Particle accelerators and detectors

In a nutshell

Particle accelerators are machines that collide particles with each other at very high speeds to investigate them. Electric fields are used to accelerate the particles while magnetic fields are used to curve their paths. Most particle detectors are based on the principle of ionisation.

Equations

description	equation
Force on a particle in a magnetic field	$F=Bqv$
Centripetal force	$F=\dfrac{mv^2}{r}$
Radius of particle path	$r=\dfrac{mv}{Bq}$
Cyclotron frequency	$f=\dfrac{Bq}{2\pi m}$

Constants

constant	symbol	value
$elementary\ charge$	$e$	$1.6\times10^{-19}\ C$
$mass\ of\ electron$	$m_e$	$9.11\times10^{-31}\ kg$

Variable definitions

quantity name	symbol	derived units	si base units
$force$	$F$	$N$	$kg\ m\ s^{-2}$
$magnetic\ flux\ density$	$B$	$T$	$kg\ s^{-2}\ A^{-1}$
$velocity$	$v$	$m\ s^{-1}$	$m\ s^{-1}$
$charge$	$q$	$C$	$A\ s$
$radius$	$r$	$m$	$m$
$mass$	$m$	$kg$	$kg$
$frequency$	$f$	$Hz$	$s^{-1}$

Smashing particles

In order to investigate their internal structure, particles can be collided with each other at very high speeds. This breaks them up and the high energies produce additional particles which are used to reveal new physical phenomena. To accelerate particles to high enough speeds, scientists use particle accelerators. These are machines that use electric fields to accelerate them and magnetic fields to curve their path.

Linear accelerators

Linear accelerators are one type of particle accelerator which consists of tubes of increasing length that use an alternating voltage supply to accelerate the particles. An example is shown below:

Physics; Particle physics; KS5 Year 12; Particle accelerators and detectors

1.	Particle beam
2.	Drift tube
3.	High frequency AC voltage

When the particle beam reaches the middle of a tube, the voltage supply switches to negative. This repels the particles to the next tube which has a positive charge and so on. The tubes get increasingly longer to keep up with the acceleration.

Cyclotrons

Cyclotrons are another type of accelerator that are composed of two semi circular electrodes with a gap between them. Particles are accelerated by an electric field in the gap, and then move to the electrodes where a magnetic field curves their path back to the gap as shown below:

Physics; Particle physics; KS5 Year 12; Particle accelerators and detectors

1.	Vacuum chamber
2.	Electrodes
3.	Magnetic field into diagram
4.	Particle source
5.	Electric field gap
6.	Beam
7.	Target

As the particles gain more momentum, their radius within the electrodes increases. Eventually, the particle will spiral out of the cyclotron and hit a target inside a chamber where the results will be analysed.

Particles in a cyclotron

When particles move across a magnetic field, they feel a centripetal force:

$F=\dfrac{mv^2}{r}$

This force is the same as the force of the magnetic field acting on them:

$F=Bqv$

By combining these two, the radius of the path taken by the particles is:

$r=\dfrac{mv}{Bq}$

To maintain the accelerations, the alternate potential difference needs to switch at the right moment. The frequency of the supply can be calculated with the equation:

$f=\dfrac{Bq}{2\pi m}$

Example

An electron moves through a magnetic field with a flux density of $0.01\ T$ with a radius of $5\ cm$ . What was the velocity of the electron while moving through the field?

Firstly, write down all the known values:

$B=0.01\ T\newline r=5\ cm=0.05\ m$ 

Next, write down the equation for the radius of a particle path:

$r=\dfrac{mv}{Bq}$ 

Rearrange this equation for the velocity:

$v=\dfrac{rBq}{m}$ 

For an electron this will become:

$v=\dfrac{rBe}{m_e}$ 

Substitute all the numbers in and calculate the velocity of the electron:

$v=\dfrac{0.05×0.01\times1.6\times10^{-19}}{9.11\times10^{-31}}=8.782 ...\times10^{7}\ m\ s^{-1}$

The electron had a velocity of $\underline{9\times10^{7}\ m \ s^{-1}}$ to one significant figure, while moving through the field.

Synchrotrons

Synchrotrons are single ring accelerators that use the same properties of cyclotrons and linear accelerators. An example is the large hadron collider (LHC) which is the largest and most powerful particle accelerator in the world located in Geneva, Switzerland. It accelerates protons for $27\ km$ and produces collisions of $14\ TeV$ ( $14\times10^{12}\ eV$ ) of energy. These collisions produce showers of particles which are analysed through particle detectors.

Particle detectors

Most particle detectors all work on the principle of ionisation. An example is the Geiger-Müller (GM) tube, a detector composed by a gas filled tube with electrodes. The idea is that when particles enter the tube they ionise the gas. The ions and electrons produced are accelerated by the electrodes. This then produces electric pulses, which are recorded on a counter.

However, these particle counting detectors don't distinguish between the particles. A proper analysis can be conducted through detectors such as a bubble chamber. This is a chamber with a constant magnetic field filled with liquid hydrogen that produces bubbles when ionised. The charged particles enter the chamber and by ionising the liquid, they leave tracks of bubbles such as the following:

Physics; Particle physics; KS5 Year 12; Particle accelerators and detectors

The radius of the tracks tells the mass of the particles, while the direction of the curves tells the charge through Fleming's left hand rule.