Small tools for quick estimates in low-temperature plasma physics, together with the databases and codes we use in our work. The calculators rely on textbook formulas and idealized assumptions, so treat the numbers as order-of-magnitude guides rather than as a substitute for a kinetic model.
Type a value in any box and the others update. The kelvin value is the temperature with kBT equal to the energy.
Photon energy, wavenumber and vacuum wavelength of the same transition. Type a value in any box and the others update.
Convert between the electric field, the reduced field E/N in townsend (1 Td = 10−17 V cm2) and E/p. Edit either E or E/N, the other follows.
The three numbers that tell you whether something is a plasma: the Debye length, the electron plasma frequency, and the number of electrons in a Debye sphere, ND, which should be much larger than one for collective behavior.
Formulas: λD = (ε0 Te/e ne)1/2, ωpe = (e2 ne/ε0 me)1/2, ND = (4π/3) ne λD3.
Generalized distribution f(ε) ∝ ε1/2 exp[−c (ε/⟨ε⟩)x], where x = 1 is Maxwellian and x = 2 is Druyvesteyn, normalized to a fixed mean energy. The plot shows the electron energy probability function f(ε)/ε1/2, which is a straight line for a Maxwellian on a semilog scale.
For a Maxwellian, Te = 2⟨ε⟩/3.
Breakdown voltage of a uniform-field gap from the Townsend criterion, VB = B pd / [ln(A pd) − ln ln(1 + 1/γ)], with the empirical constants A and B of the first Townsend coefficient α/p = A exp(−B p/E).
Constants from Raizer, Gas Discharge Physics (1991), Table 4.1. They are fits over a limited E/p range and the curve is only indicative far from the minimum.