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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 - PowerPoint PPT Presentation
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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
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