Ponderomotive energy


In strong-field laser physics, ponderomotive energy is the cycle-averaged quiver energy of a free electron in an electromagnetic field.

Equation

The ponderomotive energy is given by
where is the electron charge, is the linearly polarised electric field amplitude, is the laser carrier frequency and is the electron mass.
In terms of the laser intensity, using, it reads less simply:
where is the vacuum permittivity.

Atomic units

In atomic units,,, where. If one uses the atomic unit of electric field, then the ponderomotive energy is just

Derivation

The formula for the ponderomotive energy can be easily derived. A free particle of charge
interacts with an electric field. The force on the charged particle is
The acceleration of the particle is
Because the electron executes harmonic motion, the particle's position is
For a particle experiencing harmonic motion, the time-averaged energy is
In laser physics, this is called the ponderomotive energy.