1. Accelerating charged particles

1.1 Relativistic particle energy

The relativistic formulation is used to describe the motion of accelerated particles, which reach speeds close to that of light. A particle in motion can be defined by its absolute velocity v, or by its relative velocity β = v /c, c being the speed of light in a vacuum. Its energy at rest is equal to E ₀ = mc ² , where m is its mass. Its total energy in motion is equal to γ · mc ² where γ is the Lorentz factor relating to the particle's motion :