2. The cyclotron
• The underlying physics principles are:
• charged ions (protons, electrons, etc.)
are accelerated with electric fields
• and contained or focused by
magnetic fields.
3. Circular path of charged particle
• Consider a positive charge +q that starts to move at constant
velocity v in a uniform magnetic field B directed upward.
• The related magnetic force Fm is perpendicular to the plane
formed by v and B.
• While this force acts on this particle, the trajectory of the
particle must change to maintain F, B and V perpendicular to
each other. Therefore the particle becomes forced to moves
on a circle.
4. Principle of operation
• A cyclotron accelerates a charged particle
beam using a high frequency alternating
voltage which is applied between two hollow
"D"-shaped metal electrodes called "dees"
inside a vacuum chamber.
• The dees are placed face to face with a
narrow gap between them, creating a
cylindrical space within them for the particles
to move.
5. Principle of operation
• The particles are injected into the center of this
space.
• The dees are located between the poles of a large
electromagnet which applies a static magnetic
field B perpendicular to the electrode plane.
• The magnetic field causes the particles path to
bend in a circle due to the Lorentz force
perpendicular to their direction of motion.
6. Principle of operation
• A radio frequency (RF) alternating voltage of
several thousand volts is applied between
the dees.
• The frequency is set so that the particles
make one circuit during a single cycle of the
voltage.
• To achieve this, the frequency must match
the particle's cyclotron resonance frequency.
7. Cyclotron resonance frequency
• The cyclotron frequency or gyrofrequency is the number of cycles a particule complete around its
circular circuit every second.
• Since that motion is always circular, the cyclotron frequency is given by equality of centripetal
force and magnetic Lorentz force:
• The cyclotron frequency:
• The angular frequency
• It is notable that the cyclotron frequency is independent of the radius and velocity and therefore
independent of the particle's energy.
8. The orbit period
• A moving charge in a cyclotron will move in a circular path under the
influence of a constant magnetic field. If the time to complete one
orbit is calculated:
9. Principle of operation
• A constant frequency sinusoidal oscillating voltage on the accelerating
cavities matching the cyclotron resonance condition (ω = qB/m)
accelerates the particles twice per revolution, causing them to
increase their orbit radius as they gain energy.
• The repetitive dee gap crossing of the recirculating beam allows it to
be accelerated to high energies with relatively low dee voltages, thus
eliminating the need for the high voltages.
10. Principle of operation
• Each time after the particles pass to the other dee electrode the
polarity of the RF voltage reverses.
• Therefore each time the particles cross the gap from one dee
electrode to the other, the electric field is in the correct direction to
accelerate them.
• The particles' increasing speed due to these pushes causes them to
move in a larger radius circle with each rotation.
11. Advantage of the cyclotron
• The cyclotron was the first "cyclical" accelerator.
• The advantage of the cyclotron design was that the particles
encounter the accelerating voltage many times during their spiral
path, and so are accelerated many times, so the output energy can be
many times the accelerating voltage.
12. Particle energy
• Since the particles are accelerated by the voltage many times, the final energy of the particles is not
dependent on the accelerating voltage but the diameter of the accelerating chamber, the dees.
• For particles, the centripetal force required to keep them in their curved path is:
• This force is provided by the Lorentz force of the magnetic field
• The particles reach their maximum energy at the periphery of the dees, where the radius of their
path is the radius of the dees. Equating these two forces
• So the output energy of the particles is
13.
14.
15.
16. Medical application
• A cyclotron is a machine used to make relatively short lived radioisotopes
(radioactive atoms) that can be used for:
• medical imaging
• medical research.
• The radiotracer fluorine-18 is made using a particle accelerator (cyclotron).
• Protons must be accelerated to very high speed in order to overcome
repulsion of positively charged target nuclei.
• Fluorine-18 can be used to make radioactive glucose, which is
preferentially taken up by brain and cancer cells.
17. Medical application
• FDG is a glucose analogue widely used in PET imaging. When injected
into a patient it is taken up by high-glucose-using cells located in
areas like the brain, kidney and cancer.
• After FDG is injected the PET scanner forms images of the distribution
of FDG in the body.
