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 bywhere 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.
For typical orders of magnitudes involved in laser physics, this becomes:
where the laser wavelength is, and is the speed of light. The units are electronvolts, watts, centimeters and micrometers.
Atomic units
In atomic units,,, where. If one uses the atomic unit of electric field, then the ponderomotive energy is justDerivation
The formula for the ponderomotive energy can be easily derived. A free particle of chargeinteracts 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 kinetic energy is
In laser physics, this is called the ponderomotive energy.