# Principles of Particle acceleration

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1. May 3, 2012

### CloudChamber

Hello all,
Could anyone explain how a betatron functions and its general purpose or application?
Thanks!

2. May 3, 2012

### Bob S

The betatron accelerator is specifically used for accelerating light charged particles at or near the speed of light, which means electrons. There are three basic physics principles which are important in the basic betatron accelerator operation.

The voltage around a loop containing a changing magnetic field is
$$\oint E \space d \ell = V = - \int n \cdot \frac{dB}{dt}dA$$

2) Lorentz force law
The vector force on a charged particle with velocity v moving in a perpendicular magnetic field B is a force perpendicular to the velocity.
$$\overrightarrow{F}=q\overrightarrow{v}\times \overrightarrow{B}$$
$$B\rho=mc^2\frac{\beta\gamma}{c} \space \space Tesla-meters$$