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 e is the electron charge, E is the linearly polarised electric field amplitude, \omega_0 is the laser carrier frequency and m is the electron mass. In terms of the laser intensity I, using, it reads less simply: where \epsilon_0 is the vacuum permittivity. For typical orders of magnitudes involved in laser physics, this becomes: where the laser wavelength is, and c is the speed of light. The units are electronvolts (eV), watts (W), centimeters (cm) and micrometers (μm).

Atomic units

In atomic units, e=m=1,, \alpha c=1 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 q 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 U_p.

References and notes