Simulating Plasma Sheaths: A Langmuir Probe Tutorial in Ansys Charge Plus

Welcome to Part 2 of our Plasma Simulation series.

In this installment, we move beyond basic setups to a practical diagnostic application: simulating a Langmuir Probe. Langmuir probes are fundamental diagnostic tools used to measure the electron temperature, electron density, and electric potential of a plasma.

By the end of this tutorial, you will understand how to set up a Particle-in-Cell (PIC) simulation in Ansys Charge Plus to visualize the formation of plasma sheaths and the depletion regions that occur when a voltage bias is applied to a probe.

Catch up on the Series

Before we jump into the complexities of plasma sheaths and PIC solvers, make sure you’ve checked out Part 1 of our Plasma Simulation series: Exploring Plasma Simulation: An Introduction to Ansys Charge Plus. In that introductory post, we covered the essentials of the Ansys Charge Plus interface and established the foundational workflows for electromagnetic simulation. Building on those basics, we are now ready to advance to Part 2, where we apply those skills to a practical diagnostic application.

The Simulation Workspace

We will be working primarily within the Ansys Charge Plus interface. While the GUI offers a vast array of multiphysics tools, we will focus on the specific ribbons required for plasma dynamics: Prepare (for geometry), Charge (for physics), and EMA3D Connect (for results).

Note: Before beginning, ensure your stage is set to "EMA3D". If you see a blue box labeled "Model" at the bottom of your screen, switch the stage to access the correct physics tools.

Step 1: constructing the Geometry

Before defining physics, we must define the physical domain. We need to model two distinct regions: the probe itself and the volume of plasma surrounding it.

1. Create the Spheres: In the Prepare tab, create a 3mm sphere (the probe) and a larger 20mm sphere (the plasma volume). Crucially, ensure "No Merge" is selected so these remain distinct bodies.
   
   
   
   
2. Define the Fluid Volume: Using the Interference tool, subtract the smaller sphere from the larger one. This creates a hollow cavity inside the large sphere, effectively defining the vacuum volume where the plasma will exist.

Step 2: Configuring the Domain

With the geometry set, we move to the Charge tab to configure the global solver settings via the Domain tool.

• Simulation Type: Set this to Plasma Dynamics. This activates the solvers required for charged particle movement.
• Time Stepping: We set the Internal Time Step to 1 nanosecond with a total of 1000 time steps. This results in a total simulation time of 1 microsecond.
• PIC Options: Set the Statistical Measure to 100,000. This target ensures the solver tracks enough macro-particles to statistically represent the plasma density accurately.

Step 3: Assigning Materials

We need to define the background medium for our simulation volume. Navigate to the Materials tab, select Body Material, and choose VACUUM from the local library.

This tells the solver that the large sphere is a vacuum volume into which we will inject our plasma species.

Step 4: Creating Plasma Environments

Now we define the physics of the plasma itself. In Charge Plus, "Plasma Environments" allow you to stack multiple species (electrons, ions, neutrals) to interact simultaneously. We will use the Particle-in-Cell (PIC) solver for high-fidelity particle tracking.

1. The Electrons

We create an environment named "Electrons" with a Maxwellian distribution.

• Temperature: 2 eV
• Density: 10^14 n/m^3 (Low density)

2. The Ions (Argon)

We create a second environment for "Ar+" ions.

• Mass: 40 amu (This is critical to correctly represent Argon).
• Distribution: Matches the electrons (2 eV temperature,10^14 n/m^3  density).

Step 5: Electromagnetic Boundaries & Excitation

To simulate the Langmuir probe sweep, we need to drive the potential on the probe surface.

1. Define Boundaries: Create a Scalar Potential boundary of 0 V named "Probe" and assign it to the inner sphere. Apply a second 0 V boundary to the outer sphere to ground the simulation volume.
2. Create a Signal: In the Excitation ribbon, create a Linear Ramp signal. Set the Amplitude to 15. This will sweep the voltage from 0 V to 15 V over the course of the simulation.
3. Assign the Signal: Drag and drop the Linear Ramp signal onto the "Probe" boundary in the simulation tree.

Step 6: Environment Inlets and Outlets

Finally, we must tell the solver how particles behave at the edges of our geometry.

• Inlet (Outer Sphere): Create a Density inlet on the outer surface. Assign both Electrons and Ar+ plasmas with a fixed density of 10^14 n/m^3. This maintains the ambient plasma levels at the edge of the simulation.
  
• Outlet (Probe Surface): Create an Outlet on the inner probe surface with a Loss Fraction of 1. This makes the probe perfectly absorbing—any particle that hits the probe is removed from the simulation (and measured as current).

Step 7: Meshing and Solving

Set the Mesh Engine to Discovery and add two mesh groups that set the outer sphere to 1mm and the inner to 0.2 mm. You may choose to use a finer mesh on the probe surface to better resolve the sheath.

Once configured, click Start to run the simulation.

Analysis: Visualizing the Plasma Sheath

Once the simulation finishes, a Results object will appear in the simulation tree. You can inspect volume results here using discovery’s Graphite Visualization tool. Here we see the Argon Density in the volume. As the voltage on the probe is ramped higher, the depletion region increases due to the Debye Shielding.

We can also view our results using EMA3D Connect, a customized ParaView environment.

There is also the option to post process your results using Paraview: 

The Physics of the Sheath

While our simulation setup ramped voltage to 15V, let’s look at a comparison between two distinct static scenarios to understand the underlying physics: a constant +5V bias and a constant -5V bias.

• Positive Bias (+5V): In the top image, the probe is positively charged. It electrostatically attracts electrons (creating a high electron density zone) and repels the positive Argon ions, creating a visible ion depletion region.
• Negative Bias (-5V): In the bottom image, the physics flip. The negative probe attracts the positive Argon ions and repels the electrons. This results in an electron depletion zone (sheath) around the probe.

We also observe that as voltage magnitude increases (e.g., ramping to 15V), these depletion regions expand. This is due to plasma shielding—as the electric field becomes stronger, the plasma requires a larger volume of charged particles to effectively screen the field from the bulk plasma.

Watch the Full Video Tutorial

Prefer to follow along step-by-step? We have recorded a complete video walkthrough of this Langmuir Probe simulation. Watch the video below to see exactly how to navigate the Ansys Charge Plus interface, set up your geometry, and configure the solver in real-time.

Next Steps

You have now successfully configured a low-density PIC simulation to analyze fundamental plasma behavior. In Part 3 of this series, we will move into high-energy physics, exploring advanced pulsed power applications with a Nanosecond Discharge example.

Stay tuned!