Some Fundamentals of Plasma Physics

Plasma is loosely described as an electrically neutral medium of positive and negative particles (i.e., quasi-neutral). It is important to note that although these charged particles are unbound, but they are not totally free. When the charges move,

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they generate electrical currents with magnetic fields, and as a result, they are affected by each other’s fields. This governs their collective behavior with many degrees of freedom. A definition of plasma could have three criteria: the plasma approximation, bulk interaction, and plasma frequency [2].

The first criterion is plasma approximation. Charged particles must be close enough together that each particle influences many nearby charged particles, rather than just interacting with the closest particle. The plasma approximation is valid when the number of charge carriers within the sphere of influence of a particular particle is higher than unity to demonstrate collective behavior of the charged particles. This sphere is often called the Debye sphere whose radius is the Debye screening length.

The second criterion is bulk interaction. The Debye screening length is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place. When this criterion is satisfied, the plasma is quasi-neutral.

The third criterion is plasma frequency. The electron plasma frequency is large enough as compared to the electron-neutral collision frequency. When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics.

Briefly, collision frequency must be so sufficient that kinetic and statistical theory is valid.

In the following, some fundamentals of of plasma physics, including sheath, Debye length, Bohm velocity and plasma frequency, are described in turn next.

1.2.2.1 Debye Length

Debye length is the distance scale over which mobile charge particles screen out electric fields in plasmas and other conductors. In other words, the Debye length is the

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distance over which significant charge separation can occur. A Debye sphere is a volume whose radius is the Debye length, in which there is a sphere of influence, and outside of which charges are screened. Debye length is expressed as [2][3][4][5]:

g e

De qn

0T

   (1.1)

where 0is the permittivity of free space, Teis the electron temperature in eV, q is the elementary charge, and ngis the background gas density. Overally speaking, it is a measure of the shielding distance or thickness of the sheath.

1.2.2.2 Plasma Sheath

The sheath is generated by the interaction of the plasma with the boundary material. As positive charges and electron diffuse thermally to wall, the sheath is formed that is caused by the velocity of electron is much larger than the velocity of positive ions. Physically this means that the electron density must be always less than the ion density in the sheath region. The function of a sheath is to form a potential barrier so that the more mobile electrons are confined electrostatically in the bulk. The height of the barrier adjusts itself so that the flux of electrons that have enough energy to overcome the barrier to the wall is just equal to the flux of positive ions reaching the wall.

1.2.2.3 Bohm Velocity

As the ions enter the sheath, they are accelerated by the large electric field and their density must decrease to maintain a constant flux. If this decrease is too fast, the ion density will fall off well before the electrons (which diffuse a bit into the region of positive potential) vanish, leading to a net negative charge, which would then increase the ion velocity. The stable solution must occur when the ions entering the sheath

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have enough initial velocity to ensure that the sheath remains positive charged. The sheath can exist only if the initial ion velocity exceeds the critical condition at the presheath position, which is called Bohm sheath criterion. In the presheath region, a weak electric field penetrating into the plasma near the sheath edge, which accelerates the ions as they enter the "main" sheath. The initial velocity at the preshaeth position which could allow ion transport from the plasma bulk into the main sheath is known as Bohm velocity [3][4]:

M u qT

u_s _B  ^e (1.2)

where us is ion velocity, uB is Bohm velocity and M is ion’s mass. It only depends on electron temperature and mass of ion.

1.2.2.4 Plasma Oscillations (plasma frequency)

An important property of plasma is the time scale for plasma oscillations to occur.

Plasma oscillations, also known as “plasma frequency” and “Langmuir frequency”, are rapid oscillations of the electrons in conducting media such as plasmas or metals. The oscillations can be described as instability in the dielectric function of a free electron gas. In other words, under assumption of quasi-neutral plasma, if an electron is moved from its equilibrium position, the resulting positive charge exerts an electrostatic attraction on the electron, causing the electron to oscillate about its equilibrium position.

Because the interaction between electrons is strong, they all oscillate together at a characteristic frequency that depends on the nature of the particular plasma. Electron plasma frequency is shown as [2][3][4]:

e

pe m

n q

0 0 2

   (1.3)