Streamer Criterion: Gas models
Introduction
In the “Streamer criterion” tool two predefined gas models exist:
 Air model
 SF6 gas model
The proposed models are simple models and they are not optimal for complex cases.
However, the user can use his models which are suited to the studied devices, thanks to the Flux user model.
User defined model
The user model proposes a formula which corresponds by default to the air predefined model.
It contains two fields to complete:
 The expression of the reduced electric field Er (scalar):
With Er = Mod(E) / P ; Mod(E) is the electric field module (the value written by default defines it in kV/mm) and P is the pressure in bar (by default equal to 1 bar). It is important to enter Er in the desired unit in this field, because it is the unit which will be used in the formula following it, and K is depending on this formula. For example :
 To choose V/m/bar: define Er = Mod(E)/1
 To choose kV/mm/bar: define Er = Mod(E)/1E6/1
 To choose kV/cm/torr: define Er = (Mod(E)/1E6)*750.062
 The formula of α_{eff} (scalar):
By default : P * 1.065 * Er^{2} 6.951 * Er + 7.2371) * Valid(Er,2.0)
With P=1 bar by default
The formula must depend on “Er” (defined above).
The expression *Valid(Er,2.0) allows considering α_{eff} as equal to zero for all Er values under 2kV/mm/bar (for the air). In fact, positive α_{eff} for those low E values should not be taken into account in the integration (for negative α_{eff} values, it is automatically set to zero).
Air model
The air model formula is presented in the previous bloc.
User has only to enter the pressure value.
SF6 Model
The SF6 model formula is:
 For Er<12.36kV/mm/bar: α_{eff} = 27.9 * P * (Er 8.9246)
 For Er>12.36kV/mm/bar: α_{eff }= 22.3595 * P * (Er  8.0579)
As for the air, user has only the pressure to enter.
New model
If user would like to enter a new formula, for the air or SF6 or other gas, a free online tool is available. From the gas chemical composition, it is possible to extract the curve α_{eff} =f(E). Then, user can fit the data curve with a mathematical formula (on Excel).
The steps to identify a new mathematical model are presented in the table below:
Step  Action 

1 
Open the following tool link: http://fr.lxcat.net/data/set_databases.php 
2 
Choose one / several databases and click on “next”. For example: click on “ – ” to remove all, then select “Phelps database” 
3  Select the gas chemical components 
4  Confirm the database choice by clicking on “next” 
5 
Define the following data:

6  Click on “Run calculations” 
7  Click on “Swarm parameters in text file” 
8 

9 
With N=2.44e^{25} 
10  Plot α_{eff} depending on E in kV/mm 
11  Fit the previous curve with a mathematical model (polynomial…) 
Computation domain for the Streamer criterion
 Air or vacuum region
 Dielectric region with charge source