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

Equation

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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

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In atomic units,  ,  ,   where  . If one uses the atomic unit of electric field,[3] then the ponderomotive energy is just

 

Derivation

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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

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References and notes

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