# Arcs and Switches

Over the past few decades there has been an increase in the number of applications for arcing in various gases. Use cases include switch breakers and switches, overvoltage protection, and ionic wind devices. Medical equipment manufacturers, aerospace and automotive companies, and semiconductor producers are all using electric discharge machining, which uses arcing to remove material from a workspace. Additionally, you can assemble semiconductors using plasma enhanced chemical vapor deposition (PECVD).

*EMA Consulting Services*

EMA offers comprehensive services for the design of products that rely on arcing in various gases, including current interruption devices like breakers and switches, as well as other multi-physics applications. Our expert team can integrate electromagnetic effects, fluid dynamics, kinematic effects, and gas-phase chemical reactions to model all relevant phenomena.

Since the 1980s, EMA has been actively involved in multiphysics simulation. We proudly offer Ansys Charge Plus, the first single-product, first-principles simulation tool to model air breakdown. Our services team is globally recognized for their expertise in applying these tools to help you design products that depend on arcs and plasmas.

For designers of current interruption products, we provide the capability to model the entire lifecycle of an arc, which is a plasma. This includes:

- The initiation of the arc through gas breakdown processes
- Plasma and air heating
- Buoyant forces in air
- The forces on charged particles from electric and magnetic fields

To learn more about how we can support your projects, reach out by clicking here.

*How Do We Do It*

There are three overarching methodologies for solving plasmas.

- The microscopic approach: Transports each individual plasma particle according to the Lorentz force. It is the most accurate but is prohibitively expensive.
- Magneto-Hydro-Dynamics (MHD): Treats the plasma as a fluid and transports it according to the Navier-Stokes equations, with a term accounting for the Lorenz force. You can solve this method in a reasonable amount of time, but it lacks the greatest accuracy.
- Kinetic Theory: It is the middle ground between the two previous methods. Charge Plus uses this method and implements it with a Particle-In-Cell (PIC) solver.

The Kinetic Theory fundamentally groups all particles into macroparticles and then transports them according to the Lorentz force. The transport is consistent because the charge-to-mass radio remains constant. In order to properly simulate everything, you also need to account for some continuum physics. This is especially true when it comes to reactions. This allows us to characterize the behavior of the individual particles based on the macroparticle quantities.

To do this, we utilize a distribution function (Figure 1). This tells you that if you have a group of particles at a certain temperature what the spread of the velocity of those particles is going to be.

*Charge Plus Solvers*

Charge Plus uses several numerical methods to solve for arcing including the Finite-Element Method (Time Domain), PIC Fluid Solver, and Continuum Ideal Compressible Fluid Solver. There are many ways in which the PIC solver can influence the other solvers:

- The PIC can generate fields which are added to the fields produced by the EM solver
- PIC quantities can be used to compute reaction update quantities which are applied back to the PIC solver, as well as the to the fluid solver
- The conductivity for PIC environments can be computed and sent to the EM solver
- PIC particles can interact with solids to produce secondary electrons
- PIC particles can locally reduce the electric field through what is known as “charge limiting”

*Discharge Simulation Example *

The following is an example of a simple discharge simulation. Figure 2 shows a parallel plate setup. The plates are 12mm x 12mm x 3mm and there is a 5mm gap between them. The goal of this model is to create a breakdown voltage that agrees with Paschen’s Law, which is the voltage necessary to start a discharge between two electrodes in a gas as a function of pressure and gap length.

A DC current source drives the cathode, which appears in black in Figure 2. The anode, shown in red, is grounded. In this example, nitrogen (N_{2}) gas fills the gap, but you can use other gases or a mixture of gases.

The initial conditions are as follows:

- Initial plasma density of 1E010
*m*^{-3} - Initial plasma temperature of 0.026 eV
- Initial plasma gas pressure of 1 atm
- Initial gas temperatures of 300 Kelvin

In this nitrogen discharge model, we are considering six species in total, three charge carriers and three neutral species, shown below.

EMA provides a plasma library of reaction rates for commonly used gases, including N_{2}, H_{2}, humid N_{2}, CH_{4}, and CO_{2}. We can also provide support for setting up a plasma library for a new gas.

The system uses 49 total reactions, including electron elastic, electron excitation, dissociation, ionization, and recombination.

*Simulation Results*

This model simulated a breakdown voltage of 20.2 kV. Figure 3 shows the results. The expected breakdown voltage from Paschen’s law was 19 kV, for a 6.3% error. This only tells you the absolute minimum voltage you can have for a breakdown to occur, but it is possible for a breakdown to occur at a higher voltage.

Figure 4 is an animation of the electron density. We see that the electron density peaks at 3E+021^{#}/_{m}_{3}, this is the expected magnitude. The animation shows that the discharge forms along the edge of the cathode, which is where we expect it to occur.

We can also take a look at electron temperature. Figure 5 shows that it peaks at about 4.5 eV and then settles to about 0.1 eV after the discharge, which is an acceptable range.

*Expanding Capabilities*

EMA plans on continuing to expand out discharge simulation capabilities by adding the following features in future releases:

- Ablation model
- Moving geometry
- Temperature of solids

Watch our Solving Electromagnetic Challenges webinar “Kinetic Theory of Plasma Discharges and its Simulation Capabilities” for more detail. You can find the full video here.

EMA is here to solve your arcing problems, reach out now to learn more about how can help you.