In strong-field laser physics, ponderomotive energy is the cycle-averaged quiver energy of a free electron in an electromagnetic field.[1]

## 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,[2] 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 .