Calculator Inputs
Enter plasma, mesh, and timing values. After submission, the results will appear above this form.
Example Data Table
This sample shows a practical screening case for a low-temperature plasma setup.
| ne (m-3) | Te (eV) | Ion Mass (amu) | L (m) | Cells | Macroparticles | Δt (s) | λD (m) | Δx/λD | ωpeΔt | PPC |
|---|---|---|---|---|---|---|---|---|---|---|
| 1.0e15 | 5 | 39.948 | 0.10 | 250 | 50000 | 5.0e-11 | 5.2566e-4 | 0.7609 | 0.0892 | 200 |
Formula Used
This page is a planning calculator for common particle-in-cell setup checks rather than a full field solver.
| Quantity | Expression | Meaning |
|---|---|---|
| Debye length | λD = √(ε0Te,J / nee2) | Smallest shielding scale that the mesh should resolve. |
| Electron plasma frequency | ωpe = √(nee2 / meε0) | Main electron oscillation frequency for timestep screening. |
| Ion plasma frequency | ωpi = √(niZ2e2 / miε0) | Ion response rate for slow plasma evolution. |
| Electron thermal speed | vth = √(2Te,J / me) | Typical electron speed used in crossing checks. |
| Cell size | Δx = L / Nx | Spatial grid spacing of the domain. |
| Particles per cell | PPC = Np / Nx | Sampling depth per cell for noise control. |
| Plasma oscillation check | ωpeΔt | Lower values generally improve temporal stability. |
| Cell crossing check | vthΔt / Δx | Tracks how far fast particles travel each step. |
How to Use This Calculator
- Enter the electron density and temperature for the plasma you want to model.
- Provide ion mass and charge state to estimate ion response timing.
- Set the domain length, number of cells, and total macroparticles.
- Enter the timestep and total simulated duration.
- Use perturbation amplitude and mode number to sketch a sample profile plot.
- Press the calculate button and review the results above the form.
- Check Δx/λD, ωpeΔt, and vthΔt/Δx before running a full simulation.
- Download CSV or PDF reports for sharing, logging, or future setup comparisons.
Frequently Asked Questions
1) What does this calculator actually estimate?
It estimates common planning metrics for a one-dimensional electrostatic particle-in-cell setup, including Debye length, plasma frequency, grid spacing, timestep checks, particles per cell, and a simple profile sketch.
2) Is this a full particle-in-cell simulator?
No. It does not push particles or solve fields over time. It helps you size the mesh, timestep, runtime, and particle count before building or launching a fuller numerical model.
3) Why is Debye length so important?
Debye length sets a shielding scale in plasmas. If the cell size is too large compared with that scale, charge separation physics can be smeared and important electrostatic behavior may be misrepresented.
4) What does ωpeΔt tell me?
It compares the timestep with the fastest electron plasma oscillations. Smaller values usually mean better temporal resolution and safer numerical behavior for explicit electrostatic particle-in-cell schemes.
5) Why should I care about particles per cell?
More particles per cell usually reduce statistical noise. Too few particles can make density and field estimates noisy, which may hide real trends or create misleading fluctuations.
6) What is the crossing ratio vthΔt/Δx?
It estimates how far a typical electron travels during one step relative to a single cell. Large values suggest particles leap across cells too aggressively for accurate tracking.
7) Can I use this for magnetized or multidimensional cases?
Use it only as a first-pass estimate. Strong magnetic fields, multidimensional geometry, relativistic motion, collisions, and electromagnetic updates require additional constraints beyond this simplified screen.
8) What should I improve first if the verdict is poor?
Usually reduce the timestep, refine the mesh, or increase particles per cell. Start with the metric showing the worst label, then recalculate until the main checks are comfortably improved.