Editing Cyclotron (section)

==Advantages and limitations==

[[File:M. Stanley Livingston (L) and Ernest O. Lawrence in front of 27-inch cyclotron at the old Radiation Laboratory at the... - NARA - 558593.tif|thumb|M. Stanley Livingston and [[Ernest O. Lawrence]] ''(right)'' in front of Lawrence's {{convert|27|in|cm|order=flip|abbr=on}} cyclotron at the Lawrence Radiation Laboratory. The curving metal frame is the magnet's core, the large cylindrical boxes contain the coils of wire that generate the magnetic field. The vacuum chamber containing the "dee" electrodes is in the center between the magnet's poles.]]

The most obvious advantage of a cyclotron over a [[linear accelerator]] is that because the same accelerating gap is used many times, it is both more space efficient and more cost efficient; particles can be brought to higher energies in less space, and with less equipment. The compactness of the cyclotron reduces other costs as well, such as foundations, radiation shielding, and the enclosing building. Cyclotrons have a single electrical driver, which saves both equipment and power costs. Furthermore, cyclotrons are able to produce a continuous beam of particles at the target, so the average power passed from a particle beam into a target is relatively high compared to the pulsed beam of a synchrotron.<ref name="peach">{{cite journal |last1=Peach |first1=K |last2=Wilson |first2=P |last3=Jones |first3=B |title=Accelerator science in medical physics |journal=The British Journal of Radiology |date=December 2011 |volume=84 |issue=special_issue_1 |pages=S4–S10 |doi=10.1259/bjr/16022594 |pmid=22374548 |pmc=3473892 }}</ref>

However, as discussed above, a constant frequency acceleration method is only possible when the accelerated particles are approximately obeying [[Newton's laws of motion]]. If the particles become fast enough that [[Special Relativity|relativistic]] effects become important, the beam becomes out of phase with the oscillating electric field, and cannot receive any additional acceleration. The classical cyclotron (constant field and frequency) is therefore only capable of accelerating particles up to a few percent of the speed of light. Synchro-, isochronous, and other types of cyclotrons can overcome this limitation, with the tradeoff of increased complexity and cost.{{r|peach}}

An additional limitation of cyclotrons is due to [[space charge]] effects – the mutual repulsion of the particles in the beam.  As the amount of particles (beam current) in a cyclotron beam is increased, the effects of [[Coulomb's law|electrostatic repulsion]] grow stronger until they disrupt the orbits of neighboring particles.  This puts a functional limit on the beam intensity, or the ''number'' of particles which can be accelerated at one time, as distinct from their energy.<ref>{{cite journal |last1=Reiser |first1=Martin |title=Space Charge Effects and Current Limitations in Cyclotrons |journal=IEEE Transactions on Nuclear Science |date=1966 |volume=13 |issue=4 |pages=171–177 |doi=10.1109/TNS.1966.4324198 |bibcode=1966ITNS...13..171R }}</ref>