Isochronous cyclotron

Isochronous cyclotron

If instead the magnetic field is varied with radius while the frequency of the accelerating field is held constant, this leads to the isochronous cyclotron. $${\displaystyle B(r)={\frac {m_{0}}{q{\sqrt {\left({\frac {1}{2\pi f}}\right)^{2}-\left({\frac {r}{c}}\right)^{2}}}}}}$$