.. _func-IkedaCarpenterConvoluted:

========================
IkedaCarpenterConvoluted
========================

.. index:: IkedaCarpenterConvoluted

Description
-----------

This function is an Ikeda-Carpenter function convolved with a tophat function and a Gaussian function.  The Ikeda-Carpenter function is given by:

.. math::
    V =  Scale \times \Big\{ (1-R)(\alpha t')^2 e^{-\alpha t'} + 2R\frac{\alpha^2 \beta}{(\alpha-\beta)^3} \times
    \big[ e^{-\beta t'} - e^{-\alpha t'}  (1 + (\alpha - \beta)t' + \frac{1}{2}(\alpha-\beta)^2t'^2) \big]    \Big\}

This is convolved with a tophat function (of width **hatWidth**) and a Gaussian function :math:`exp(-k_{conv} t^2)`.

.. attributes::

There are no attributes for this function.

.. properties::

See Ikeda, S. & Carpenter, J.M. (1985). *Nuclear Instruments and Methods in Physics Research Section A* **239**, 536-544 for additional details on parameters

Usage
~~~~~

Here is an example of generating an Ikeda-Carpenter function:

.. code-block:: python
    :linenos:

    import numpy as np
    import matplotlib.pyplot as plt
    fICC = IkedaCarpenterConvoluted()
    fICC['scale'] = 1.0
    fICC['A'] = 0.1
    fICC['B'] = 1.e-2
    fICC['R'] = 0.3
    fICC['T0'] = 27000.
    fICC['hatWidth'] = 0.5
    fICC['k_conv'] = 120.

    x = np.linspace(26000, 28000,100)
    y = fICC(x)
    plt.plot(x,y)

.. categories::

.. sourcelink::
    :filename: ICConvoluted