where [[omega].sub.pe] and [[omega].sub.pm] are the electric plasma frequency
and the magnetic plasma frequency
where [[beta].sub.g], [psi]([??],z,t), and [[omega].sub.p]([??]) are the normalized group velocity, normalized electric field amplitude, and plasma frequency
where [[omega].sub.p] is the plasma frequency
, v is the electron collision frequency, [omega] is the angular frequency of the propagating electromagnetic wave, n is the electron density, e is the electron's charge, m is its mass, and 0 is the permittivity of free space.
All of the parameters are dimensionless with normalizations of n by [n.sub.0]; (x, y, z) by electron Debye length [[lambda].sub.De]; u by [c.sub.s]; p by [p.sub.0]; B by a pseudo-magnetic field [B.sub.0]=[m.sub.e][[omega].sub.pi]/e ([[omega].sub.pi] is the ion plasma frequency
,); E by [E.sub.0]=[C.sub.s][B.sub.0].
Table 1 shows the calculated values of Debye length ([[lambda].sub.D]), plasma frequency
([f.sub.p]) and Debye number ([N.sub.d]) for DC discharge in argon gas at the three regions with different applied voltage.
3 shows more detail about the distributions of the electron density ([N.sub.e]), plasma frequency
([f.sub.p]) and collision frequency ([v.sub.e]) near the wall.
[[omega].sub.p] and [omega] are plasma frequency
and frequency of the wave, mass of electron (m), with [[epsilon].sub.o], medium characteristic constants (Ghosh, 1998).
In the expression, the [gamma] is the phenomenological collision frequency, and [w.sub.p] = [square root of ([e.sup.2][n.sub.0]/[m.sub.e][[epsilon].sub.0])] is the bulk plasma frequency
according to the well-known Drude model of gold.
The y is collision frequency, and [w.sub.p] = [[e.sup.2][n.sub.n][m.sub.2][epsilon] is the plasma frequency
and any frequency, like the plasma frequency
, or dissipation parameter, [gamma] or [sigma], by
The plasma frequency
[[omega].sub.p] in uniform, cold, dusty unmagnetized plasma can be described as follows :
Also, it proves that SRRs contribute to effective permittivity of composite MTM (CMM), causing downward shift on the plasma frequency
determined solely from wire structures.