Particle Physics Tutorial 4 - Particle Accelerators (Extension)

This will be useful background for A-level students studying the EDEXCEL syllabus.

This will be useful to students studying the Scottish Higher syllabus


How do we probe the nucleus?

Van der Graaff Generator

The Cathode Ray Tube

Energy of accelerated particles

Larger Machines

Cockcroft and Walton Accelerator


How do we probe the nucleus?

Much of the evidence for the structure of the nucleus comes from studies using particle accelerators.  These machines make charged particles move at high speed, hence high kinetic energies, which are needed to investigate the structure of particles.  The charged particles can be:


They are made to move by both attracting them and repelling them.  The easiest particle to use is the electron.  You will remember from GCSE that you charge objects by moving electrons.  Protons never move.  While you are not expected to recall details of particular particle accelerators, it’s worth mentioning a couple.


Van der Graaff Generator

These machines can produce very high potential differences.  The diagram below shows a typical machine you will find in a school physics laboratory.



The machine pumps electrons upwards to the top sphere.  The electrons crowd onto the top sphere and make the potential difference very large indeed.


If the breakdown voltage of air, 3000 V/mm is exceeded, a spark will jump to the discharge sphere.  The charge will be conducted back to the base through the wire.

When a big charge is being made on the top sphere, you can hear the motor slowing down as it has to work harder.


Question 1

A spark from a van der Graaff generator is 10 cm long.  What voltage is this? 



Some machines pump electrons off the top sphere, making it positive. 


Large machines are filled with sulphur hexafluoride, a gas that is very good insulator.  Very high voltages can be obtained.



The Cathode Ray Tube

This is another common accelerator, commonly found in old-style TV sets.



At its heart is the electron gun, in which current passes through a filament, which glows just like in a light bulb.  The filament is connected to a source of electrons (the negative terminal of a high voltage source), called the cathode.  Electrons are boiled off by a process of thermionic emission.  They are attracted to a positively charged anode.   Most hit the anode and go back to the source.  Some go through a small hole in a narrow beam. (This was called the cathode ray.)


Since they are attracted by the very high potential difference, the electrons accelerate.  Once they get to the anode (and pass out of the little hole), the electrons are moving very fast.  All their energy is kinetic.


Energy of accelerated particles

The electron is a fundamental particle, with no substructure.  All the energy of a moving electron is kinetic; there are no bonds to vibrate.


From GCSE physics, we know that:

Energy = charge × voltage


E = QV


We also know that kinetic energy is given by:

So we can equate the two equations and write:


We can rearrange this to give:



Since the Q term is the electronic charge, e (= 1.6 × 10-19 C), we can rewrite the equation as:
The mass of an electron is 9.11 × 10-31 kg.
Worked example
An electron is accelerated by a potential difference of 1500 volts.  What is its speed as it passes through the electron gun?
Use the equation above:
 = 2.3 × 107 m s-1
This is 8 % of the speed of light, so you can see that the little brutes are moving like greased lightning.


Question 2

A proton of mass 1.67 × 10-27 kg and charge 1.6 × 10-19 C is accelerated by a potential difference of 4000 V.  Calculate its speed. 

Express this as a percentage of the speed of light (c = 3.0 × 108 m/s)



Positively charged particles like hydrogen ions (protons) can be accelerated in a similar way.  Chemists use a machine called a mass spectrometer that accelerates positively charged particles.

There is a limit to the speed to which particles can be accelerated, the speed of light (3.0 × 108 m s-1).  As electrons get towards the speed of light, they start to turn their energy into mass (this may sound strange, but mass and energy are the same thing at this level).  This is called a relativistic effect.


Question 3

Work out the potential difference through which electrons have to be accelerated to travel at the speed of light.



The equation for kinetic energy that we know does not work at these speeds; another equation has to be used.


Larger Machines

The electron gun is the device that makes the electron microscope work.  The electron microscope can resolve to about the diameter of an atom (10-10 m).  A light microscope can resolve (pick out)  objects down to about 0.5 mm, about the size of a bacterium.  However we need to have resolutions of 10-14 m and 10-15 m in order to resolve the nucleus.  We can only achieve this by using powerful particle accelerators.  The accelerator works by attracting a charged particle by a very large voltage and intense magnetic fields.


The linear accelerator is set out like this:

Let's suppose that the source gives out electrons.  The electrons are given off by thermionic emission, in the same way as the cathode ray tube.  The electrons are attracted by the first electrode which is positive.  They accelerate towards the positive electrode.   As the electrons pass into the electrode, the polarity changes (as it's AC), so the electrode becomes negative, and the second electrode becomes positive.  So the electrons are repelled by the first electrode and attracted to the next electrode.   As the they pass each electrode, the little brutes are given a kick up the backside.  Therefore they travel faster, towards the speed of light.  The electrodes are longer the further up the accelerator they are.  As the electrons get closer to the speed of light, relativistic effects occur and the kinetic energy is turned into mass.  Then the electrons strike the target.


Protons in the form of H+ ions can be injected into the source.  They have a higher mass, so can achieve the same levels of energy and momentum at a lower speed.


Click HERE to show an animation.  I am most grateful to Stephen Lucas, a past student of mine, who produced it.  Here are some further links:


Notes on the Cyclotron and the Synchrotron can be found in Magnetic Fields Tutorial 3.


Accelerators are huge and massively expensive, as they require precision construction.  The largest of these machines is to be found at CERN (Centre Europienne de la Recherche Nucleaire) in Geneva, Switzerland.  The Large Hadron Collider (LHC) lives in a circular tunnel, 27 km long. The detector has a mass of 14 000 tonnes, about the same size as a car ferry.


(Photo by Alpinethread, published by Wikimedia Commons)


It has been so expensive to build and run that no one country could afford it.  It a joint collaboration between states and universities.  The World Wide Web grew from CERN from the need for universities to share the data from the experiments.  A physicist, Tim Berners-Lee invented the language of the Web, hypertext mark-up language (html) after about 3 hours' work on Christmas Day in 1989 (an alternative to The Sound of Music on the box).  And we know how useful it is.


The LCH has accelerated particles to an energy of 14 TeV (14 × 1012 eV).


Question 4

How much energy in joules does a 14 TeV particle have?



Recent data from CERN suggested that neutrinos can travel faster than light.  This has got physicists into a real twist, because we all know that nothing can travel faster than light, don't we?  Physicists have always found neutrinos difficult to understand, and the idea of the little brutes going faster than light, well really!  (Later it was found that there was some problem with cables between CERN and a remote site which led to a false conclusion, and some very red faces.)



Cockcroft and Walton Accelerator (Irish Syllabus, Higher Level)

This machine was named after the English physicist John Douglas Cockcroft (1897 - 1967) and the Irish physicist Ernest Thomas Sinton Walton (1903 - 1995).  It is also referred to as a voltage multiplier.  The machine looks like this:


Image by Geni, Wikimedia Commons


The voltage multiplier consists of two simple components,  diodes and capacitors.  You can see more about diodes and capacitors by clicking on the links.  They are arranged in a ladder network like this:

Image by Chetvorno, Wikimedia Commons


The ladder generates a high voltage direct current output from a low frequency alternating current or using pulsed direct current.  Charged is pumped up the ladder.  The circuit is, as a result, also called a charge pump.  You could use a suitable transformer, but transformers are bulky and not easy to insulate at very high voltages.  You can take a voltage off each rung of the ladder.


You do not need to know how it works, but if you are into electronics, this is what happens:


The output voltage is twice the peak voltage multiplied by the number of stages:


Vout = 2Vp × N


High voltage power supplies such as those in old CRT TV sets, and electrical insect killers use voltage ladders.


In 1932, Cockcroft and Walton made a machine that could generate a voltage up to 700 kV.  It was used to accelerate protons with an energy of 700 keV into a target of lithium.  For each proton that collided with a lithium nucleus, two helium atoms were given off according to the equation:



Each interaction gave off energy of 17.3 MeV.


The element lithium was transformed or transmuted into another element, helium.  It was the first experiment of its kind, and won the two physicists a Nobel Prize.


The splitting of a lithium atom by high speed proton collision is NOT an example of nuclear fission. 

 Fission works by neutron collision with large nuclei.