Energy Calculator

Background

This calculator takes as inputs any two of Dee size, magnetic field strength and particle energy, and returns the third value along with the resulting magnetic rigidity, resonant frequency and particle speed. The beam particle type may also be changed. These values are only valid for classical cyclotrons with no relativistic effects, and no sanity checks are applied. Energy $E$ , magnetic field strength $B$ , Dee radius $r$ , and particle charge $q$ and mass $m$ are related by

$E= \frac{q^2B^2r^2}{2m},\qquad B= \sqrt{\frac{2Em}{qr}}, \qquad r= \sqrt{\frac{2Em}{qB}}.$

Resonant frequency and (non-relativistic) particle speed $v$ are computed using

$f=\frac{qB}{2\pi m}, \qquad v= \sqrt{\frac{2E}{m}}.$

Magnetic ridigity $B\rho$ , where $\rho$ is the bending radius of a particle exposed to magnetic field $B$ is computed using $B\rho = \frac{p}{q}$ , where $p$ is the particle’s momentum (including relativistic effects).

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