Introduction to Plasma

Our Universe is made of 69% dark energy, 27% dark matter, 1% normal matter.

What is plasma?

Plasma is also called the “fourth state of matter”. Solid is heated to become a liquid, liquid is heated to become a gas.
Upon further heating, the gas is ionized into a plasma. Since plasma usually exists only in a vacuum, we need to pump the air out of a vacuum chamber in the laboratory.

The Definition of Plasma

A plasma is a quasineutral gas of charged and neutral particles which exhibits collective behavior.

• The Coulomb force between A and B diminishes as $1/r^2$.
• However, for a given solid angle($\Delta$r/r = constant), the volume of plasma in B that can affect A increases as $r^3$.

The Saha Equation

$$\frac{n_i}{n_n}\approx2.4\times10^{21}\frac{T^{3/2}}{n_i}e^{-U_i/KT}$$ $$n_i\ is\ the\ density\ of\ ionized\ atoms$$ $$n_n\ is\ the\ density\ of\ neutral\ atoms$$ $$K\ is\ Boltzmann's\ constant$$ $$U_i\ is\ the\ ionization\ energy\ of\ the\ gas$$

Physical meaning

• When temperature is raising, the whole value is increasing exponentially with $U_i/KT$.

• The higher value of $n_i$, the lower recombination rate of ionized atoms.

The Maxwellian Distribution

The one-dimensional Maxwellian distribution

$$f(u)=Aexp(-\frac{1}{2}mu^2/KT)$$ $$fdu\ is\ the\ number\ of\ particles\ per\ m^3\ with\ velocity\ between\ u\ and\ u+du$$ $$\frac{1}{2}mu^2\ is\ the\ kinetic\ energy$$

Boltzmann’s constant K

$$K=1.38\times10^{-23}J/^{\circ}K$$

The particles density n

$$n=\int_{-\infty}^{\infty}f(u)du$$

The constant A is related to the density n

$$A=n(\frac{m}{2\pi KT})^{1/2}$$

The average kinetic energy is $\frac{1}{2}KT$

The three-dimensional Maxwellian distribution

$$f(u,v,w)=A_3exp[-\frac{1}{2}m(u^2+v^2+w^2)/KT]$$

Reference Book
Introduction to Plasma Physics and Controlled Fusion by Francis F. Chen