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.

GUI

Select your implementation from the Parameters menu.

API

Instantiate your model with:

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

More specific documentation in vaughan.Vaughan.set_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.
In reality, SPARK3D implementation of Vaughan models EBEEY too!
Threshold energy in CST cannot be negative.