Vaughan

Presentation

This is the most basic Vaughan model, as defined in original Vaughan paper [Vau89, Vau93]. It gives the TEEY, and takes the incidence angle of PEs into account.

Input files

You must provide measured TEEY at normal incidence.

	Emission Yield	Emission energy distribution	Emission angle distribution
“True” secondaries	❌	❌	❌
Elastically backscattered	❌	❌	❌
Inelastically backscattered	❌	❌	❌
Total	✅	❌	❌

Definitions

The TEEY is given by:

\[\begin{split}\sigma(E, \theta) &= \sigma_\mathrm{max}(\theta) \times (\xi \mathrm{e}^{1-\xi} )^k \mathrm{\quad if~} \xi \leq 3.6 \\ &= \sigma_\mathrm{max}(\theta) \times \frac{1.125}{\xi^{0.35}} \mathrm{\quad if~} \xi > 3.6\end{split}\]

\(\xi\) is defined by:

\[\xi = \frac{E - E_0}{E_\mathrm{max} - E_0}\]

Under the limit \(E_0\) (\(12.5\mathrm{\,eV}\) by default), the TEEY is set to a unique value (\(0.5\) by default).

\[ \begin{align}\begin{aligned}\sigma_\mathrm{max}(\theta) = \sigma_\mathrm{max}(\theta = 0^\circ) \times \frac{1}{k_s\theta^2/\pi}\\E_\mathrm{max}(\theta) = E_\mathrm{max}(\theta = 0^\circ) \times \frac{1}{k_{se}\theta^2/\pi}\end{aligned}\end{align} \]

The \(k_s\) and \(k_{se}\) are both set to unity by default.

The factor \(k\) is given by:

\[\begin{split}k &= 0.56 \mathrm{\quad if~} \xi \leq 1 \\ &= 0.25 \mathrm{\quad if~} 1< \xi \leq 3.6 \\\end{split}\]

Model parameters

The parameters list is dynamically created here: Vaughan API documentation.

Implementations

Two alternative implementations for Vaughan are implemented: CST and SPARK3D. Just instantiate your model with:

model = Vaughan(implementation="CST") # or "SPARK3D"
# alternative:
model = Vaughan()
model.preset_implementation("CST")

From the GUI, manually reproduce the steps described in the vaughan.Vaughan.preset_implementation() method. More specific documentation is also listed in vaughan.Vaughan.preset_implementation().

Parameter Vaughan with \(E_{\mathrm{c,\,1}}\) instead of \(E_0\)

When \(E_0\) is unlocked, a fit over this variable is performed to match \(E_{\mathrm{c,\,1}}\). You must provide either a TEEY file path, either enter the other Vaughan parameters yourself (see image below), and click Fit!.

To-do list

Todo

• Unlock \(k_s\), \(k_{se}\) to have better overall fit? In particular: if several incidence angles are provided.

• Instructions to match CST Vaughan.

• Instructions to match SPARK3D Vaughan.