Streamer Criterion: Gas models


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 αeff (scalar):

By default : P * 1.065 * Er2 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 αeff as equal to zero for all Er values under 2kV/mm/bar (for the air). In fact, positive αeff for those low E values should not be taken into account in the integration (for negative αeff 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: αeff = 27.9 * P * (Er -8.9246)
  • For Er>12.36kV/mm/bar: αeff = 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 αeff =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

Open the following tool link:


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

Define the following data:

  • E/N range in Td (at 1.013 bar and 293.15K, to convert E from kV/mm to Td, divide by 2.45e-2)
  • Gas temperature
  • The exported points number
  • The normalized fraction of each gas chemical component
6 Click on “Run calculations
7 Click on “Swarm parameters in text file
  • Copy the txt file content from “SWARM PARAMETERS” to “PROCESSES AND REACTION RATES
  • Paste in an Excel file and “convert” the data to separate the columns
  • Create a new column for E in kV/mm (at 1.013 bar and 293.15K, convert E/N from Td to kV/mm by multiplying by 2.45e-2)
  • Create a new column for the αeff coefficient. The formula to obtain it is: αeff = (alpha / Neta / N) * N/1000

With N=2.44e25

10 Plot αeff depending on E in kV/mm
11 Fit the previous curve with a mathematical model (polynomial…)

Computation domain for the Streamer criterion

The user must choose the Regions of the streamer propagation, the selectable regions are:
  • Air or vacuum region
  • Dielectric region with charge source
Selecting these regions, the steamer will cross every faces (Flux 2D) or volumes (Flux 3D) associated to the air or vacuum region for the gas and dielectric region for the insulator, as shown in the following figure:
Figure 1. Simple problem showing the extension of the streamer through the dielectric according to the selected regions, (a) only air is selected (labeled Gas in the figure), (b) dielectric and air are selected.