Calculator Input
Use ion number density, not mass density. The form uses a 3-column layout on large screens, 2 columns on smaller screens, and 1 column on mobile.
Formula Used
di = c / ωpi
ωpi = √( ni · (Z e)² / (ε0 mi) )
c = speed of light, ni = ion number density, Z = charge state, e = elementary charge, ε0 = vacuum permittivity, mi = ion mass.
Because ωpi rises with density and charge, the inertial length becomes smaller at higher density or higher charge state. Heavier ions increase the inertial length when other inputs stay fixed.
How to Use This Calculator
- Select a preset ion or choose Custom Ion.
- Enter ion mass in amu and charge state Z.
- Type ion number density and choose its unit.
- Select the output length unit you want.
- Optionally set graph point count and display precision.
- Press the submit button to view results above the form.
- Use the CSV button for spreadsheet-friendly output.
- Use the PDF button to save a formatted report.
Example Data Table
| Case | Ion | Density | Mass (amu) | Z | Ion Inertial Length (m) | Ion Inertial Length (km) |
|---|---|---|---|---|---|---|
| Solar Wind H+ | Proton | 5.0000 cm⁻³ | 1.007276 | 1 | 1.018353e+5 | 101.835327 |
| Ionospheric O+ | Oxygen | 1.0000e+11 m⁻³ | 15.999000 | 1 | 2,869.826503 | 2.869827 |
| Fusion D+ | Deuteron | 1.0000e+19 m⁻³ | 2.013553 | 1 | 0.101810 | 1.018101e-4 |
| Alpha Plasma He2+ | Alpha | 1.0000e+18 m⁻³ | 4.001506 | 2 | 0.226930 | 2.269295e-4 |
These rows help users compare low-density space plasma with denser laboratory plasma conditions.
Frequently Asked Questions
1. What is ion inertial length?
It is a characteristic plasma scale showing where ion motion begins to decouple from electron-scale behavior. It is often written as di and linked to the ion plasma frequency.
2. Which density should I enter?
Enter ion number density, not mass density. For a single-species plasma, use the ion population density that matches the ion mass and charge state used in the calculator.
3. Does charge state change the result?
Yes. A larger charge state increases ion plasma frequency, which reduces the ion inertial length when density and ion mass stay unchanged.
4. Why does the graph slope downward?
Ion inertial length varies inversely with the square root of density. As density increases, the characteristic length becomes smaller, so the plotted curve drops.
5. Can I use heavy ions?
Yes. Choose a preset or enter a custom ion mass in amu. Heavier ions usually produce larger inertial lengths if density and charge state are unchanged.
6. Is this the same as Debye length?
No. Debye length is an electrostatic shielding scale. Ion inertial length is tied to ion plasma response and inertial dynamics. They describe different plasma behaviors.
7. Why offer multiple output units?
Plasma studies span huge scale ranges. Space plasmas may be easier to read in kilometers, while laboratory or device plasmas are often better shown in meters, millimeters, or micrometers.
8. What should I export?
Use CSV for spreadsheets, batch review, or reports. Use PDF when you want a clean shareable summary with the computed values and page layout preserved.