Olav Ullaland / PH department / CERN

Particle interaction with matterand magnetic fields

Tracking detectors Calorimeters Particle Identification

CERN Summer Student Lectures 2004Detectors

These lectures in Detectors are based upon:

John David Jackson Classical Electrodynamics

John Wiley & Sons; ISBN: 047130932X

Dan GreenThe Physics of Particle Detectors

Cambridge Univ Pr (Short); ISBN: 0521662265

Fabio SauliPrinciples of Operation of Multiwire Proportional and Drift Chambers

CERN 77-09

Christian JoramParticle Detectors

Lectures for Postgraduates Students, CERN 1998

CERN Summer Student lectures 2003

A good many plots and pictures fromhttp://pdg.web.cern.ch/pdg/http://www.britannica.com/

Other references are given whenever appropriate.

Help from collaborators is gratefully acknowledged.

DisclaimerThe 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 SchinzelandKen Wyllie

Some units which we will use and some relationships that might be useful.

220

222 cmcpE

energy E: measured in eVmomentum p: measured in eV/cmass m0: measured in eV/c2 10

c

v

11

12

E

pccmpcmE 0

20

1 eV is a small energy. 1 eV = 1.6·10-19 Jmbee = 1g =5.8·1032 eV/c2

vbee = 1 m/s Ebee = 10-3 J = 6.25 ·1015 eV

ELHC = 14 · 1012 eV

However, LHC has a total stored beam energy1014 protons 14 · 1012 eV 108 J

or, if you likeOne 100 T truckat 100 km/h

C. Joram, SSL 2003

Cross section.

Cross section or the differential cross section d/dis an expression of the probability of interactions.

=N1/t

=N2/t

Beam spot area A2

Beam spot area A1

The interaction rate, Rint, is then given as:

L

tA

NNR 21

int has the dimension area.1 barn = 10-24 cm2

The luminosity, , is given in cm-2s-1L

TargetnA: area density of scattering centers in the target

Incident beam

Interactions

dnNd

d

dnNN

Ainc

Aincscat

,

),(

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

Lots of collabor-ators

and a cafeteria

Easy access to the experiment

Data analysisand a

Nobel prize

OK, let us start

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 vapourthat condenses to tiny liquid droplets around ions produced by the passage of energetic charged particles, such as alpha particles, beta particles, or protons.

NA49 CERNA study of the production of charged hadrons (pi+-, K+-, p, pbar), and neutral strange particles (K0s, lambda, 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.

Turn of a century. 1900

Turn of another century. 2000

Central collision of lead projectile on a Lead nucleus at 158 GeV/nucleon as measured by the four large Time Projection Chambers (TPC) of the NA49 experiment.

> 1000 tracks

The experi-mental set-ups are not what they used to be!

Les notes de Henri Becquerel 24 février 1896

General (and nearly self evident) Statements

Any device that is to detect a particle must interact with it in some way. 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

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 are 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.

A word of encouragement:

Let us make a simple and visual experiment first.

We do not need much:

An accelerator

A detectorA trigger system

A read-out systemA pattern recognition systemA data storage system

CERN photo 1964

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 1987a Fireball Resolved Credit: C. S. J. Pun & R. Kirshner, WFPC2, HST, NASA

Comet Hyakutake and a Solar Flare Credit: G. Brueckner and the LASCO Team, SOHO, ESA, NASA

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

DANGERCOSMIC

Anode

CathodeQ

Is that all?Then you do not need

me.

Simple, is it not?

Some (little) theory.

Let an electron fall in a constant electric field.If an electron creates new electrons in a path length of 1 cm in the field direction, then, after a distance x

xenn 0

where n0 is the initial electron concentration.

is the First Townsend Coefficient.

We can also write

00

VVenn

Where V is the voltage drop and V0 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:

110

x

x

e

eii

is the Second Townsend Coefficientwill also include other secondary processes in the gas, metastable ions, ionic collisions, photons, space charge ......

E0

E1>E0

E2<E0

E3>E0+

-

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

hd

r

and we have the abnormal

In addition, all these special cases

The - 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

2a

d

s r

eE

When Es=E, the avalanche stops growing, but the velocity of the electrons is unaffected.

a neutral plasma is left behindPlasma = Conductor

a secondary avalanche will therefore travel with a much enhanced speed.

a streamer is formed 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)

b

m1, Z1e, v0

m2, Z2e

r2r1

r12

123120

221

21

211221 4

rr

eZZ

mm

mmrrr

bv

Ktg CM

202

rm

eZZK

0

221

4

21

21

mm

mmmr

Angular deflection is then

where

and b is the impact parameter

Integrating over b

2422

0121

422

212

02

0

sin

11

256 CMvmeZZnt

N

d

dN

N0 number of beam particles n target material in atoms/volumet target thickness

cm > min since there is a screening of the electric field of the atom.

0min

2

pva

Z where a0 is the first Bohr radius

Upper and Lower limits for single scattering angle.

Proton in 0.1 g/cm2 at Z=13

1.E-06

1.E-05

1.E-04

1.E-03

100 1000 10000

Momentum(MeV/c)

up

per

low

er

min

max2min

2 ln2

for a single scattering

ln()2

22

022

cp

Z

A

dxNN sscatteringMS

Alpha particles in silver

1

10

100

1000

10000

100000

1000000

0 30 60 90 120 150 180

Mean angle of scattering

Relative number of

scattered

2sin

1

4

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)

Z

Zi ie I

E

vm

eNZ

dx

dE

'

max20

20

421 ln

8

Multiple Coulomb Scattering (after Rutherford)Energy Transfer = Classic RutherfordIf 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 H2 ; the open point at 19.2 is for H2 gas. Also shown are the I/Z = 10 ±1 eV band and an early approximation.

Z

Zi ie

r

e Im

vm

vm

eNZ

dx

dE

'

20

2

20

20

421 2

ln8

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 (dE/dx) depends on other properties than atomic number.

Ionization Loss -1/dE/dx for protons in Mev cm2/g

1

10

100

1 10 100 1000 10000 100000

Kinetic Energy (MeV)

Ioni

zatio

n L

oss

Be

C

Al

Cu

Pb

Air

H

100 Momentum (MeV/c) 100001000

21307075.0 cmMeVg AcmrNA

KeeA /4 22

2

2ln

2

11 22

max222

22

I

Tcm

A

ZKz

dx

dE e

for A=1 g/mol

Current wisdom on Bethe-Bloch

2

222

max )(21

2

Mm

Mme

ee

cmT

1.E-041.E-031.E-021.E-011.E+001.E+011.E+021.E+031.E+041.E+05

10 100 1000 10000 100000

Momentum proton (MeV/c)

Tm

ax (

MeV

)

1

10

100

1000

10000

100000

10 100 1000 10000 100000

Kinetic Energy Proton (MeV)

Range in Iron (g cm-2)

as energy square

as energy

Range of particles in matter.Poor man’s approach:Integrating dE/dX from Rutherford scattering and ignoring the slowly changing ln(term),

221

21

.KineticE

mZ

ConstRRange

Range is approximately proportional to the kinetic energy square at low energy and approximately proportional to the kinetic energy at high energy where the dE/dX is about constant.

Bremsstrahlung and Photon Pair Production.

Radiative Process

e Ze

Zee

Impact parameter : b (non-relativistic!)Peak electric field prop. to e/b2 Characteristic frequency c1/tv/2b

[ln()]422

2

d

dUd

d

dUbdbd

d

dEdudU

[ln()]112)(

2

d

dN

Insert N : photon density Insert the Thomson cross section

2hom )(

3

8 sonT

[ln()])( 22

2

Z

d

dNZ

d

dT

B

or

B 0.58mb Z 2

E

B dd

d

A

dxNdE

0

0

dx

dE

EX 11

0

A

ZZ

A

NX

22201

0 [ln()])(3

16

Radiative Energy Loss.

Define X0 as the Radiative Mean Path.X0 : Radiation Length

1

10

100

1 10 100

Z

Rad

iatio

n L

engt

h X

0 (g

/cm

2 )

2Z

A

Hey!!I just asked

how many X0 you had upfront

ln()2

22

022

cp

Z

A

dxNN sscatteringMS

A

ZZ

A

NX

22201

0 [ln()])(3

16

The multiple scattering angle can now be expressed in units of X0

and

Introduce the characteristic energy MeVcmE eS 205.2142

tp

E

X

dx

p

E SSMS

0

2

Pions in 10%X0

0.001

0.01

0.1

100 1000 10000

Pion momentum (MeV/c)

Mea

n M

ultip

le S

catte

ring

Ang

le

Energy deposit by 1 MeV electrons in 0.53 mm of silicon

The most probable energy loss of an electron of energy 1 MeV in the Si layer is around 200 keV. However, due to the multiple scattering and delta ray production theprimary electron can deposit more energy or even it can be completly absorbed in the detector (in about 4 % of the cases).

http://wwwinfo.cern.ch/asd/geant4/reports/gallery/electromagnetic/edep/summary.html

Electrons of energy 100 MeV have been tracked in aluminium and the longitudinal (z) and tranverse (r)distances travelled by the electrons have been plotted.

1

10

100

1000

1 10 100

Z

Crit

ical

ene

rgy

Ec

(MeV

)

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

-0.8844Z

Photon total cross sections as a function of energy in carbon andlead, showing the contributions of different processes

pe= Atomic photo-effect (electron ejection, photon absorption)coherent = Coherent scattering (Rayleigh scattering-atom neither ionised nor excited) incoherent = Incoherent scattering (Compton scattering off an electron)n = Pair production, nuclear fielde = Pair production, electron fieldnuc = Photonuclear absorption (nuclear absorption, usually followed by emission of a neutron or other particle)

e Ze

Zee

Bremsstrahlung Pair production

258.9

7ZmbBpair

Ze

Zee-

e+

0.1

1

10

100

0.1 1 10 100

Radiation length X0 (cm)

Ela

stic

ity c

onst

ant (

1010

N/m

2 )

W

Pb Sn G10

Fe

Cu

Alglass

Charged Particles in Magnetic Fields.

Dipole Bending Magnet. Quadrupole lens.

Sextupole correction lens.Rare Earth Permanent Magnet. Low -insertion.

Beam Transport System. Spectrometer Dipole.

l1 l2

L

R

B

zz

x1 x2x2'

x1'

Dipole Bending Magnet. Rectangular bending magnet. The initial and final displacement and divergence (x1,x1’), (x2,x2’) is defined with respect to the central particle of the beam.(xi’=dxi/dz)It is usual to operate the magnet symmetrical:

pBL

x

xR

x

x

x

xR

x

x/03.0

10

sin1

0

sin

1

1

2

2

1

1

coscos

coscos

2

2

kGm/GeV/c

-4

-3

-2

-1

0

1

2

3

4

-00004 -00003 -00002 -00001 00000 00001 00002 00003 00004

NS

N S

R

Quadropole Magnet.

xy=RBx=kyBy=kx

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.5 0 0.5 1 1.5 2

Fie

ld G

radi

ent

z

0 d

k

Assume a simple rectangular model.

dd

ddM

dd

ddM

gDefocu

gFocu

coshsinh

sinhcosh

cossin

sincos

sin

sin

Depending on the plane ( XZ or YZ), the field is either focusing or defocusing.

)/(

)/(3)( 22

cGeVp

cmkGkm

Thin Lens Approximation.+ no fringe field d=effective length pole-length + g*R where g1 drift length * instantaneous change in divergence * drift length

fs

fs

fs

f

ss

f

s

1

21

10

1

1

01

10

111

d

ds

df

d

ds

df

sinh

cosh1

sinh

sin

cos1

sin

1

1

Focusing

Defocusing

20

20

1

dd

d

s

df

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-, proton-emitting and spontaneously fissioning nuclei far from stability with halflives as short as microseconds and formation cross-sections down to the picobarn region.

Analog Simulation of the Particle Trajectory.Floating Wire.

Take a magnet.Install a (near) mass-less non-magnetic 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(GeV/c) 3 10-3 M (g)/i(A)

K. R. Crandall “TRACE: An Interactive Beam-Transport Program,”orMAFIA, Solution of MAxwell's equations using a Finite Integration Algorithm.or something similar.

One can also use:

But floating wire is more fun.

B

Annihilation of an antiproton in the 80 cm Saclay liquid hydrogen bubble chamber. A negative kaon (K- meson) and a neutral kaon (K0 meson) are produced in this process as well as a positive pion (+ meson).

Z

Y

X

B

qe,p

RT

Momentum Measurement and Magnetic Fields.

Solenoidal magnetic field.ALEPH event.WW -> 4 jets

sin3

BRq

p

sin3TBRq

p

With B in tesla, momentum in GeV and R in m

or

0

1

2

34

5

6

7

8

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Radiation Length (X0)

Mul

tiple

Sca

tterin

g pi

ons

(mra

d)

2 GeV/c 3 GeV/c

4 GeV/c

SC

sin28

sin

3

2 S

S

CqBp

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

Y1

Y2

Y3

Y4

Y5

Y6

Dense MaterialX1

X2

X3

X4

X5

High Precision Detector

X6

vn

R vt

R

PP'M

Oobserver

Q

b

dtd

rxR

cv

n

1

)(

/)(

000

Charged particles do things (particularly if they are moving).

unit vector along )(rx

After some manipulation of the 4-vector potential caused by a charge in motion, it can be shown:

retardedretarded

retarded

Rn

nn

c

e

Rn

netxE

EnB

1)1(),(

232

Velocity field acceleration field

2

1

R

R

1

BE & transverse to the radius vector n

It is well known that accelerated charges emit electromagnetic radiation.J. D. JacksonClassical Electrodynamics

Let us assume that the charge is accelerated and the observer is in a frame where the velocity v<<c(we go classic!)

The Lorentz equivalent expression

2262

32

2

)()(3

2

3

2

c

e

d

dp

d

dp

cm

eP

22

3

2222

2

sin444

44

vc

enn

c

eER

c

d

dP

nEc

BEc

S

R

nn

c

eE

retarded

daccelerate

The energy flux

The radiated power / unit solid angle

The Larmor equation

||

That is linear acceleration

P negligible

Circular acceleration

442

223

32

2

3

2

3

21

ecp

cm

eP

d

dE

cp

d

pd

c

Energy loss/revolution

)(

)(1085.8)(

3

42 42

143

2

m

GeVEMeVE

eP

cE

Take one LEP

GeVE 100

E

21027 3 2 GeV

3.2 10-10 J

0.3 10-5 W/particle

0.3 106 W/bunch

1 eV=1.6 10-19 J

90 s

1011 particles/bunch

5

2

3

2

//5

22

cos1

sin

414

)'(

c

ve

n

nn

c

e

d

tdP

The angular distribution of the energy loss for a circular acceleration

22

3

2

1sin

4v

c

e

which is the Larmorequation (again).

0

100000

200000

0 100000 200000

=1.000052 dP(t)/d

=2250 dP(t)/d

=4v

522

28

3

22

01

8)'(

c

ve

d

tdP

1

2

12 and independent of the

vectorial relationship between &

Synchrotron radiation is normally produced when electrons are deflected by bending magnets in anelectron storage ring. An undulator combines 10-100 bends, which enhances the spectral brightness by afactor of 10-10,000. The highest enhancements are achieved when the electron beam and the undulatormagnets are precise enough that the radiation from all bends adds up coherently, thereby enhancing thebrightness by the square of the added amplitudes.

View into the light beam emitted by an undulator

Synchrotron Radiation

Center University

of Wisconsin Madison

0

1

2

0.01 0.1 1 10

Synchrotron radiation spectrum as function of frequency.Circular motion.

c

ce

ddI

2

c

mc

Ec

3

23

The critical frequency beyond which there is negligible radiation at any angle:

We will now go on to detectors