Here is a schematic diagram of such an arrangement:

If the field is in phase with the ions, they receive a kick from it every half cycle. These kicks increase the kinetic energy of the particle and hence the radius of the orbit of the ions until they exit through the window.

Q1) Explain why the dees must shield the particles from electric fields. What would be a suitable metal to make them from ?

Q2) Why must the dees be placed inside a vacuum tank ?

Q3) Derive a formula for the frequency at which the ions circle the cyclotron

(a) If relativistic increase in mass is ignored.

(b) If relativistic increase in mass is accounted for.

Hence deduce that the answer is independent of the kinetic energy of the ions
if v << c.

Q4) Evaluate (a) for protons if the magnetic field strength B is 1.5 Tesla. Would it matter which way the apparatus was oriented in the Earth's magnetic field ? Explain.
 

Q5) Explain as fully as you can why the ions are forced to spiral outwards.

Q6) For protons show that the maximum speed in a 60cm diameter cyclotron is approximately 4.3x10⁷ ms^-1
 

Q7 (a) Show from first principles that the kinetic energy of a particle of rest mass m_o is given by

(b) Show that this is roughly 9.8 Mev for a proton. What fraction of its rest mass / energy is this?
 

Q8)(a) If the protons redeive a kick of 10⁵ volts each time they pass through a gap, then calculate the number of revolutions they make before leaving through the window.

(b)If the relativistic increase in mass is ignored then calculate the time it takes for a proton to exit the cyclotron.
 

Q9)(Hard) (a) If the increase in mass is taken into account show thatif the energy given to the particle on each cycle is DK, then the time spent inthe first half cycle is given by the equation

(b) Hence deduce that the total time spent in the cyclotron is given by:

and evaluate this for the proton.

Q10) Comment on the significance of this correction.