Transcript transparencies - Indico

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: 047130932X
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.
2 2
E  p c  m02 c 2
2
energy E:
momentum p:
mass m0:
v

c
measured in eV
measured in eV/c
measured in eV/c2
0    1
E  m0c
2

1
1 
p  m0c
2
1     
pc

E
1 eV is a small energy.
1 eV = 1.6·10-19 J
mbee = 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 energy
1014 protons  14 · 1012 eV  108 J
or, if you like
One 100 T truck
at 100 km/h
C. Joram, SSL 2003
Cross section.
Cross section s or the differential cross section ds/dW
is an expression of the probability of interactions.
Beam spot
area A1
Beam spot
area A2
F2=N2/t
F1=N1/t
The interaction rate, Rint, is then given as:
N1 N 2
Rint 
At
 sL
s has the
dimension area.
1 barn = 10-24 cm2
The luminosity,
Target
nA: area
density of
scattering
centers in
the target
L
, is given in cm-2s-1
Interactions
N scat (, F )  N incn A dW

ds
N incn A dW
dW, F 
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
NA49 CERN
A 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.
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
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
 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
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 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.
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 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
DANGER
COSMIC
This experiment
with cosmic rays at
the Jungfraujoch
was the first
practical
involvement of
CERN into particle
physics.
CERN photo 1955
Anode
Cathode
Q
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,
ax
after a distance x
n  n0 e
where n0 is the initial electron concentration.
a is the First
Townsend Coefficient.
 V V0 
n  n0 e
We can also write
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:
ax
i0e
i
1   eax  1

 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.
E1 > E0
-
E2 < E0
+
E3 > E0
E0
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
d
r
h
The a - processes alone can not produce a break-down in a
DC field as the produced electrons are continuously swept
away.
ad
Assume that the space charge takes
e
the form of a sphere of radius ra ,
Es  2
then the field is given by
r
a
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 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)
r2
r1
m1, Z1e, v0

b
r12
m2, Z2e
m1  m2 Z1Z 2 e 2
r 1  r 2  r 12 
r
3 12
m1m2 40 r12
Angular deflection is then

K
tg CM  2
2
v0 b
Z1Z 2 e 2
where K 
40 mr
mr 
m1m2
m1  m2
and b is the impact parameter
Integrating over b
N0
dN
2 2 4



nt
Z
1 Z2 e
2 2
dW 256  0
N0
n
t
number of beam particles
target material in atoms/volume
target thickness

1
1
2

2 2
1 0
mv
1
sin 4
CM
2
cm > min
since there is a screening of the electric field of the atom.
  min  
2 Za
pva0
where a0 is the first Bohr radius
Upper and Lower limits for single scattering angle.
Proton in 0.1 g/cm2 at Z=13
upper lower
1.E-03
1.E-04
1.E-05
1.E-06
100
1000
10000
Momentum(MeV/c)
  2   2 2min ln
 max
 min
for a single scattering
2
N dx  2Za 
 2MS   N scatterings   2   0
2 
 ln() 
A
p

c



1

sin
2
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)
Multiple Coulomb Scattering (after Rutherford)
Energy Transfer = Classic Rutherford
If Energy > Ionization Energy  electron escape atom
<
 No energy transfer
Emax
dE
NZ12e 4 Z

ln
2
2 
dx 80 me v0 i  Z '
Ii
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:
2 2
2
m
dE
NZ e
r v0

ln
2
2 
dx 80 me v0 i  Z ' me I i
2 4
1
Z
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.
Ionization Loss -1/  dE/dx for protons in Mev cm2 /g
100 Momentum (MeV/c)
100
1000
10000
Be
Ionization Loss
C
Al
Cu
Pb
Air
H
10
1
1
10
100
1000
10000
100000
Kinetic Energy (MeV)
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.
Current wisdom on Bethe-Bloch
2 2 2

2
m
c
  Tmax
dE
Z
1
1

2
2
e
 Kz
ln
  
2 
2
dx
A  2
2
I
Tmax
2me c 2  2 2

1  2 me M  (me M ) 2
Tmax (MeV)
K
 4N A re2 me c 2 / A
A
 0.307075MeVg 1cm 2
for A=1 g/mol
1.E+05
1.E+04
1.E+03
1.E+02
1.E+01
1.E+00
1.E-01
1.E-02
1.E-03
1.E-04
10
100
1000
Momentum proton (MeV/c)
10000
100000
Range  R 
Const. 2
EKinetic
2 2
Z1 m1
100000
Range in Iron (g cm -2)
Range of particles in matter.
Poor man’s approach:
Integrating dE/dX from
Rutherford scattering and
ignoring the slowly changing
ln(term),
10000
as energy
1000
as energy square
100
10
1
10
100
1000
10000
Kinetic Energy Proton (MeV)
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.
100000
Bremsstrahlung and Photon Pair Production.
Ze
e
e
Ze
Impact parameter : b
(non-relativistic!)
Peak electric field prop. to e/b2
Characteristic frequency c1/tv/2b
Radiative Process
dU
dU
a
 dE 
dU   du   
d 
 4 2 [ln()]
 d  2bdb  
d
d

 d 
2
Insert N : photon density
dN  ( )
d

2a 1 1
  
2
[ln()]
Insert the Thomson cross section
s T hom son 
8
(a ) 2
3
2
dN
ds B
Z
a

 Z2
sT 
(a ) 2 [ln()]
d
d

or
sB  0.58mb  Z 2
Hey!!
I just
asked
how many
X0 you
had up
front
Radiative Energy Loss.
dE  
E
0
N 0 dx ds B

d
A
d
Define X0 as the Radiative Mean Path.
X0 : Radiation Length
1
1 dE

X 0 E dx
2
Radiation Length X0 (g/cm )
X 01
2
16 N 0 2
Z

Z a (a ) 2 [ln()] 
3 A
A
100
A
 2
Z
10
1
1
10
Z
100
The multiple scattering angle can now be expressed in units of X0
2
N dx  2Za 
 2MS   N scatterings   2   0
2 
 ln() 
A
p

c


and
X
1
0
16 N 0 2
Z2
2

Z a (a ) [ln()] 
3 A
A
Introduce the characteristic energy ES  me c 2 

2
MS
ES

p
4
a
 21.205MeV
dx ES

t
X 0 p
Mean Multiple Scattering
Angle
Pions in 10%X0
0.1
0.01
0.001
100
1000
Pion momentum (MeV/c)
10000
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 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 MeV
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/geant4/reports/gallery/electromagnetic/edep/summary.html
Fractional energy loss per radiation length for electrons and
positrons in lead.
Critical Energy, Ec , when Bremsstrahlung = Ionization
Critical energy Ec (MeV)
1000
100
10
Z
-0.8844
1
1
10
Z
100
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)
e
Ze
e
ee
+
Ze
Bremsstrahlung
Ze
Ze
Pair production
7
s pair  s B  .58mb  Z 2
9
100
Fe
Elasticity constant (10
10
2
N/m )
W
Cu
10
glass
Al
Pb Sn
G10
1
0.1
0.1
1
10
Radiation length X0 (cm)
100
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.

L
x1'
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:
 a00/2
B
x1
x2'
x2
a
l1 R 
l2

z
z
 x2  cos  cosa
 x    0
 2 
R sin a     x1   x2  1 R sin    x1 
       
  x     0.03BL / p
cosa
x
x
0
1
cos 
 1 
 1  2  
kGm/GeV/c
Quadropole Magnet.
Assume a simple rectangular model.
4
3
1
0
-00004 -00003 -00002 -00001
N
2
R
00000
00001
00002
-1
-2
N
-3
S
k
1.2
00003
00004
Field Gradient
S
xy=R
Bx=ky
By=kx
0.8
0.6
0.4
z
0.2
0
-1
-4
1
-0.5
0
0
0.5
1
1.5
2
d
Depending on the plane ( XZ or YZ), the field is either
focusing or defocusing.
sin d 

cos

d
M Focu sin g  
 
  sin d cos d 


sinh d 

cosh

d
M Defocusin g  
 
 sinh d cosh d 


 2 (m 2 )  3
k (kG / cm)
p(GeV / c)
Thin Lens Approximation.
+ no fringe field  d=effective length  pole-length + g*R where g1
 drift length * instantaneous change in divergence * drift length
1 s   1 0 1 s  1  s f
0 1  f 1 1 0 1   f 1



 
s2 
1
s
s
f
f



f 1   sin d
Focusing
Defocusing
1  cos d
 sin d
f 1   sinh d
s
s
 1  cosh d
 sinh d
2
f 1 




d
d 0
d
s 


2
d 0
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.
B
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(GeV/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 (K0 meson) are
produced in this process as well as a positive pion (+ meson).
Momentum Measurement and Magnetic Fields.
Solenoidal magnetic field.
ALEPH event.
WW -> 4 jets
B
a
With B in tesla, momentum
in GeV and R in m
p
q
BR sin a
3
or
q BRT
p
3 sin a
Z
qe,p
RT
X
Y
C
S
qB  C 2 sin a
S 
p



3  8S
2 sin a 
Momentum measurement can also
be done by measuring the multiple
scattering.
Dense Material
X1
Y1
Y2
X2
Y3
X3
Multiple Scattering pions (mrad)
X4
8
7
6
5
4
3
2
1
0
High Precision Detector
Y4
X5
Y5
X6
Y6
2 GeV/c
3 GeV/c
4 GeV/c
0.1
0.2
0.3
0.4
0.5
0.6
Radiation Length (X0)
0.7
0.8
0.9
Charged particles do things
(particularly if they are moving).
n
unit vector along
  v( ) / c
x  r ( )
O
observer
R  x0  r0 ( 0 )
d 
1

dt
R
It is well known that
accelerated charges
emit electromagnetic
radiation.
J. D. Jackson
Classical
Electrodynamics
b
Q

n v
P'
R
P
vt
M
After some manipulation of the 4-vector potential caused by a
charge in motion, it can be shown:
B  n  E retarded

 
 



n
e n n    
E ( x, t )  e  2
 

3 2

(
1



n
)
R

 retarded c  1    n R

Velocity field

1
R2
E&B
retarded
acceleration field

1
R
transverse to the radius vector
n
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

e n n  
E accelerated  

c
R
 retarded

c
c
2
S
EB 
E n
4
4
dP
c
e2
2

RE 
n  n  
dW 4
4c


2
2
e2
2


v
sin

3
4c
The Larmor equation
The Lorentz equivalent expression

2 e 2  dp dp   2 e 2 6  2
 )2
P


(

)

(





3 m 2c 3  d d  3 c

 || 
That is linear acceleration
 P  negligible
Circular
acceleration


c

dp
1 dE
2 e 2 3 2 2 2 ec 4 4
  p 
P
  p 
 
d
c d
3 m 2c3
3 2
Energy loss/revolution
4
2
4e 2 3 4
 2 E (GeV )
E 
P
  

 E ( MeV )  8.85 10
1
c
3
 (m)
Take one LEP
E
E  100GeV
  27 10 2
3
1 eV=1.6 10-19 J
2 GeV
3.2 10-10 J
90 s
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
2
dP(t ' ) e

dW
4c
    ev
4c
1  n   
n  n    
2
2
 // 
5
2
e2
2




v
sin

1
3
4c
3
sin 2 
1   cos 5
which is the Larmor
equation (again).
200000
 =1.00005
210 5  dP(t)/d W
100000
 =2
250 dP(t)/d W
 =4
v
0
0
100000
200000
dP(t ' )
8 e 2v 2 8 

 

0
3
dW
 c
1   22
2

and

1
2 2

1


5
independent of the
vectorial relationship between
 & 
2
dI
d
Synchrotron radiation spectrum as function of frequency.
Circular motion.
The critical frequency
beyond which there is
negligible radiation at
any angle:
e
c
2
1
3
 E  c
 c  3 2 
 mc  
0
0.01
0.1

c
1
10
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