Plasma (Part-IV)- Mathematical Model and Artificial Formation

Image for representative purpose only.

How is Plasma described mathematically? What are Artificial Plasma and how are they categorized? 

Here we continue with the fourth part of our blog on plasma. Those who have missed our third blog can read it from Here. It will help to connect with this fourth part of the blog discussing details about the mathematical description of plasma and also artificial plasma along with their category. To know in details let us explore this blog. In words of Hannes Alfven:

"I have never thought that you could obtain the extremely clumpy, heterogeneous universe we have today, strongly affected by plasma processes, from the smooth, homogeneous one of the Big Bang, dominated by gravitation".

Mathematical Description of Plasma

To completely describe the state of a plasma, all of the particle locations and velocities that describe the electromagnetic field in the plasma region would need to be written down. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicists commonly use less detailed descriptions, of which there are two main types- the first one is Fluid Model and the second one is Kinetic Model.

Fluid Model

Fluid models describe Plasma in terms of smoothed quantities, like density and averaged velocity around each position (see Plasma parameters). One simple fluid model, magneto hydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier–Stokes equations. A more general description is the two-fluid plasma picture, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell–Boltzmann distribution. Because fluid models usually describe the plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers, nor resolve wave-particle effects.

Kinetic Model

Kinetic models describe the particle velocity distribution function at each point in the plasma and therefore do not need to assume a Maxwell–Boltzmann distribution. A kinetic description is often necessary for collision less Plasma. There are two common approaches to kinetic description of a plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe the dynamics of a system of charged particles interacting with an electromagnetic field. In magnetized Plasma, a gyro-kinetic approach can substantially reduce the computational expense of a fully kinetic simulation.

What are Artificial Plasma? How they are Categorised?

Most artificial Plasma are generated by the application of electric and/or magnetic fields through a gas. Plasma generated in a laboratory setting and for industrial use can be generally categorized by:

The type of power source used to generate the plasma—DC, RF and microwave. The pressure they operate at—vacuum pressure (< 10 mTorr or 1 Pa), moderate pressure (≈1 Torr or 100 Pa), atmospheric pressure (760 Torr or 100 kPa)The degree of ionisation within the plasma—fully, partially, or weakly ionised. The temperature relationships within the plasma thermal plasma , non-thermal or "cold" plasma. The electrode configuration used to generate the plasma. The magnetization of the particles within the plasma magnetized partially magnetized (the electrons but not the ions are trapped by the magnetic field), non-magnetized.

Continued in the next blog...