Micro‐arc discharge - vonkarmaninstitute/pantera-pic-dsmc GitHub Wiki
Introduction
This tutorial example consists of a 1D simulation of a micro-arc discharge sustained by thermionic emission, originally inspired by Y. Zhong 2022, showcasing the usage of PIC method with MCC collisions and the inclusion of external circuit solver (ngspice)
Suppose a confined 1D region between two electrodes filled with argon gas at 1 bar pressure. The electrodes are connected to the external DC voltage source U0 through RC circuit. The RC elements of the circuit will serve as external ballast and will stabilize the micro-arc discharge. Furthermore, we assume that the temperature of the gas is 2500 K which is also the temperature of the electrode surfaces $T_\mathrm{w}$. In this case, the full parameters of argon gas is
| Gas parameters | |
|---|---|
| Pressure | $1 \ \textrm{atm}$ |
| Temperature | $2500 \ \mathrm{K}$ |
| Density | $2.94 \cdot 10^{24} \ \mathrm{m^{-3}}$ |
In the simulation, we assume only electrons and ions as particles. Electrons are initially emitted from the heated cathode surface into the argon gas. The resulting flux of electrons is given by the Richardson-Laue-Dushamn equation
$J = \lambda_r A_0 T^2 \exp(-\frac{W}{k T_\text{w}})$
where $W = 4.55 \ \mathrm{eV}$ is the copper work function and $\lambda_r = 0.5$ is the correction factor, typical value for most metals. Particles are then emitted with velocities sampled from the Maxwell-Boltzmann distribution function given by the surface temperature $T_\text{w}$. These electrons will then randomly collide with the background gas using MCC algorithm where we assume these types of collisions: elastic, excitation and ionization. The probabilities are given by the tabulated cross sections (lxcat.net - Phelps database for argon). Ionization leads to the creation of electron and ion pair. Ions collide with neutral gas elastically only.
The 1D domain is assumed 0.1 mm long and 6 mm x 6 mm wide which represents the surface area of the electrode and the resulting flux of electrons.
| Simulation parameters | |
|---|---|
| Domain size | 0.1 mm × 6 mm x 6 mm |
| Number of cells | 100 |
| Time step | 5e-13 s |
| Particle weight | 1e4 |
The closed-loop current is modelled by external library ngspice that is coupled to Pantera. The outcoming or incoming charge at the cathode is assigned to the ngspice solver to solve for the potential across the discharge gap (anode is grounded). The following picture depicts the situation
using the followig values for the circuit elements
| Simulation parameters | |
|---|---|
| Voltage source U0 | 50 V |
| Resistor R | 50 ohm |
| Capacitor C | 10p F |
Pantera input files
An input file needs to be set up for Pantera before launching the simulation. We will see how to set it up in individual parts, starting from gmsh generation, then particle initialization, boundary conditions, and finally the setup of electric circuit for ngspice.