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--- un:plasma [2024/10/06 03:59] – asad
+++ un:plasma [2024/10/06 13:29] (current) – [4. Plasma Theory] asad
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 Plasma is an ionized gas of charged particles with an equal number of free positive and negative charge carriers. For this reason plasma is considered quasineutral at stationary state. From the outside it looks neutral. A free particle is one whose kinetic energy is greater than its potential energy. Because of this the temperature of the plasma is also high, because temperature is a measure of kinetic energy.
-===== Debye shielding =====
+===== - Debye shielding =====
 In order for the plasma to be quasineutral at stationary conditions, the charges of the particles on the microscopic scale must cancel out such that the gas appears neutral on the macroscopic scale. Coulomb potential at a distance $r$ from a charge $q$
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 This figure compares Coulomb and Debye potentials in nanovolt units. The distance on the x axis is given in proportion to the Debye length. As can be seen, the Debye potential (orange) approaches zero much faster than the Coulomb potential (blue) beyond the Debye length.
-===== Plasma parameters =====
+===== - Plasma parameters =====
 A Debye sphere can be thought of with a radius of Debye length. In order to form a plasma, this sphere must contain a sufficient number of particles. The volume of the sphere $(4\pi/3)\lambda_D^3$ multiplied by the electron density gives the total number of particles.
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 Which clarifies the meaning of the second criterion. Since the potential energy is proportional to the electron density above, the mean potential energy must be much less than the mean energy $\langle E \rangle$ .
-===== Plasma frequency =====
+===== - Plasma frequency =====
 When a quasineutral plasma is disturbed from outside, its electrons tend to return to their previous neutral state. The speed of the electron rather than the ion is being referred to because the electron is much lighter than other ions. External disturbances cause an average oscillation in plasma electrons around relatively massive ions. The frequency of this oscillation is called the plasma frequency, mathematically
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 where $\tau_n$ is the average time between two collisions between an electron and a neutral. The bottom line is this: the plasma frequency must be much higher than the collision frequency.
+===== - Plasma Theory =====
+Plasma dynamics refers to the interaction of electric and magnetic fields with different types of charge carriers. Space plasmas have many external influences as well as many influences inside the plasma, making its dynamics very complex. To create its perfect mathematical model, the equations of motion for each particle must be known, and since each particle is affected by all the other particles, the equations for all particles must be  simultaneously. This is practically impossible and unnecessary, since we only want to know the average properties of the plasma. So four types of approximations or simplifying approaches are used to construct the plasma theory.
+//Single Particle Motion// is the simplest approach. Here only the effect of external electric and magnetic fields on an individual particle is considered. Here the overall behavior of the plasma is neglected. But this approach is sufficient to explain the type of low-density plasma found in ring currents.
+//Magnetohydrodynamics// is at the other extreme, where the entire plasma is considered as a whole, excluding individual particles. Plasma is here a single conductive fluid with some average properties, eg, density, temperature, velocity. Here the plasma is assumed to be in local equilibrium. This approach is good for studying low frequency waves in many conducting magnetic fluids.
+The //multi-fluid// approach is similar to magnetohydrodynamics, only here different species of particles are considered separately, eg, electrons, protons, heavier ions. A separate fluid is assigned to each species.
+//Kinetic theory// is the most advanced approach, as statistics are well used here. A variety of statistical distribution functions in phase space are used instead of equations of motion for individual particles.