Download Appendix A2. Particle Accelerators and Detectors

Appendix A2. Particle Accelerators
and Detectors
The Large Hadron Collider (LHC) in Geneva, Switzerland on the Border of France.
Prepared by: Arash Akbari-Sharbaf
Why Build Accelerators?
Probe deeper
From the uncertainty principle large momentum
transfers correspond to small distances.
  h/ p
Find new particles
Some fundamental particles are short lived and
have enormous masses
Ex. Top quark has a life time of 5x10-25s and a
mass of ~173GeV/c2 (~184u)
Tandem Van de Graaff Accelerator
The key is to establish a very large voltage
A belt carries charge from a source and
places it onto the outer surface of a hollow
conductor.
Ions from an ion source accelerate
towards the charged surface and enter the
hollow conductor.
Inside the hollow conductor the ion beam
passes through a stripper foil (ie., carbon
foil) and becomes positively ionized.
The beam leaves the interior of the
conductor and gets accelerated further.
This device can achieve a potential of
about 30-40MeV for singly-charged ions.
It is the most common DC accelerator
used.
Voltage
Source
+
+
+
+
Belt
+
+
+
+
Conducting
Brush
+
+
+
+
+
+
Stripper
+
+
+++++++ Ion Beam
-
Ion Source
+
+
+
+
Hollow
Conductor
Vacuum
Tube
The Cyclotron Accelerator
The cyclotron shown consists of two dshaped hollow conductors with an r.f.
Source connected between them.
Particles are injected into the center of
the apparatus where the electric field in
the gap causes them to accelerate.
Charges are constrained to move in nearcircular orbits due to a magnetic field
perpendicular to the plane of motion.
The r.f. source is synced with the
cyclotron frequency (ω = qB/m for nonrelativistic motion) to insure the right
polarity of the dees.
 The largest cyclotron accelerator is 18m
in diameter located at the university of
British Columbia (TRIUMF) and can produce
protons with energies of 500MeV.
AC Linear Accelerator
Ion Beam
Drift
Tubes
-V
-V
Ion
Source
rf
+V
+V
Vacuum
Pipe
Particles pass through a series of metal pipes called drift tubes, located in a
vacuum vessel.
The drift tubes are successively connected to alternate terminals of an r.f. source.
The r.f. frequency is adjusted such that when the ions come into the gap between
two drift tubes, the potential on both tubes accelerate the ion forward.
The increasing length of the tubes insures that the ions reach the gap in-sync
with the r.f. frequency as the ions pick up speed.
The largest electron linear accelerator (SLAC) in Stanford, USA is 3km long and
can attain maximum energy of 50GeV.
Synchrotron Accelerator
Synchrotron accelerators work much like linear
accelerators except that the beam path is circular.
This is done by arrays of dipole magnets called
bending magnets.
Acceleration is achieved as the beam repeatedly
traverses one or more cavities placed in the ring.
Particles traveling in a circular orbit continuously
emit radiation (synchrotron radiation) and thus
continuously lose energy.
The amount of energy radiated per turn by a
relativistic particle of mass m is proportional to 1/m4.
For electrons the losses are severe.
Reducing the curvature of the ion beam reduces
energy lose due to radiation.
The largest synchrotron accelerator is in Geneva on
the border of France and Switzerland. It is 27km in
circumference and can produce protons with energy
7TeV and lead nuclei with energy 574TeV
Cyclotron Frequency of Relativistic
Particles
To find the cyclotron frequency we set the centripetal force equal to the Lorentz
force
 
 
p    qv  B
Using the expression for the relativistic momentum we have





v  m  qB  0
where
  1/ 1  v2 / c2

qB
qB
f 


1 v2 / c2
2 2m 2m
Note that the cyclotron frequency now depends on the speed of the particle. Since
the particle is being accelerated the r.f. frequency must be reduced with time or the
magnetic field must be increased to keep in sync.
Available Energy for producing new
particles
In particle collision we often want to know what is the available energy for
producing new particles.
A simple method for finding this value is by considering the following scalar quantity
s  E1  E2 
2


  2 2
 P1  P2 c
Where E 2  m2c 4  P 2c 2 is the total relativistic energy of the particle.
This scalar quantity is the same in all inertial reference frame.
If we consider the center of mass frame, where the total momentum of the two
colliding particles is zero, we have
s  E1CM  E2CM 
2
Note that in this frame all the energy can be used to produce new particles since the
momentum after the collision is zero (no energy is needed to conserve momentum).
2
We see that s / c can be regarded as the rest mass or invariant mass of the two
colliding particles.
Example
consider a collision involving a projectile colliding with a fix target particle as
observed in the laboratory reference frame.
Writing down s in this frame we get

s  E1  m2c
 P c
2 2
2 2
1
Which can be re-expressed as
s  E12  m22c 4  2m2 E1c 2  P12c 2  m12c 4  m22c 4  2m2 E1c 2
The invariant mass is therefore,
s / c 2  m12c 4  m22c 4  2m2 E1c 2 / c 2
For high energies of the incident particle the expression reduces to
s / c 2 ~ 2m2 E1c 2 / c 2
This is the mass available for converting into new particles. It depends on E1
The rest of the incident energy is used to conserve momentum.
To maximize the available energy for producing new particles, beams of equal and
opposite momentum are used.
Particle Detectors
Atlas, one of four detector at the LHC in Geneva, Switzerland.
Gas Detectors (Cloud Chamber)
Particles directed into a cloud chamber collide with supersaturated vapours such
as water or alcohol and produce ions.
These ions act as condensation centers, around which a mist forms, because the
mixture is at the point of condensation.
The mist allows an observer to visualize the trajectory of particles.
This apparatus is typically placed in a magnetic field perpendicular to the plane
of motion in order to extract particle momentum from the curvature of its path.
This was discuss during cyclotron motion.
Apart from the observed curvature, different particles have distinctive track
features. For instance alpha particles have thicker tracks as a result of scattering
effects.
Gas Detectors
(Multiwire Proportional Counter)
These detectors consist of arrays of wires with a large potential across them.
Incoming particles ionize inert gas (ex. Ar) atoms in the chamber creating electronion pairs.
The electric potential on the anodes accelerate the ions and electrons which then
collide into other inert atoms causing secondary ionization (Townsend avalanche).
The large number of ions produced registers a measurable current on nearby
anodes.
The output signal at the anode is proportional to the energy lost by the original
particle.
The trajectory of the particle can be found by noting the locations of the activated
anodes.
MWPC have spatial resolution of 200μm or less, and time resolutions of about 3ns.
Particle
Trajectory
Anode
Wire
Scintillation Counters
Particle traversing through suitable materials excite a small fraction of atoms
within the medium. Subsequently these atoms de-excite emitting light, which can
then be detected by a photo detector.
One of the most important examples of a photo detector is the photomultiplier
tube shown below.
An in coming photon strikes a cathode ejecting an electron due to the
photoelectric effect. A large electric potential is set up across a series of dynodes
accelerate the electron which then collides with the first dynode producing more
electrons as a result of the gained energy.
These electron are then accelerated to a
second dynode and so on producing an
avalanche of electrons, which can then
be detected by an ammeter.
The most efficient PMTs can detect a single
Photon.
A scintillation counter can even detect
a neutron if the appropriate material is
used.
n105B37Li 24He
Identifying Particles
Typically, particles are identified by their mass.
 A particle’s mass can be determined by the simultaneous measurement of its
momentum together with some other quantity, such as velocity or energy.
The momentum of a particle is usually determined from the curvature of its track in
an applied magnetic field. such an apparatus is called a spectrometer.
A simple means of measuring the particles velocity is measuring the time of flight of
the particle between two points. This can be done by using two scintillation counters
placed a distance L apart.
The more common apparatus used for measuring velocities of particle is called the
Cerenkov counter.
When a charged particle with velocity v traverses a dispersive medium faster than
the speed of light in that medium, the medium radiates at a characteristic angle θ with
respect to the direction of motion. This angle of radiation is related to the velocity of
the particle by cos(θ) = c/vn, where n is the refractive index of the medium.
An apparatus that detects particle energy is called a calorimeter. Scintillation
counters and multiwired proportional counters can be used as calorimeter since these
devices can measure energy losses. Calorimeter can also measure energies of neutral
particles.
Neutrino Detectors
Neutrinos can be detected with extreme



n

e
p
e
difficulty because they interact only weakly
with matter.
  n    p
Electron neutrinos and antineutrinos of
sufficient energy can be detected by observing
the inverse β-decay processes.
The probability of these processes occurring
is extremely small. The mean free path of a
1MeV neutrino in matter is 106 km.
The Super Kamiokande detector is a tank
containing about 50 000 metric tons of very
pure water buried deep under a mountain in
Japan. This protect the detector from cosmic
ray muons.
The walls of the tank are lined with 11 200
photomultipliers, which detect the presence of
electron and muons produced in the weak
interaction by detecting the light from Cerenkov
radiation.
 e  p  e  n
  p    n