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.
For typical orders of magnitudes involved in laser physics, this becomes:
- ,[2]
where the laser wavelength is , and is the speed of light. The units are electronvolts (eV), watts (W), centimeters (cm) and micrometers (μm).
Atomic units
In atomic units, , , where . If one uses the atomic unit of electric field,[3] 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 .
See also
References and notes