solprop.tools.pulse#

Pulse shape numbers: the natural width, peak power and energy of a pulse.

The sech and Gaussian shapes the design numbers are defined for, and the carrier frequency of a vacuum wavelength the other tools modules share.

Module Attributes

PulseShape

The two pulse shapes the design numbers are defined for.

Functions

`pulse_energy`(peak_power, fwhm[, shape])	Return the energy of a pulse of given peak power, duration and shape.
`pulse_peak_power`(energy, fwhm[, shape])	Return the peak power of a pulse of given energy, duration and shape.
`pulse_width`(fwhm[, shape])	Return the natural width of a pulse from its full width at half maximum.

solprop.tools.pulse.PulseShape#

The two pulse shapes the design numbers are defined for.

alias of Literal[‘sech’, ‘gauss’]

solprop.tools.pulse.pulse_energy(peak_power, fwhm, shape='sech')[source]#

Return the energy of a pulse of given peak power, duration and shape.

The inverse of pulse_peak_power(), for the same shape.

Parameters:

peak_powerfloat: Peak power in W, > 0.
fwhmfloat: Full width at half maximum of the power in s, > 0.
shape{‘sech’, ‘gauss’}, optional: The pulse shape; see pulse_width().

Returns:

float: Pulse energy in J.

Raises:

ToolsError: If the shape is unknown or a quantity is not positive.

Examples

>>> from solprop.tools import pulse_energy
>>> f"{pulse_energy(88.137e9, 10e-15) * 1e3:.4f}"
'1.0000'

solprop.tools.pulse.pulse_peak_power(energy, fwhm, shape='sech')[source]#

Return the peak power of a pulse of given energy, duration and shape.

Parameters:

energyfloat: Pulse energy in J, > 0.
fwhmfloat: Full width at half maximum of the power in s, > 0.
shape{‘sech’, ‘gauss’}, optional: The pulse shape; see pulse_width().

Returns:

float: Peak power in W: \(E/(2\tau_0)\) for sech and \(E/(\sqrt\pi\,\tau_0)\) for a Gaussian, the integrals of the two shapes.

Raises:

ToolsError: If the shape is unknown or a quantity is not positive.

Examples

>>> from solprop.tools import pulse_peak_power
>>> f"{pulse_peak_power(1e-3, 10e-15) / 1e9:.3f}"
'88.137'
>>> f"{pulse_peak_power(1e-3, 10e-15, 'gauss') / 1e9:.3f}"
'93.944'

solprop.tools.pulse.pulse_width(fwhm, shape='sech')[source]#

Return the natural width of a pulse from its full width at half maximum.

Parameters:

fwhmfloat: Full width at half maximum of the power in s, > 0.
shape{‘sech’, ‘gauss’}, optional: "sech" for \(P\propto{\rm sech}^2(t/\tau_0)\), "gauss" for \(P\propto\exp(-t^2/\tau_0^2)\).

Returns:

float: \(\tau_0\) in s: fwhm / (2 ln(1 + sqrt 2)) or fwhm / (2 sqrt(ln 2)).

Raises:

ToolsError: If the shape is unknown or the width is not positive.

Examples

>>> from solprop.tools import pulse_width
>>> f"{pulse_width(10e-15) * 1e15:.4f}"
'5.6730'
>>> f"{pulse_width(10e-15, 'gauss') * 1e15:.4f}"
'6.0056'