Stepwise ionization
Stepwise ionization (also called multistep ionization) is the ionization of an atom through two or more successive electron collisions: a first collision excites the atom to an intermediate state, and a later collision ionizes it from that state. It contrasts with direct ionization, in which a single electron collision supplies the full ionization energy.
In ION-I’s IonSpark cathode, argon is first ionized by electrons emitted from the tungsten pin; once the discharge is established, stepwise ionization becomes the main source of electrons for the plasma.1
Argon
The ionization energy of ground-state argon is about 15.76 eV.2 The lowest excited states of argon lie near 11.5–11.8 eV. Two of them, the 1s5 and 1s3 levels (Paschen notation), are metastable: radiative decay to the ground state is forbidden, so atoms in these states persist far longer than in ordinary excited states.
An electron with only a few electronvolts of energy cannot ionize a ground-state atom, but it can ionize a metastable one. From the 1s5 level, at about 11.55 eV, the remaining energy needed is roughly 4.2 eV. In a discharge with many metastable atoms and relatively few high-energy electrons, the two-step path can therefore dominate.
Modeling
A simple zero-dimensional (0D) model tracks the densities of each species over time with rate equations. For argon the minimum set of species is:
- neutral argon (Ar)
- metastable argon (Ar*)
- argon ions (Ar+)
- electrons (e−)
The main processes are:
| Process | Reaction |
|---|---|
| Excitation | e− + Ar → e− + Ar* |
| Direct ionization | e− + Ar → 2e− + Ar+ |
| Stepwise ionization | e− + Ar* → 2e− + Ar+ |
Rate coefficients come from electron-impact cross sections integrated over the electron energy distribution function. Particle-in-cell simulations with Monte Carlo collisions (PIC-MCC) resolve the same processes in space and time, at much greater computational cost.