Editing Cyclotron (section)

=== Post-war ===
By the late 1930s it had become clear that there was a practical limit on the beam energy that could be achieved with the traditional cyclotron design, due to the effects of [[special relativity]].<ref>{{cite journal |last1=Bethe |first1=H. A. |last2=Rose |first2=M. E. |date=15 December 1937 |title=The Maximum Energy Obtainable from the Cyclotron |journal=Physical Review |volume=52 |issue=12 |pages=1254–1255 |bibcode=1937PhRv...52.1254B |doi=10.1103/PhysRev.52.1254.2}}</ref>  As particles reach relativistic speeds, their effective mass increases, which causes the resonant frequency for a given magnetic field to change.  To address this issue and reach higher beam energies using cyclotrons, two primary approaches were taken, [[Synchrocyclotron|synchrocyclotrons]] (which hold the magnetic field constant, but decrease the accelerating frequency) and isochronous cyclotrons (which hold the accelerating frequency constant, but alter the magnetic field).<ref name="craddock2">{{cite conference |last=Craddock |first=M.K. |date=September 10, 2010 |title=Eighty Years of Cyclotrons |url=http://accelconf.web.cern.ch/Cyclotrons2010/papers/mom1cio02.pdf |access-date=January 24, 2022 |book-title=Proceedings of Cyclotrons 2010 |place=Lanzhou, China}}</ref>

Lawrence's team built one of the first synchrocyclotrons in 1946. This {{convert|184|in|m|abbr=on}} machine eventually achieved a maximum beam energy of 350&nbsp;MeV for protons. However, synchrocyclotrons suffer from low beam intensities (<&nbsp;1&nbsp;μA), and must be operated in a "pulsed" mode, further decreasing the available total beam. As such, they were quickly overtaken in popularity by isochronous cyclotrons.{{r|craddock}}

The first isochronous cyclotron (other than classified prototypes) was built by F. Heyn and K.T. Khoe in Delft, the Netherlands, in 1956.<ref name="heyn2">{{cite journal |last1=Heyn |first1=F. |last2=Khoe |first2=Kong Tat |date=1958 |title=Operation of a Radial Sector Fixed-Frequency Proton Cyclotron |journal=Review of Scientific Instruments |volume=29 |issue=7 |page=662 |bibcode=1958RScI...29..662H |doi=10.1063/1.1716293}}</ref> Early isochronous cyclotrons were limited to energies of ~50&nbsp;MeV per nucleon, but as manufacturing and design techniques gradually improved, the construction of "spiral-sector" cyclotrons allowed the acceleration and control of more powerful beams. Later developments included the use of more compact and power-efficient [[superconducting magnets]] and the separation of the magnets into discrete sectors, as opposed to a single large magnet.{{r|craddock}}