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A Maxwellian Perspective on Particle Acceleration

In a Maxwellian view, an accelerator of charged particles converts electromagnetic field energy into mechanical energy of the particles. A conventional accelerator based on a resonant cavity emphasizes interference between the drive fields and the the spontaneous radiation fields (those fields radiated when charged particles pass through an otherwise empty cavity). In this case the interference term, and hence the particles’ energy gain, is linear with the drive field. Particles can also extract positive mechanical energy from a drive wave in free space, where the corresponding decrease in field energy occurs due to interference between the drive fields and the radiated fields of the charged particles as a result of their motion in the drive field. This viewpoint leads to the conclusion that a focused laser pulse in vacuum (far from any matter) can impart an energy gain ΔUmax ≈ γ 0 η 2 mc 2 to a free electron of initial Lorentz factor γ 0 . This gain is quadratic in the strength η = eE0/mωc of the laser field. A condition for maximal energy gain is that the Rayleigh range of the laser focus be equal to the formation length γ 2 η 2 λ, and consequently the maximal accelerating gradient varies inversely with electron energy. The maximal energy gain can, in principle, be achieved with linearly or circularly polarized laser beams with optical elements far from the laser focus, or with an axicon beam where the optical elements form a laser cavity of length approximately equal to the Rayleigh range.