Editing Linear particle accelerator (section)

=== Radiofrequency acceleration ===

When a [[charged particle]] is placed in an [[electromagnetic field]] it experiences a force given by the [[Lorentz force]] law:

:<math>\vec{F} = q \vec{E} + q \vec{v} \times \vec{B}</math>

where <math>q</math> is the charge on the particle, <math>\vec{E}</math> is the electric field, <math>\vec{v}</math> is the particle velocity, and <math>\vec{B}</math> is the magnetic field. The cross product in the magnetic field term means that static magnetic fields cannot be used for particle acceleration, as the magnetic force acts perpendicularly to the direction of particle motion.<ref name="conte">{{cite book |last1=Conte |first1=Mario |last2=MacKay |first2=William |title=An introduction to the physics of particle accelerators |date=2008 |publisher=World Scientific |location=Hackensack, N.J. |isbn=9789812779601 |pages=1 |edition=2nd}}</ref>

As [[Electrical breakdown|electrostatic breakdown]] limits the maximum constant voltage which can be applied across a gap to produce an electric field, most accelerators use some form of RF acceleration. In RF acceleration, the particle traverses a series of accelerating regions, driven by a source of voltage in such a way that the particle sees an accelerating field as it crosses each region. In this type of acceleration, particles must necessarily travel in "bunches" corresponding to the portion of the oscillator's cycle where the electric field is pointing in the intended direction of acceleration.<ref name="edwards">{{cite book |last1=Edwards |first1=D. A. |last2=Syphers |first2=M.J. |title=An introduction to the physics of high energy accelerators |date=1993 |publisher=Wiley |location=New York |isbn=9780471551638}}</ref>

If a single oscillating voltage source is used to drive a series of gaps, those gaps must be placed increasingly far apart as the speed of the particle increases. This is to ensure that the particle "sees" the same phase of the oscillator's cycle as it reaches each gap. As particles asymptotically approach the speed of light, the gap separation becomes constant: additional applied force increases the energy of the particles but does not significantly alter their speed.{{r|conte|p=9-12}}