## 2 Plasma Physics
### Ionization  
A plasma system can have several different paths toward ionization. The simplest of the paths is the direct ionization path in which a free electron with sufficient kinetic energy, which is greater than the ionization energy collides with a neutral atom, ejecting one of its bound electrons as shown in (1).  
\[\mathrm{A+e}\ \leftrightarrow\ \mathrm{A^{+}+2e} \tag{1}\]  
This creates a new free electron and a positive ion. Figure 2 below depicts how free electrons collide with atoms (or molecules), knocking an orbital electron out of its orbital. This maintains this ionization process which, in turn, sustains the plasma process [10].  
This figure illustrates the fundamental ionization process that sustains a plasma. In a plasma environment, free electrons--particles with sufficient kinetic energy--collide with neutral atoms or molecules. During these collisions, if the free electron has enough energy to overcome the atom's ionization potential, it can eject an electron from one of the atom's orbitals, thereby ionizing the atom. This ejected electron becomes a new free electron, contributing to the population of charged particles in the plasma.  
This process is known as electron impact ionization and is a key mechanism for maintaining the plasma state. Each ionization event produces one positive ion and one additional free electron, which can further collide with other atoms or molecules, continuing the chain reaction. This cascade effect ensures a sustained plasma, as the number of charged particles remains sufficient to support the ionized state.  
The ionization process is inherently inelastic because the kinetic energy of the incident electron is partially used to overcome the binding energy of the orbital electron. The newly freed electron and the ionized atom both carry energy away, and the plasma's overall energy balance depends on continuous input (e.g., from electric fields) to maintain sufficient electron energies for ongoing ionization.  
Figure 2: Schematic diagram representing the ionization process. The orange particles are the electrons which are in the orbitals with the black particles symbolise the free electrons.  
Moreover, the collisions are part of a complex network of collisional and radiative processes within the plasma, including excitation, recombination, and elastic scattering. The balance between ionization and recombination rates determines the plasma density and stability.  
In summary, Figure 1 captures the essential electron-atom collision that ejects an orbital electron, generating ions and free electrons. This ionization process is self-sustaining and fundamental to plasma maintenance [13; 14].  
The reverse process occurs when an ion captures an electron and transitions back from an ionized state to a neutral atom. This is known as radiative recombination when a single electron is captured, releasing the excess energy as a photon. Alternatively, in three-body recombination, the ion captures one electron while a second electron simultaneously absorbs the excess energy to conserve momentum. The latter is a process dominant in high-density plasmas. Both mechanisms restore neutrality, but differ in their energy dissipation pathways.  
This ionization process can also occur in what is known as a two-step process (stepwise ionization), where a species which had been previously excited could be ionized by the impact of a second electron. Should a heavy atom hit a particle, this could also cause ionization known as heavy particle impact ionization. This process may be dominant in low-temperature plasmas, such as glow discharges or where heavy-particle kinetics dominate.  
Ionization can also occur through the interaction between photons and a neutral atom. In this case, it is called photoionization. The particles forming the plasma can interact with other particles and react with them after colliding. This brings about the creation of charged species and is called associative ionization [15].