian Joram Particle Detectors Lectures for Postgraduates Students, CERN 1998 CERN Summer Student lectures 2003 A good many plots and pictures from http: //pdg. web. cern. ch/pdg/ http: //www. britannica. com/ Other references are given whenever appropriate. Help from collaborators is gratefully acknowledged. Disclaimer The data presented is believed to be correct, but is not guaranteed to be so. Erich Albrecht, Tito Bellunato, Ariella Cattai, Carmelo D'Ambrosio, Martyn Davenport, Thierry Gys, Christian Joram, Wolfgang Klempt, Martin Laub, Georg Lenzen, Dietrich Liko, Niko Neufeld, Gianluca Aglieri Rinella, Dietrich Schinzel and Ken Wyllie

Some units which we will use and some relationships that might be useful. energy E: momentum p: mass m 0: measured in e. V/c 2 1 e. V is a small energy. 1 e. V = 1. 6· 10 -19 J mbee = 1 g =5. 8· 1032 e. V/c 2 vbee = 1 m/s Ebee = 10 -3 J = 6. 25 · 1015 e. V ELHC = 14 · 1012 e. V However, LHC has a total stored beam energy 1014 protons 14 · 1012 e. V 108 J or, if you like One 100 T truck at 100 km/h C. Joram, SSL 2003

Cross section s or the differential cross section ds/d. W is an expression of the probability of interactions. Beam spot area A 1 Beam spot area A 2 F 2=N 2/t F 1=N 1/t The interaction rate, Rint, is then given as: s has the dimension area. 1 barn = 10 -24 cm 2 The luminosity, Target n. A: area density of scattering centers in the target , is given in cm-2 s-1 Interactions Incident beam C. Joram, SSL 2003

To do a HEP experiment, one needs: A theory and an Idefix Clear and easy to understand drawings and a cafeteria A tunnel for the accelerator and magnets and stuff and a cafeteria Easy access to the experiment Lots of collaborators and a cafeteria Data analysis and a Nobel prize

OK, let us start

Turn of a century. 1900 Cloud Chamber radiation detector, originally developed between 1896 and 1912 by the Scottish physicist C. T. R. Wilson, that has as the detecting medium a supersaturated vapour that condenses to tiny liquid droplets around ions produced by the passage of energetic charged particles, such as alpha particles, beta particles, or protons. Turn of another century. 2000 NA 49 CERN A study of the production of charged hadrons (pi+-, K+-, p, pbar), and neutral strange particles (K 0 s, lambdabar), in a search for the deconfinement transition predicted by lattice QCD. Uses two large volume, fine granularity Time Projection Chambers (TPC's), and two intermediate size TPC's for vertex tracking of neutral strange particle decays. Also performs high precision measurements of particle production and correlations in proton-proton and proton-nucleus reactions. Central collision of lead projectile on a Lead nucleus at 158 Ge. V/nucleon as measured by the four large Time Projection Chambers (TPC) of the NA 49 experiment. > 1000 tracks

Les notes de Henri Becquerel 24 février 1896 The experimental set-ups are not what they used to be!

General (and nearly self evident) Statements è Any device that is to detect a particle must interact with it in some way. è If the particle is to pass through essentially undeviated, this interaction must be a soft electromagnetic one. http: //cmsdoc. cern. ch/ftp/TDR/TRACKER/tracker_tdr. html

A word of encouragement: This detector can't be built (without lots of work) Breidenbach, M; Stanford, CA : SLAC, 30 Aug 2002. - 4 p Abstract: Most of us believe that e+ e- detectors are technically trivial compared to those for hadron colliders and that detectors for linear colliders are extraordinarily trivial. The cross sections are tiny; there approximately no radiation issues (compared to real machines) and for linear colliders, the situation is even simpler. The crossing rate is miniscule, so that hardware triggers are not needed, the DAQ is very simple, and the data processing requirements are quite modest. The challenges arise from the emphasis on precision measurements within reasonable cost constraints.

Let us make a simple and visual experiment first. We do not need much: An accelerator A detector A trigger system CERN photo 1964 A read-out system A pattern recognition system A data storage system

Cosmic rays are mysterious streams of extremely fast moving subatomic particles (mainly protons and electrons) produced in space. Astronomers don't know precisely where all these particles come from. The sun is a known source of cosmic rays which are produced by high energy explosions (solar flares) in the sun's atmosphere, but the amount of cosmic rays emitted by the sun is too low to account for all the cosmic rays which strike earth. Astronomers for a long time have suspected that supernova explosions might be an important source of cosmic rays in the Galaxy. In a supernova, an enormous amount of material is exploded from a dying star; as this material encounters the surrounding gas in the galaxy, it produces a strong shock which might accelerate protons and electrons into cosmic rays. Supernova 1987 a Fireball Resolved Credit: C. S. J. Pun & R. Kirshner, WFPC 2, HST, NASA Comet Hyakutake and a Solar Flare Credit: G. Brueckner and the LASCO Team, SOHO, ESA, NASA

DANGER COSMIC This experiment with cosmic rays at the Jungfraujoch was the first practical involvement of CERN into particle physics. CERN photo 1955

Simple, is it not? Is that all? Then you do not need me.

Some (little) theory. Let an electron fall in a constant electric field. If an electron creates a new electrons in a path length of 1 cm in the field direction, then, after a distance x where n 0 is the initial electron concentration. a is the First Townsend Coefficient. We can also write Where V is the voltage drop and V 0 is a constant that is needed because the energy distribution becomes steady only after the electrons have travelled a certain distance from the cathode We now have an amplification process and we have positive ions and electrons. When a beam of positive ions strikes a surface, secondary electron emission is likely to occur. We then have to modify the current: g is the Second Townsend Coefficient will also include other secondary processes in the gas, metastable ions, ionic collisions, photons, space charge. . .

What do we have and what do we see. S. C. Brown, Introduction to Electrical Discharges in Gases, 1966

What is an electrical discharge. We have the "normal" Paschen curves and we have the abnormal In addition, all these special cases

The a - processes alone can not produce a break-down in a DC field as the produced electrons are continuously swept away. Assume that the space charge takes the form of a sphere of radius ra , then the field is given by When Es=E, the avalanche stops growing, but the velocity of the electrons is unaffected. a neutral plasma is left behind Plasma = Conductor a secondary avalanche will therefore travel with a much enhanced speed. a streamer is formed towards the cathode When the streamer hits the cathode, anode and cathode are connected with a conductor which breaks down in form of a spark. Formation lag time in the range of ns. Spark = Lightning lightning speed 107 m/s

Particle interaction with matter and magnetic fields. Things we need to know before we proceed.

Rutherford Scattering (non relativistic) Angular deflection is then where and b is the impact parameter Integrating over b N 0 n t number of beam particles target material in atoms/volume target thickness

Qcm > Qmin since there is a screening of the electric field of the atom. where a 0 is the first Bohr radius for a single scattering

Rutherford was astounded by the results of bombarding gold foil with alpha particles (helium nuclei): "It was as though you had fired a fifteen-inch shell at a piece of tissue paper and it had bounced back and hit you. " Ernest Rutherford and Hans Geiger with apparatus for counting alpha particles, Manchester, 1912 (Source: Science Museum)

Multiple Coulomb Scattering (after Rutherford) Energy Transfer = Classic Rutherford If Energy > Ionization Energy electron escape atom < No energy transfer where the sum is taken over all electrons in the atom for which the maximum energy transfer is greater than the ionization energy. Substituting in the maximum (non relativistic) energy transfer: Excitation energies (divided by Z) as adopted by the ICRU [Stopping Powers for Electrons and Positrons, " ICRU Report No. 37 (1984)]. Those based on measurement are shown by points with error flags; the interpolated values are simply joined. The solid point is for liquid H 2 ; the open point at 19. 2 is for H 2 gas. Also shown are the I/Z = 10 ± 1 e. V band an early approximation.

Stopping power at minimum ionization for the chemical elements. The straight line is fitted for Z >6. A simple functional dependence is not to be expected, since (d. E/dx) depends on other properties than atomic number.

Current wisdom on Bethe-Bloch for A=1 g/mol

Range of particles in matter. Poor man’s approach: Integrating d. E/d. X from Rutherford scattering and ignoring the slowly changing ln(term), Range is approximately proportional to the kinetic energy square at low energy and approximately proportional to the kinetic energy at high energy where the d. E/d. X is about constant.

Bremsstrahlung and Photon Pair Production. Impact parameter : b (non-relativistic!) Peak electric field prop. to e/b 2 Characteristic frequency c 1/ t v/2 b Radiative Process Insert Ng : photon density or Insert the Thomson cross section s. B 0. 58 mb * Z 2

Radiative Energy Loss. Define X 0 as the Radiative Mean Path. X 0 : Radiation Length Hey!! I just asked how many X 0 you had up front

The multiple scattering angle can now be expressed in units of X 0 and Introduce the characteristic energy

Energy deposit by 1 Me. V electrons in 0. 53 mm of silicon The most probable energy loss of an electron of energy 1 Me. V in the Si layer is around 200 ke. V. However, due to the multiple scattering and delta ray production the primary electron can deposit more energy or even it can be completly absorbed in the detector (in about 4 % of the cases). Electrons of energy 100 Me. V have been tracked in aluminium and the longitudinal (z) and tranverse (r) distances travelled by the electrons have been plotted. http: //wwwinfo. cern. ch/asd/geant 4/reports/gallery/electromagnetic/edep/summary. html

Fractional energy loss per radiation length for electrons and positrons in lead. Critical Energy, Ec , when Bremsstrahlung = Ionization

Photon total cross sections as a function of energy in carbon and lead, showing the contributions of different processes spe= Atomic photo-effect (electron ejection, photon absorption) scoherent = Coherent scattering (Rayleigh scattering-atom neither ionised nor excited) s incoherent = Incoherent scattering (Compton scattering off an electron) kn = Pair production, nuclear field ke = Pair production, electron field snuc = Photonuclear absorption (nuclear absorption, usually followed by emission of a neutron or other particle)

Bremsstrahlung Pair production

W Fe Cu Al Pb Sn glass G 10

Charged Particles in Magnetic Fields. Dipole Bending Magnet. Quadrupole lens. Sextupole correction lens. Rare Earth Permanent Magnet. Low -insertion. Beam Transport System. Spectrometer Dipole.

Dipole Bending Magnet. Rectangular bending magnet. The initial and final displacement and divergence (x 1, x 1’), (x 2, x 2’) is defined with respect to the central particle of the beam. (xi’=dxi/dz) It is usual to operate the magnet symmetrical: a 0= 0=f/2 k. Gm/Ge. V/c Quadropole Magnet. S N R N S xy=R Bx=ky By=kx Field Gradient Assume a simple rectangular model. k z 0 d Depending on the plane ( XZ or YZ), the field is either focusing or defocusing.

Thin Lens Approximation. + no fringe field d=effective length pole-length + g*R where g 1 drift length * instantaneous change in divergence * drift length Focusing Defocusing

The Velocity Filter SHIP is an electromagnetic separator, designed for in-flight separation of unretarded complete fusion reaction products. The main subjects of investigation are alpha-, protonemitting and spontaneously fissioning nuclei far from stability with halflives as short as microseconds and formation crosssections down to the picobarn region.

Analog Simulation of the Particle Trajectory. Floating Wire. Take a magnet. Install a (near) mass-less nonmagnetic conductive wire. Let the wire pass over a (near) frictionless pulley. Add weight on one end of the wire and fix the other. Add current through the wire. The central momentum is then given as p(Ge. V/c) 3 10 -3 M (g)/i(A) One can also use: K. R. Crandall “TRACE: An Interactive Beam-Transport Program, ” or MAFIA, Solution of MAxwell's equations using a Finite Integration Algorithm. or something similar. But floating wire is more fun.

Annihilation of an antiproton in the 80 cm Saclay liquid hydrogen bubble chamber. A negative kaon (K- meson) and a neutral kaon (K 0 meson) are produced in this process as well as a positive pion (p+ meson).

Momentum Measurement and Magnetic Fields. Solenoidal magnetic field. ALEPH event. WW -> 4 jets With B in tesla, momentum in Ge. V and R in m or

Momentum measurement can also be done by measuring the multiple scattering.

Charged particles do things (particularly if they are moving). unit vector along It is well known that accelerated charges emit electromagnetic radiation. J. D. Jackson Classical Electrodynamics After some manipulation of the 4 -vector potential caused by a charge in motion, it can be shown: Velocity field acceleration field transverse to the radius vector

Let us assume that the charge is accelerated and the observer is in a frame where the velocity v<<c (we go classic!) The energy flux The radiated power / unit solid angle The Larmor equation The Lorentz equivalent expression That is linear acceleration P negligible

Circular acceleration r Energy loss/revolution Take one LEP 2 Ge. V 1 e. V=1. 6 10 -19 J 3. 2 10 -10 J 90 ms 0. 3 10 -5 W/particle 1011 particles/bunch 0. 3 106 W/bunch

The angular distribution of the energy loss for a circular acceleration which is the Larmor equation (again). v and independent of the vectorial relationship between

Synchrotron radiation spectrum as function of frequency. Circular motion. The critical frequency beyond which there is negligible radiation at any angle: Synchrotron Radiation Center University of Wisconsin Madison Synchrotron radiation is normally produced when electrons are deflected by bending magnets in an electron storage ring. An undulator combines 10 -100 bends, which enhances the spectral brightness by a factor of 10 -10, 000. The highest enhancements are achieved when the electron beam and the undulator magnets are precise enough that the radiation from all bends adds up coherently, thereby enhancing the brightness by the square of the added amplitudes. View into the light beam emitted by an undulator

We will now go on to detectors