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 by
:$U_p =$,

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 $I=c\epsilon_0 E^2/2$, it reads less simply:
:$U_p$

\cdot ,

where $\epsilon_0$ is the vacuum permittivity.

For typical orders of magnitudes involved in laser physics, this becomes:

:$U_p (\mathrm) = 9.33 \cdot I(10^ \mathrm^2) \cdot \lambda(\mathrm)^2$,

where the laser wavelength is $\lambda= 2\pi c/\omega_0$, and $c$ is the speed of light. The units are electronvolts (eV), watts (W), centimeters (cm) and micrometers (μm).

Atomic units

In atomic units, $e=m=1$, $\epsilon_0=1/4\pi$, $\alpha c=1$ where $\alpha \approx 1/137$. If one uses the atomic unit of electric field,CODATA Value
atomic unit of electric field
/ref> then the ponderomotive energy is just
:$U_p = \frac.$

Derivation

The formula for the ponderomotive energy can be easily derived. A free particle of charge
$q$ interacts with an electric field $E \, \cos(\omega t)$. The force on the charged particle is
:$F = qE \, \cos(\omega t)$.

The acceleration of the particle is
:$a_ = = \cos(\omega t)$.

Because the electron executes harmonic motion, the particle's position is
:$x = = -\frac \, \cos(\omega t) = -\frac \sqrt \, \cos(\omega t)$.

For a particle experiencing harmonic motion, the time-averaged energy is
:$U = \textstylem\omega^2 \langle x^2\rangle =$.

In laser physics, this is called the ponderomotive energy $U_p$.

See also

*Ponderomotive force
*Electric constant
*Harmonic generation
* List of laser articles

References and notes

Laser science
Energy (physics)

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