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- Aimee Hopper
November 28, 2013
1 Briefly describe the differences between the following ac- celerators and give their advantages and disadvantages
Accelerates Protons/Ions with a Kinetic Energy of 20-35 MeV.
The work done on the particle is proportional to the voltage of the terminal. (W =qVterminal). The voltage of the terminal is dependent on the height of the device (V _ kQL )
where Q is the total charge of the particles, k is the Coulomb constant and L is the total length of the accelerating chamber, i.e. the total height of the device through which the ion falls.
- very simple to make, and the principles behind the acceleration are very well understood.
- easy and cheap to maintain
- very difficult to get to very high energies, as the only way to do so it so make a very high, stable structure.
- only allows one route for particles to travel.
- Betraton (6 Marks)
Accelerates electrons with a kinetic energy of 10-300 MeV
The betatron is a type of accelerator which uses an induced magnetic field to accelerate electrons to high energies in circular orbits. Uses solenoids with an electric current passing through to produce large magnetic fields to bend the particles.
- Simple design – solenoids and their properties are well understood and can easily be tested and manufactured.
- Requires a huge amount of coils to get the induced magnetic fields required – therefore very heavy and costly.
- As the coils aren’t superconducting, this system is also very lossy, and so wastes a lot of energy.
- Cyclotron (6 Marks)
Figure 2: 
Accelerates Protons/Ions with a kinetic energy of 10 – 100 MeV.
A circular device which operates using large magnets to bend the particles. Two semi-circular plates are connected to an AC source, applying a voltage across a gap between the plates. This applied voltage causes the particle to accelerate. However, as there is also a large magnetic field present, the particle is forced to bend its path as it accelerates, following a circular path. The more energy the particle gets, the larger its radius becomes until eventually it is extracted from the device. (v = qBr m where q is the charge of the particle, B is the magnetic field strength applied across the plates, r is the radius of curvature of the particle and m is the mass of the particle.)
- The same gap can be used for all energies of particles, as the kick that is received will always be in-phase with the kick produced by the AC source. This is because as the particles speed up, they have a longer path, therefore take longer to arrive to the same point they were originally.
- To have a small device, large magnetic fields are required, which could pose a hassle to the set-up and cost of the project.
- As the particles become relativistic, the AC source lags behind, therefore not producing the correct kick to the particles, possibly removing energy from the system.
- Synchro-cyclotron (6 Marks)
Accelerates Protons/Ions with a kinetic energy of 100-750 MeV
Special form of cyclotron – takes into account relativistic lag from the AC sources.
- There is no need for a narrow gap between the plates as in the case of conventional cyclotron, because strong electric fields for producing large acceleration are not required.
- So, only one plate is required instead of two, the other end of the oscillating voltage supply being connected to earth.
- The magnetic pole pieces can be brought closer, thus making it possible to increase greatly the magnetic flux density.
- The frequency valve oscillator is able to function with much greater efficiency.
- The machine produces high energy ions with a comparatively low intensity.
- Synchrotron (6 Marks)
Figure 3: [?]
Accelerates either electrons (kinetic energy of 1-10 GeV) or protons/ions (kinetic energy of 1-1000 GeV).
Utilises a number of different types of magnets – dipoles (bend the beam), quadrupole (focus the beam), sextupoles (account for chromaticity of the beam) etc.
Uses RF cavities to insert energy into the particle beam to account for synchrotron losses and increase the energy of the beam
- Can generate a high luminosity beam at very high energies.
- The Synchrotron radiation lost can be used for other applications which require a very specific wavelength, such as medical applications.
- Suffers from radiation losses
- A synchrotron cannot use relativistic particles, as RF lag would become an issue.
- Storage ring (6 Marks)
Accelerates electrons with a kinetic energy of 1-7 GeV [European Synchrotron Radiation Facility].
A storage ring is a particle accelerator that keeps a particle beam at a certain energy for a long period of time. This is useful, especially in synchrotrons, as the beam can be kept at a certain energy ensuring that a specific frequency is emitted in the form of radiation.
- Stores a particle beam at a certain energy, so don’t have to increase beam energy from 0 (time consuming).
- Systems have to be very precise and stable – costly
- Collider ring (6 Marks)
Accelerates electrons (kinetic energy of 10-100 GeV) or protons/ions (kinetic energy of 1-7
TeV [Large Hadron Collider]).
Particles of a particular energy are injected into the ring and stored there until they are forced to collide at set points throughout the structure.
- Can reach higher energies than in a LINAC at much lower cost due to giving each beam half the required centre of mass energy.
- if using particle-antiparticle, then the same equipment will accelerate the two beams in opposite directions (due to difference in charge)
- Beam pipe needs to hold 2 beams, which need to only interact with each other when required – need very accurate equipment to ensure beam stays separated.
- Linacs (6 Marks)
Accelerates electrons (kinetic energy of 20 MeV to 50 GeV) or protons/ions (kinetic energy of 50-800 MeV [Los Alamos Meson Physics Facility])
A Linear Accelerator accelerates the particle beam along a straight line as opposed to a circular path.
- No energy loss due to particles accelerating in a curve.
- Can accelerate heavy ions to far higher energies than possible in the circular accelerators.
- Can produce a continuous stream of particles as opposed to bunched particles present in circular accelerators.
- Need to be very long to get up to high energies.
- A high number of AC driver sources are required, which is both costly and introduces possible errors due to out-of-phase issues.
- Linear collider (6 Marks)
Accelerates electrons from 50-1000 GeV.
A linear collider is used to collide particles in a straight line towards one another.
- No energy needs to be pumped into the beam to account for radiation losses.
- beams will never be able to interact with each other before the collision points, therefore can use smaller beam pipes.
- can accelerates heavier particles since they don’t need to be bent.
- For collisions with the highest possible energy, two linacs producing beams with the same energy headed towards each other, the complete machine would need to be very long!
2 Explain the advantages of using a collider rather than a single beam for collision experiments. Illustrate your answer by considering 7 TeV proton beams. (10 Marks)
By using 7 TeV proton beams in a collider, a centre of mass energy of 14 TeV can be achieved by sending both beams in opposite directions to collide. This is obviously very useful when probing matter, as a higher energy will result in higher mass particles / more low mass particles being produced, therefore available for analysis. The single beam would only be able to reach 7 TeV, and so has a limited range by comparison to the collider.
To obtain a centre of mass energy of 14 TeV in a single beam is also incredibly difficult to produce, both due to the cost and the size of the equipment required. Therefore a 14 GeV beam isn’t feasible to produce. Whereas 7 TeV is relatively easy. Also, when 14 GeV does become easy to produce, a centre of mass energy of 28 GeV would then be possible, which is far more attractive for high energy energy studies.
3 Explain briefly how a laser-plasma wakefield accelerator works. What determines the limit in energy for a uniform plasma density? (13 Marks)
In laser-plasma wakefield acceleration, a laser pulse is used to excited very high electric fields in a following plasma wave. Efficient energy transfer is made between laser pulse and plasma wave if both the wave and the pulse are travelling at the same speed, with a high energy gain being obtainable in low-density plasmas, in which the phase velocity of the laser-plasma is equal to the laser pulse group velocity, which is very close to the speed of light. This allows the longitudinal electric fields associated to the fast plasma wave to accelerate relativistic particles within the plasma, and can even trap the particles to the electrostatic wave. This allows particles to be boosted to very high energies in a very short distance.
It is important that the density of the plasma is below the critical density (nc =1:1 _ 1021=_20
We know that the maximum energy of a wave is related to the 2g of the wave by the equation
E _ epn _1g (1)
where g is the lorentz factor associated with the group velocity of the laser pulse
which is equal to
g =!0!p (2)
So the more dense the plasma, the lower g is, and therefore the slower the wave travels. If the wave travels too slowly, then the particles will move away from the wave faster.
4 Briefly describe how a FEL and synchrotron radiation source works. What is the advantage of a free-electron laser? (10 Marks)
A free-electron laser utilises both undulator and radiation fields to produce ponderomotive (essentially a light-radiation pressure”) on the particles. This forces the electrons to oscillate at the fundamental frequency. If the electrons can be forced to bunch together on a wavelength scale (given by equation 3), then the electrons emit coherently.
_ =_u22_1 +a2u2_ (3)
Synchrotron radiation works by accelerating a particle in a circular path, therefore producing radiation. This generally gives an incoherent beam of radiation, as any discrepancies in the individual particle energies will result in a slightly different frequency radiation coming o_. It is caused by undulators, wigglers and bending magnets, and due to the high speeds of the particles, comes out the acceleration device in a cone, with an opening angle equal to _1 .
The benefits of the free-electron laser are that it produces a much higher brightness due to the coherence of the wave, therefore producing a significantly higher photon flux for a given energy, as compared to the synchrotron.
Synchrotrons currently produce an average brilliance of 1011. The FEL is able to produce a brilliance of up to 6 orders of magnitude higher, however there are currently issues with regards creating coherence throughout the whole length of the laser pulse.
5 Describe how particles and X-rays can be used to treat cancer and give the advantages and disadvantages of the different radiation types used for radiotherapy. (13 Marks)
With regards to cancer, the aim is to damage or destroy the DNA of the tumour to kill it by disrupting the cell cycle of the tumour in one way or another.
X-Rays produced in 5-20 MeV linacs are currently used to treat most patients. They can cure up to 45% of cancers, 50% of which is by radiation therapy alone, or combined with chemotherapy and/or surgery.
This is achieved by using 3D Conformation therapy, where multiple X-Rays are used to concentrate the beam energy onto the tumour, whilst minimising the damage caused to surrounding cells.
Particles that can be used to treat cancers include electrons (positrons), protons, neutrons and ions. These can either be used directly, or can help in producing radio-isotopes to also assist in treating cancer through Positron Emission Tomograohy (PET) or Single Photon Emission Computed Tomography (SPECT).
If used directly, then the particles are _red at the tumour. Charged particles interact with electrons in the body, and a vast majority of the energy of the particle is deposited according to its Bragg Peak (energy loss vs distance plot of the Bethe-Bloch formula).
The aim is to get this depth to correspond to that of the tumour, so the energy deposited causes maximal damage to the cancer whilst causing very little damage to surrounding tissue.
The advantages of particle therapy are
- All (most) energy deposited where required, with little to no damage of surrounding cells.
- Very few side effects
- Seems to have a higher cure rate with certain types of cancers (i.e. uveal melanoma).
- Massively reduces the damage done to children sufferers as less of their healthy tissue is effected, reducing the chances of side-effects caused by traditional methods.
- Particles can be accelerated to whatever energy is required to reach the tumour.
The disadvantages of particle therapy are:
- It requires a huge capital investment, and is massively expensive by comparison to X-Ray treatments.
- Requires hospitals to have room for a large particle accelerator to accelerate the ions, which isn’t always possible.
- Expensive to run, due to energies required.
 http://www.lbl.gov/abc/wallchart/chapters/11/2.html as viewed on the 25/11/13
 http://commons.wikimedia.org/wiki/File:Wideroe linac en.svg as viewed on the 25/11/13
 http://images.yourdictionary.com/cyclotron as viewed on the 25/11/13
 http://www.schoolphysics.co.uk/age16-19/Nuclear physics/Accelerators/text/ Synchrotron /index.html as viewed on the 25/11/13
 V. Malka, J. Faure, Y. Glinec, A. Lifschitz, LASER-PLASMA WAKEFIELD AC-CELERATION: CONCEPTS, TESTS AND PREMISES”, EPAC, 2006
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