The decay of plasma by diffusion refers to the process by which a plasma loses its energy and particles through the process of diffusion. Diffusion is the process by which particles move from an area of high concentration to an area of low concentration.

In the context of plasma, this means that the high-energy particles in the plasma tend to move away from regions where there are fewer high-energy particles. This movement of particles can lead to a loss of energy and a decrease in the density of the plasma.

There are different mechanisms by which plasma can lose its energy and particles, including collisions with other particles or with a boundary, radiation, and diffusion. Diffusion is particularly important in situations where the plasma is confined to a small volume or when there are large temperature or density gradients within the plasma.

One way to quantify the rate of plasma diffusion is through the diffusion coefficient, which is a measure of the rate at which particles diffuse in a given medium. The diffusion coefficient depends on the temperature, density, and properties of the plasma, as well as the characteristics of the medium in which the plasma is confined.

Overall, the decay of plasma by diffusion is an important process to consider in a variety of plasma physics applications, including fusion energy research, plasma processing, and space plasmas.

Ambipolar diffusion: Ambipolar diffusion is a phenomenon that occurs in plasmas when there is a mismatch in the motion of the charged particles (ions and electrons) and neutral particles. In a plasma, the charged particles are free to move around and can carry an electric current, while the neutral particles do not carry any electric charge and are not affected by electric fields.

When there is a gradient in the plasma density or temperature, the charged particles will move in response to the electric and magnetic fields, while the neutral particles will not. This creates a drag force that can cause the charged particles to collide with the neutral particles and transfer some of their momentum to them. This momentum transfer can cause the neutral particles to move, creating a flow that is coupled to the motion of the charged particles. This phenomenon is called ambipolar diffusion.

Ambipolar diffusion can have important effects on the behavior of plasmas, particularly in astrophysical and fusion plasmas. In fusion plasmas, for example, ambipolar diffusion can affect the rate at which the plasma heats up and the way in which it is confined. In astrophysical plasmas, ambipolar diffusion can play a role in the formation and evolution of stars and planetary systems.

The mathematical description of ambipolar diffusion involves a set of equations that describe the motion of the charged and neutral particles in response to the electric and magnetic fields. The resulting equations can be quite complex and require sophisticated numerical methods to solve, but they provide a powerful tool for understanding the behaviour of plasmas in a wide range of contexts.

In case of partially ionised plasma, the continuity equation for jth space is

Since flux is given by

It is different for ion and electrons. If flux vector Γi and vector Γe weren't equal, a serious charge imbalance will occur soon. The electrons have higher thermal velocities (being lighter than ions) and tends to leave the plasma first. A positive charge is left behind and an electric field is set up of such a polarity as to regard the loss of electrons and accelerates the loss of ions. The required electric field is found by setting

Comparing this equation 5 with the Fick's law of diffusion.

which is known as the ambipolar diffusion coefficient. Using this in equation 2, we get

which is the continuity equation for Ambipolar diffusion coefficient. Since μe>>μi we can neglect μi in comparison to μe. Thus Da can be approximate to

Using Einstein relation, we get

Using equation 9 in equation 8, we get

Thus at Te = Ti, the effect of Ambipolar electric field is to enhance the diffusion of ions by a factor of 2. But the diffusion rate of the two species together is primarily control by the slower species. This is a special case where the specific approximations for the ion sound speed and ion-neutral collision frequency lead to this relationship. However, it is important to note that this relationship is not generally true for all plasma phenomena and conditions.

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