.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_gallery/ionisation/plot_ionisation_rates.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_gallery_ionisation_plot_ionisation_rates.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_gallery_ionisation_plot_ionisation_rates.py:


Ionisation: the rates of the noble gases
========================================

The default ionisation rates
(:func:`optmat.gas.ionisation_rates.ionisation_rate_model`).

**Left:** the cycle-averaged rate of each gas at 800 nm against the intensity, up to
twice the barrier-suppression field, the range over which the static correction was
fitted. The circles mark a Keldysh parameter of 1 and the squares the
barrier-suppression intensity.

**Centre:** argon at 400, 800 and 1030 nm and in a static field (the cycle average of
the static rate). The rate tends to the static one as the intensity rises and the
Keldysh parameter falls.

**Right:** the average of the instantaneous rate over a cycle, over the
cycle-averaged rate, for argon at 800 nm. In the default model the two are related
through the local slope and curvature of the rate
(:func:`optmat.gas.ionisation_rates.cycle_average`) and agree to 3 %. With the factor
of the tunnelling limit, :math:`(3F/\pi F_0)^{1/2}`, which the literature's forms use
(here ``ppt_larochelle``), the instantaneous rate ionises more over a cycle than the
cycle-averaged rate it was made from (TC-662).

.. GENERATED FROM PYTHON SOURCE LINES 31-102



.. image-sg:: /auto_gallery/ionisation/images/sphx_glr_plot_ionisation_rates_001.svg
   :alt: 800 nm, Ar, Ar, 800 nm
   :srcset: /auto_gallery/ionisation/images/sphx_glr_plot_ionisation_rates_001.svg
   :class: sphx-glr-single-img





.. code-block:: Python

    import math

    import matplotlib.pyplot as plt
    import numpy as np
    from _helpers import COLOURS

    from optmat.constants import EPS0, C
    from optmat.gas.ionisation_rates import ionisation_rate_model
    from optmat.gas.ionisation_validation import amplitude


    def intensity_of(field):
        """Return the intensity in W/cm^2 of a field's amplitude in V/m."""
        return 0.5 * EPS0 * C * field**2 / 1e4


    fig, axes = plt.subplots(1, 3, figsize=(14, 4.6), layout="constrained")
    for colour, gas in zip(COLOURS, ("Xe", "Kr", "Ar", "Ne", "He"), strict=False):
        model = ionisation_rate_model(gas, 800e-9)
        field = np.geomspace(
            0.2 * model.barrier_suppression_field, model.maximum_field, 200
        )
        rate = model.cycle_averaged_rate(field)
        axes[0].loglog(intensity_of(field), rate, color=colour, label=gas)
        unity = np.interp(-1.0, -model.keldysh(field)[::-1], field[::-1])
        for mark, at in (("o", unity), ("s", model.barrier_suppression_field)):
            axes[0].loglog(
                intensity_of(at), model.cycle_averaged_rate(at), mark, color=colour, ms=5
            )
    axes[0].set_ylim(1e4, 1e16)
    axes[0].set_xlabel("intensity (W/cm$^2$)")
    axes[0].set_ylabel("cycle-averaged rate (1/s)")
    axes[0].set_title("800 nm")
    axes[0].legend()

    argon = ionisation_rate_model("Ar", 800e-9)
    field = np.geomspace(0.2 * argon.barrier_suppression_field, argon.maximum_field, 200)
    for colour, wavelength in zip(
        COLOURS, (400e-9, 800e-9, 1030e-9, math.inf), strict=False
    ):
        label = "static" if math.isinf(wavelength) else f"{wavelength * 1e9:.0f} nm"
        rate = argon.at_wavelength(wavelength).cycle_averaged_rate(field)
        axes[1].loglog(intensity_of(field), rate, color=colour, label=label)
    axes[1].set_ylim(1e4, 1e16)
    axes[1].set_xlabel("intensity (W/cm$^2$)")
    axes[1].set_ylabel("cycle-averaged rate (1/s)")
    axes[1].set_title("Ar")
    axes[1].legend()

    phase = np.linspace(0, math.pi / 2, 2001)
    intensity = np.geomspace(2e17, 2.4e18, 30)
    for name, colour, label in (
        ("default", "#0b0b0b", "optmat `default`: through the slope and curvature"),
        ("ppt_larochelle", COLOURS[1], "the factor of the tunnelling limit"),
    ):
        model = ionisation_rate_model("Ar", 800e-9, name)
        ratio = [
            np.trapezoid(model.instantaneous_rate(peak * np.cos(phase)), phase)
            * 2
            / math.pi
            / float(model.cycle_averaged_rate(peak))
            for peak in amplitude(intensity)
        ]
        axes[2].semilogx(intensity / 1e4, ratio, color=colour, label=label)
    axes[2].axhline(1.0, color="#52514e", lw=0.8)
    axes[2].set_ylim(0.9, 1.6)
    axes[2].set_xlabel("intensity (W/cm$^2$)")
    axes[2].set_ylabel("average of the instantaneous rate / cycle-averaged rate")
    axes[2].set_title("Ar, 800 nm")
    axes[2].legend(fontsize=8)
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.306 seconds)


.. _sphx_glr_download_auto_gallery_ionisation_plot_ionisation_rates.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_ionisation_rates.ipynb <plot_ionisation_rates.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_ionisation_rates.py <plot_ionisation_rates.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_ionisation_rates.zip <plot_ionisation_rates.zip>`