Detectors and Detectors and AcceleratorsAccelerators

How do you find these particles, anyways?How do you find these particles, anyways?

High Energy, High Energy, Please.Please.

We have seen that the electromagnetic interaction allows for the process where an electron -positron pair create a new particle-antiparticle out of the vacuum.

-e

High Energy, High Energy, PleasePlease

To create this particle-antiparticle pair, energy is needed.

E=mc2 is the rest energy for each particle. This is the energy needed to create the particle at rest.

If the particle and antiparticle each has a kinetic energy of EK after it is created, then the total energy that must be supplied is

E =2(mc2 + EK) The very minimum energy needed is E = 2mc2

This energy must come from the rest energy and the kinetic energy of the electron and positron before the collision.

ResolutionResolutionIt is clear that if we wish to produce particle of large mass,

then very large amounts of kinetic energy are needed.

We also know that in order to ‘see’ something very small, the object ‘thrown’ at it, must have a wavelength of a comparable size. Otherwise, the wave is not deflected; it just continues along its original path.

Since the constituents of the particles are assumed to be very small, the wavelength used must be very small.

For example, if a photon is used to detect a particle that has a radius of ~10-15m, it must have a energy of

Visible Light has E ~ 10’s eVGamma Radiation: E ~ MeV

AcceleratorsAccelerators

To get these high energies, particle accelerators are used. We will look at three types.

1) The linear accelerator2) The cyclotron3) The synchrotron

1) In the linear accelerator, particles are accelerated along a straight path by electric fields.

2) The cyclotron accelerates particles through a potential difference. Magnets are used to curve the path of the particles back to the gap. The path of the particles’ gets bigger and bigger.

3) The synchrotron accelerates the particles like the cyclotron but they follow a path of constant radius.

LinacsLinacs

Linear Accelerators, or linacs, consist of a series of evacuated tubes.

An alternating voltage is applied across the gaps between consecutive tubes. The charged particles accelerate every time they move from one tube to another.

The length of the tubes increases so that the particles spend an equal time in each tube.

The beam can be accelerated to hit a fixed target or two beams can be accelerated along the same straight line from opposite ends and made to collide with each other.

CyclotronCyclotronThe cyclotron consists of two D shapes, with a gap between them, placed in a uniform magnetic field.

A charged particle is accelerated from the center. A magnetic field pushes the particle back toward the gap RHR #3)

When the particle reaches the gap, the polarity of the voltage is switched so that the particle accelerates through the potential difference.

Remember: you discovered that the period of the particle’s rotation is constant.The radius increases but the velocity also increases proportionally.

qvB = mv2/rWhere v = 2πr/T

T = 2πm/(qB)Cyclotron frequency: f = qB/(2πm)

The SynchrotronThe SynchrotronProtons move along a circular path of fixed radius.

electromagnet

Acceleration takes place here

Electric field

+ _

A

B

A B

Accelerating region

The positive particles will accelerate across the gap. The electric potentials in the gaps must be carefully established by carefully timing the arrival of the beam at every gap. The period of the electric field must be synchronous with the beam.

As the particles move closer to the speed of light, their energy becomes

E2 = (pc)2 +(mc2)2

E2 = (pc)2 E = pc

(When the momentum is very large, we may ignore its rest energy)

Fc = Fm

Mv2/R = qvB

R = mv/qB

R = _E_ qBc

The magnetic field must be constantly increasing as the particle’s energy increases (that’s why they’re electromagnets).

Storage RingsStorage Rings

Two oppositely charged beams can be made to move around the same ring in opposite directions. This is called a storage ring.

The two beams could be made to collide at set places and at specific times.

CERN’s LEP (large electron-positron) collider had a circumference of 27 km and 100 m underground.

The W and Z bosons were discovered there.

The LHC has now replaced the dismantled LEP.

RadiationRadiationWe have seen that accelerating charges emit radiation (hence the need for the Bohr and quantum models of the atom).

In the cyclotron and the synchrotron, the charged particles are continuously accelerated by the magnetic fields.

There is a large amount of radiation (energy) lost due to this acceleration. This radiation is called:

synchrotron radiation.

Electrons have a much smaller mass than protons which means if they have the same energy, the electrons move faster. The acceleration (v2/r) depends on speed and therefore the electrons would radiate (and lose) a lot more energy than the protons.

Most synchrotrons use protons.

Available EnergyAvailable EnergyConsider a target of mass M bombarded by a particle of rest mass ‘m’ and total energy E.

The energy available to create new particles in this case is given by the formula

EA2 = 2Mc2E + (Mc2)2 + (mc2)2

Insert waving hand here

This equation comes from special relativity.

EA is an invariant quantity like ‘c’: All frames measure this energy.

Available EnergyAvailable Energy

Ex. p + π- Λ0 + K0

p (938 MeV) π- (140MeV)Λ0 (1100 MeV) K0 (500 MeV)

What is the minimum kinetic energy of the proton in order to produce these particles in a collision with the stationary pion π-?E is a min when all particles created are at rest.

We need 1100 MeV + 500 MeV = 1600 MeV.This is the EA.

EA2 = 2Mc2E + (Mc2)2 + (mc2)2 Solve for E.

(1600)2 = 2(140)E+(140)2 +(938)2

E = 5930 MeV. This is the total energy of the proton: it is its rest energy plus its kinetic energy.

KE = 4990 MeV

Comparing Comparing AcceleratorsAccelerators

The antiproton was discovered in a collision of two protons, one of the at rest, according to the reaction:

p + p p + p +p + p

a. What is the minimum kinetic energy to which the proton must be accelerated?

EA = 4 (938 MeV) = 3752 MeV

EA2 = 2Mc2E + (Mc2)2 + (mc2)2

37522 = 2(938)E +2 (938)2

E = 6566 MeV

KE = 5630 MeV

b. Compare this with the kinetic energy needed in a storage ring synchrotron.In the synchrotron, each

proton is accelerated to the same KE. EA still equals 3752 MeV.

This comes from the total energy of both protons. This means each proton has 1876 MeV of energy.

KE = 1876 MeV – 938 MeV = 938 MeV

Comparing Comparing AcceleratorsAccelerators

Accelerator Advantages Disavantages

Linac Have lower energy losses due to synchrotron radiation

A very long accelerator is required to reach very high energies.No control of collision time.

Cyclotrons Compact size, low costGood for biomedical research

Only uses fixed target.Limit to energy since it is dependent on the magnet size

Synchrotrons Can accelerate particles to very high energies (massive particles can be produced).Collisions can be controlled with storage rings.

High proportion of energy lost due to synchrotron radiation.Low probability of collisions.

DetectorsDetectors

Not only do we need to detect the particles created in the collisions, but there needs to be ways of measuring their momentum, electric charge, mass, velocity and energy.

Particle detectors around placed around the point of the collision and have a layered structure. Each layer has a specific function in the detection process.

The tracking chamber is the layer closest to the collision point. It records the path of the particles.

Bubble chambers were used originally. You know ALL about bubble chambers.

DetectorsDetectorsNow the wire chamber or proportional wire chamber are used.

These chambers can digitized the information so a computer can reconstruct the path of the particles.

The wire chamber has a number of wires immersed in a gas. The wires are kept at different potentials.

The ions and electrons created by the charged particle as it moves through the gas collect at the wires.

Their arrival at a particular point on the wire is recorded as a current.

The electrons or ions take a certain time to drift to the nearest wire. This time is recorded and used to calculate the precise location where the electron or ion was created and its momentum .

DetectorsDetectors

The next layer is the electromagnetic calorimeter.

When charged particles in a given medium move faster than light in that medium, they give off radiation.

This radiation can be detected using the photoelectric effect.

The current of photoelectrons is very small so it is amplified with photomultipliers.

These detectors can detect the presence of a single photon!

Knowledge of the intensity of the radiation allows for the determination of the speed of the charged particle that caused the radiation.

Knowing the particle’s momentum and now its speed, we can calculate its mass.