In many experiments, a plasma maintained in a steady steady state equation is

In steady state, we set ∂n/∂t = 0

In many weakly ionized gases, ionization is produced by energetic electrons in the Maxwellian distribution.

Q ∝ n

Q = 2n

where z = ionization function

∇²n = - zn/ D ........2

This is the same as the spatial function consequently the density profile is a cosine or Bessel. Here the density remains constant.

a. Plane source: Consider a localised source on the x=0 plane (eg a beam of uv light strong enough to ionize the ionized gas). The steady state diffusion equation is

d²n / dx² = - Q/D 𝛿(0) ....3

Except at x=0 density must satisfy d²n/ dx² = 0

The solution will be

n = no ( 1 - l x l / L ) ....4

b. Line source: Consider a cylindrical plasma with a source located in the axis. Except at r =0, the density must satisfy.

Solution that vanishes at r = a is

n = no ln (a/r) ....2

The density becomes infinite at r=0 and hence it is not possible to determine the density near the axes accurally without considering the finite width of the source.

Recombination

In plasma, when an electron and ion collide particularly at low relative velocity they have a finite probability to recombining into a neutral atom. In a plasma, which is a highly ionized state of matter consisting of charged particles, recombination occurs when electrons and ions collide and undergo a series of interactions. These interactions can include electron-electron recombination, electron-ion recombination, or three-body recombination involving two electrons and one ion.

The recombination process is governed by the principles of charge conservation and energy conservation. When an electron and an ion combine, they must have enough energy to overcome the electrostatic repulsion between them. Once they come close enough, the electron can settle into a lower energy state around the ion, resulting in the formation of a neutral atom or molecule.

Recombination is an important phenomenon in plasma physics and plays a significant role in various plasma systems. It affects the overall plasma composition, dynamics, and energy balance. Recombination processes can have implications for the behaviour and stability of plasmas in different applications, such as in fusion reactors, plasma processing, and astrophysical plasmas.

Understanding recombination in plasma is essential for controlling and manipulating plasma properties. Researchers study recombination rates, cross-sections, and associated reaction pathways to gain insights into plasma behaviour and develop strategies to optimize plasma conditions for specific applications.

In summary, recombination in plasma refers to the process of charged particles combining to form neutral atoms or molecules. It is an important aspect of plasma physics and has implications for plasma behaviour and applications in various fields.

To conserve momentum, a third body must be present. If the third body is an emitted photon, the process is called a 'three body recombination'.

The loss of plasma by recombination can be represented by a negative source term in the continuity equation. This term will be proportional to neni = n². In the absence of diffusion term, the equation of continuity then becomes

∂n/∂t = - ∝ n² ......1

In this equation:

∂n/∂t represents the rate of change of the number density of charged particles with respect to time.
α is the recombination coefficient, which depends on the specific recombination process and plasma conditions.
n represents the number density of charged particles (electrons or ions).

The equation states that the rate of decrease in the number density of charged particles due to recombination is proportional to the square of the number density itself. This means that as the number density of charged particles increases, the rate of recombination becomes more significant, leading to a faster decrease in the number density.

It is important to note that this simplified equation assumes a uniform plasma without considering additional factors such as spatial variations, competing processes, or external influences. The actual recombination dynamics in a plasma can be more complex and may require more detailed models to accurately capture the behaviour.

The constant of proportionality ∝ is called the recombination coefficient. Integrating 1,

This is fundamentally different behaviour from the case of diffusion in which time variation is exponential.

When the density is high, the recombination which is proportional to n² is dominant and density decays reciprocally. After the density has reached a low value, diffusion becomes dominant and the decay is then exponential.

Next topic: Diffusion across the magnetic field

This note is a part of the Physics Repository.

Explore

posts on Naya and its networks

Collections