McXtrace - An X-ray ray-trace simulation package

3.5  The Source_lab McXtrace Component

Laboratory x-ray source.

Identification

• Author: Erik B. Knudsen

• Origin: Kgs. Lyngby

• Date: May 2012

Description

Model of a laboratory x-ray tube, generating x-rays by bombarding a target by electrons. Given a input energy E0 of the electron beam, x-rays are emitted from the accessible emission lines The geometry of the tube is assumed to be: # The electron beam hits a slab of surface material surface at a right angle illuminating an area of width by height, # where width is measured along the component X-axis. # The centre of the electron beam at the anode surface is the origin of the component. # The Z-axis of the component points at the centre of the exit window (focus_xw by focus yh) placed at a distance dist from the origin. # The angle between the Z-axis and the anode surface is the take_off angle. For a detailed sketch of the geometry see the componnent manual.

The Bremsstrahlung emitted is modelled using the model of Kramer (1923) as restated in International Tables of Crystallography C 4.1 Characteristic radiation is modelled by Lorentzian (default) or Gaussian energy profiles with line-energies from Bearden (1967), widths from Krause (1979) and intensity from Honkimäki (1990) and x-ray data booklet. Absoprtion of emitted x-rays while travelling through the target anode is included.

Example: Source_lab(material_datafile=”Cu.txt”,Emin=1, E0=80)

Input parameters

Parameters in boldface are required; the others are optional.

Links

• Component source code found in file Source_lab.comp.

X-ray tube laboratory source

Source_lab is a model of a laboratory X-ray tube. An electron ray hits a target of specified material. Currently, only single material targets are allowed. To model multiple material targets one could construct a model with two or more sources simultaneously. This has consequences for intensity of the source which should be downscaled accordingly.

An electron beam of rectangular transverse crossection (width,height) and energy E0 impinges on the target of material. Wrt. the electron beam, the target is considereded infinitely thick. The beam is considered to have uniform intenisty. Thus, the spatial distribution of x-ray generation will be exponential in the depth of the material.

Further, an exit aperture is defined with dimensions (focus_xw,focus_yh). The centre of the aperture is situated at a distance dist \(\mathrm {m}\) from where the electron beam hits the target slab at an elevation of take_off (see Figure 3.5).

The Source_lab coordinate system has its origin in the center of the elctron beam at the surface of the anode material and is oriented such that the z-axis points at the center of the exit window, and the x-axis is parallel to the width of the electron beam.

Note that the exit aperture is merely an opening. If the material absorption of a window, e.g. Be, is to be taken into account a Filter (section 4.6) should be inserted after the exit aperture.

For each photon ray to be generated, a Monte Carlo choice is made to generate either a Bremsstrahlung photon or one from one of the x-ray emission lines of the material. \(( 1-\mathit {frac} )\) of the rays are generated from characteristic emission, and \(( \mathit {frac} )\) from Bremsstrahlung. In most cases Bremsstrahlung is unwanted background, which is why the default is \(0.1\). Note that this only governs how much of the available statistics is diverted into simulating Bremsstrahlung. It does not have an impact on what intensity is detected in subsequent monitors — only on the errorbars of the detected numbers.

The spectral characteristics of the generated Bremsstrahlung is goverened by the model suggested by Kramer [Kra23]. Although disputed in several subsequent papers, the model is simple, and sufficiently accurate for many background estimation purposes.

Characteristic emission on the other hand is sampled from a set of Lorentzian functions with central wavelengths found in the work by [Bea67] with spectral widths taken from [KO79].

An example of beam spectral characteristics emitted from a Cu-anode target detected \(1\) mm from an exit aperture of \(1\times 1\) \(\mathrm {cm}^{2}\) \(10\) \(\mathrm {cm}\) downstream from the target at a take_off angle of \(6\si {\degree }\) is seen in figure 3.5.

Source_lab includes a set of common anode materials: {Cr, Co, Cu, Ga, Mo, Ag, W}. More materials can be added by the following procedure:

1. Find the atomic number, \(Z\), for the material you want to add. So far only single materials are supported.

2. Look up (and note down) the central energies of (up to) 6 characteristic lines for the material in e.g. [Bea67]. Also note down the number lines you have recorded.

3. Look up the natural spectral widths of those lines in [KO79].

4. Find the relative intensity of the the set of lines. For instance from the x-ray data booklet.

5. Note down the ionization energy \(E_I(Z)\), and flourescence yield, \(Y(Z)\), of the anode material.

With this information assemble a code line as:
{\(Z\),\(E_I(Z)\),\(Y(Z)\),\(n\),{\([E_C]\)},{\([W]\)},{\([I]\)}},
and put it in the source file Source_lab.comp, just above the line that reads
{0,0.0,0.0,0,{0,0,0,0,0,0},{0,0,0,0,0,0},{0,0,0,0,0,0}}
in the SHARE section of the component source code. Here \([E_C]\) refers to a comma separated list of characteristic energies in \(\mathrm {keV}\), \([W]\) a list of characteristic widths in \(\mathrm {keV}\), and \([I]\) a list of relative line intensities. Lastly, \(n\) denotes the number of x-ray lines.