McWhirter Density Threshold

Calculate the McWhirter LTE minimum electron density and compare a measurement.

Description

The McWhirter criterion compares electron density with a temperature-and-transition-energy threshold.

The McWhirter criterion compares electron density with a temperature-and-transition-energy threshold. Satisfying a necessary LTE screen alone does not establish local thermodynamic equilibrium.^{[1, 2]}

Calculate the McWhirter LTE minimum electron density and compare a measurement.

When to use McWhirter Density Threshold

Use this tool to calculate the McWhirter LTE minimum electron density and compare a measurement.

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.

How to use McWhirter Density Threshold and understand its results

Prepare the optical measurements, geometry, fitted coefficients or caller-selected thresholds requested. Confirm wavelength, radius/diameter, pulse-width, angle and unit conventions before running the calculation.
Enter plasmaTemperatureKelvin, transitionEnergyEv, measuredElectronDensityCm3 using the field table and calculation rules, then run the tool.
Read minimumElectronDensityCm3, meetsCriterion. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
plasmaTemperatureKelvin	Plasma temperature (K)	number; minimum: 0	Required
transitionEnergyEv	Transition energy separation (eV)	number; minimum: 0	Required
measuredElectronDensityCm3	Measured electron density (cm⁻³)	number; minimum: 0	Required

Enter nonnegative temperature, transition energy and measured density. Return threshold and inclusive ≥ flag; zero temperature or energy gives zero threshold.

minimumDensity_cm⁻³=1.6e12 sqrt(T_K)(ΔE_eV)³

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
minimumElectronDensityCm3	McWhirter minimum density (cm⁻³)	number; minimum: 0
meetsCriterion	Meets criterion	boolean

json

{
  "input": {
    "plasmaTemperatureKelvin": 10000,
    "transitionEnergyEv": 2,
    "measuredElectronDensityCm3": 2000000000000000
  },
  "output": {
    "minimumElectronDensityCm3": 1280000000000000,
    "meetsCriterion": true
  }
}

Limitations and assumptions

No plasma gradients, timescales, optical thickness or full LTE validation is examined.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use QD Inhomogeneous Broadening: Propagate quantum-dot size dispersion into Gaussian transition-energy broadening. For a complementary task, use Inverse-Compton Photon Energy: Estimate low-recoil head-on inverse-Compton backscatter photon energy as 4γ²E.

Further background: Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion.

References

McWhirter Density Threshold — tool.io
Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion — Cristoforetti and colleagues

Similar or alternative tools

QD Inhomogeneous Broadening
Propagate quantum-dot size dispersion into Gaussian transition-energy broadening.
Inverse-Compton Photon Energy
Estimate low-recoil head-on inverse-Compton backscatter photon energy as 4γ²E.