Accelerator physics

As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams and their interaction with accelerator structures by electromagnetic fields.

Furthermore, due to electrostatic fields being conservative, the maximum voltage limits the kinetic energy that is applicable to the particles.

These impedances will induce wakefields (a strong warping of the electromagnetic field of the beam) that can interact with later particles.

In most accelerator concepts (excluding compact structures like the cyclotron or betatron), these are applied by dedicated electromagnets with different properties and functions.

For preliminary calculations, neglecting all fields components higher than quadrupolar, an inhomogenic Hill differential equation can be used as an approximation,[2] with thus identifying the system as a parametric oscillator.

The general equations of motion originate from relativistic Hamiltonian mechanics, in almost all cases using the Paraxial approximation.

Even in the cases of strongly nonlinear magnetic fields, and without the paraxial approximation, a Lie transform may be used to construct an integrator with a high degree of accuracy.