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Lecture 13: Detectors
•
Visual Track Detectors
•
Electronic Ionization Devices
•
Cerenkov Detectors
•
Calorimeters
•
Phototubes & Scintillators
•
Tricks With Timing
•
Generic Collider Detector
Useful Sections in Martin & Shaw:
Sections 4.3, 4.4, 4.5
Consider a massless qq pair linked by a rotating string with ends moving at the
speed of light. At rest, the string stores energy  per unit length and we assume
no transverse oscillations on the string. This configuration has the maximum
angular momentum for a given mass and all of both reside in the string - the
sheet 4 quarks have none. Consider one little bit of string at a distance r from the
middle, with the quarks located at fixed distances R. Accounting for the varying
velocity as a function of radial position, calculate both the mass, M, and
angular momentum, J, as a function of  and R.
3
At rest: dM/dr = k
In motion: dM/dr = gk
R
g = (1-b2)-½ = [1-(r/R)2]-½
Thus,
∫
M = 2k
= kRp
[1-(r/R)2]-½ dr
R
Similarly,
J = 2k
∫
vr [1-(r/R)2]-½ dr
0
In natural units
v = b = (r/R)
R
∫∫
= (2k/R)
r2 [1-(r/R)2]-½ dr
= kR2p/2
0
but M = kRp
thus, J = M2/(2pk)
From experimental measurements of J versus M (“Regge trajectories”) it is found
that  ∼ 0.18GeV2 when expressed in natural units. Convert this to an equivalent
number of tonnes.
~15
Now consider the “colour charge” contained within a Gaussian surface centred
around a quarks and cutting through a flux tube of cross sectional area A .
By computing an effective “field strength” (in analogy to electromagnetism),
derive an expression for the energy density of the string (i.e.  ) in terms
of the colour charge and the area A .
In analogy with EM:
Ec = rc/ec
Gaussian
surface
Flux
tube
Ec A = qc/ec
Ec = qc/(Aec)
Assume A ~ 1 fm2
k = energy/length = (energy density) x A
= qc2/(2Aec)
qc2/(4pecħc) = kA/(2pħc)
as ≈
(14.4x104 kg m/s2)(10-15m)2
2p (10-34 J s)(3x108 m/s)
= ½ ec Ec2 A
= 0.76
Lecture 13: Detectors
•
Visual Track Detectors
•
Electronic Ionization Devices
•
Cerenkov Detectors
•
Calorimeters
•
Phototubes & Scintillators
•
Tricks With Timing
•
Generic Collider Detector
Useful Sections in Martin & Shaw:
Section 3.3, Section 3.4
Wilson Cloud Chamber:
Antimatter
Anderson
1933
Evaporation-type Cloud Chamber:
Photographic Emulsions

p
Discovery of the Pion
(Powell et al., 1947)
e

e

DONUT (Direct Observation of NU Tau)
July, 2000
Bubble Chamber
Donald Glazer (1952)
Bubbles form at nucleation sites
in regions of higher electric fields
 ionization tracks
Bubble Chamber
Donald Glazer (1952)
Bubbles form at nucleation sites
in regions of higher electric fields
 ionization tracks
Steve’s Tips for Becoming a Particle Physicist
1) Be Lazy
2) Start Lying
3) Sweat Freely
4) Drink Plenty of Beer
Liquid superheated by sudden expansion
hydrogen,
deuterium,
propane
Freon
Bubbles allowed to
grow over 10ms
then collapsed during
compression stroke
Acts as both
target & detector
Difficult to trigger
Track digitization
cumbersome
High beam
intensities
swamp film
Mechanically
Complex
Spatial resolution
100200 m
Slow repetition rate
Ionization Detectors
Electric field imposed to prevent recombination
Medium must be chemically inactive (so as not to gobble-up drifting electrons)
and have a low ionization threshold
(noble gases often work pretty well)
heavily
ionizing
particle
minimum
ionizing
particle
signal smaller
than initially
produced pairs
signal reflects
total amount
of ionization
initially free electrons
accelerated and further
ionize medium
such that signal is
amplified proportional
to initial ionization
acceleration causes
avalance of pairs
leads to discharge
where signal size
is independent of
initial ionization
continuous
discharge
(insensitive
to ionization)
Proportional
Counter
Typical Parameters
rin = 10-50 m
E = 104 V
Amplification = 105
E(r) =
V0
r log(rout/rin)
Multiwire Proportional Counter (MWPC)
Typical wire
spacing ~ 2mm
George Charpak
use of MWPC in
determination of
particle momenta
Drift Chamber
Field-shaping wires provide
~constant electric field so
charges drift to anode wires with
~constant velocity (~50mm/s)
Timing measurement compared
with prompt external trigger can
thus yield an accurate position
determination (~200m)
Time Projection Chamber (TPC)
One Application of a TPC:
n  p + e + e
n  p + e + e
but sometimes...
''double bdecay"
but what if
e = e ?
(Majorana particle)
then the following
would be possible:
n  p + e + e
e + n  p + e
''neutrinoless double bdecay"
 occurs as a single
quantum event
 within a nucleus
Example of a radial drift chamber (''Jet Chamber")
Angular segment of
JADE Jet Chamber
Reconstruction of 2-jet
event in the JADE
Jet Chamber at DESY
Spark Chamber
Silicon Strip Detector
etched
electron-hole pairs instead of electron-ion pairs
3.6 eV required to form electron-hole pair
 thin wafers still give reasonable signals and good timing (10ns)
Spatial resolution 10m
CDF Silicon Tracking Detector
Cerenkov
Radiation
Cerenkov
Radiation
cosC = ct/(nvt) = 1/(nb)
vt

(c/n)t
d2Ng
dxdE
=
az2
ℏc
(
1 
# photons ∝ dE
1
)
b2n2
∝ d/2
 blue light
Threshold Cerenkov Counter:
discriminates between particles of similar momentum
but different mass (provided things aren’t too relativistic!)
m1 , b1
m2 , b2
( 1 - 1/(b22n2) ) = ( 1 - b12/b22)
just below
threshold
= (b22 b2)/b22
1/(nb1) = 1
1/n2 = b12
b2
[(1m22/E22)  (1m12/E12)]
=
=1
= 1  m2/E2
1/g2
(1m22/E22)
=
≃
length of radiator needed increases
as the square of the momentum!
(m12/E12  m22/E22)
(1 m22/E22)
(m12  m22)
(E2 m22)
= (m12  m22)/p2
Medium n1
helium
CO2
pentane
aerogel
H2O
glass
g (thresh)
3.3x105
123
4.3x104
34
1.7x103
17.2
0.0750.025 2.74.5
0.33
1.52
0.750.46
1.221.37
Muon Rings
liquid
radiator
Ring Imaging CHrenkov
detector
gaseous
radiator
light detectors
on inner surface
Calorimeters
Above some ''critical" energy, bremsstrahlung
and pair production dominate over ionization
EC ~ (600 MeV)/Z
Assume each electron with E > EC
undergoes bremsstrahlung after
travelling 1 radiation length, giving
up half it’s energy
Assume each photon with E > EC
undergoes pair production after
travelling 1 radiation length, dividing
it’s energy equally
t=0
1
2
3
4
Depth in radiation lengths
Neglect ionization loss above EC
Assume only collisional loss below EC
# after t radiation lengths = 2t
Avg energy/particle:
Maximum development
will occur when E(t) = EC :
tmax =
log(E0/EC)
log(2)
E(t) = E0/2t
Nmax = E0/EC
 Depth of maximum increases logarithmically with primary energy
 Number of particles at maximum is proportional to primary energy
 Total track length of particle is proportional to primary energy
 Fluctuations vary as ≃ 1/N ≃ 1/E0
Typically, for an electromagnetic calorimeter:
Scale is set by radiation length: X0 ≃ 37 gm/cm2
For hadronic calorimeter, scale
set by nuclear absorption length
iron  nuc = 130 gm/cm2
lead  nuc = 210 gm/cm2
~ 30% of incident energy is lost
by nuclear excitations and the
production of ''invisible" particles
E
E
0.5
≃
EGeV
E
E
≃
0.05
EGeV
Examples of Calorimeter Construction:
Photomultiplier Tubes (PMTs)
A Typical ''Good" PMT:
quantum efficiency30%
collection efficiency80%
signal risetime2ns
Scintillator
Inorganic
Usually grown with small admixture of impurity centres.
Electrons created by ionization drift through lattice,
are captured by these centres and form an excited state.
Light is then emitted on return to the ground state.
Most important example  NaI (doped with thallium)
Organic
Cons: relatively slow time
response (largely due
to electron migration)
Excitation of molecular energy levels.
Medium is transparent to produced light.
Why isn’t light self-absorbed??
Pros: very fast
Cons: smaller light
output
potential energy
Pros: large light output
excited
state
ground
state
interatomic spacing
Some Commonly Used Scintillators:
Scintillator
organic
anthacene
toluene
polystyrene
{
{
Relative
light yield
Decay
max
time (ns) (nm)
Density
(gm/cm3)
1.0
0.7
0.3
25
3
3
450
430
350
1.25
0.9
0.9
2.2
2.4
0.5
250
900
300
410
550
480
3.7
4.5
7.1
+ p-terphenyl
inorganic
NaI (Tl)
CsI (Tl)
BGO
(Bi4Ge3O12)
some ways of coupling plastic
scintillator to phototubes to
provide fast timing signal :
Time Of Flight (TOF): An Application of Promt Timing
(used to discriminate particle masses)
t = Lc/b
t = Lc (1/b/b2)
b2 = 1  1/g2
/b = ( 1  1/g2 )1/2
≃ 1  1/(2g2)
t ≃ Lc/2 (1/g22/g2)
= Lc/2 ( m22/E22  m12/E12 )
≃ Lc/2 ( m22  m12 )/E2
High Energy Particle
Detectors in a Nutshell: