normalized_vector_potential

plasmapy.formulary.laser.normalized_vector_potential(
intensity: Annotated[Quantity, Unit('W / m2')],
wavelength: Annotated[Quantity, Unit('m')],
) → float | ndarray[source]

Calculate the normalized vector potential \(a_0\) from the intensity \(I\) and the wavelength \(\lambda\).

The normalized vector potential is also known as a dimensionless oscillation amplitude, quiver velocity, or normalized quiver momentum of an electron.

The normalized vector potential of a laser is calculated using:

\[a_0= \frac{e E_0}{m_e \omega c}=\frac{e \lambda}{m_e \pi} \sqrt{\frac{I} {2 \epsilon_0 c^5}},\]

where \(e\) is the fudamental charge, \(E_0\) is the electric field amplitude, \(m_e\) is the mass of an electron, \(\omega\) is the angular frequency of the electromagnetic wave, \(c\) is the speed of light, \(\lambda\) is the wavelength, \(I\) is the intensity of the elecromagnetic wave, and \(\epsilon_0\) is the permitivity of free space.

Aliases: a0_

Parameters:

  • intensity (Quantity) – Intensity of the laser pulse (convertible to W / m2).

  • wavelength (Quantity) – Wavelength of the laser (convertible to m).

Returns:

a_0 – The normalized vector potential of a plasma given the intensity and wavelength of a laser.

Return type:

float | numpy.ndarray

Notes

For details, see Gibbons [2016].

Examples

>>> import astropy.units as u
>>> normalized_vector_potential(1e18 * u.watt / u.cm**2, 1 * u.um)
np.float64(0.8549297...)