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Also, the plasma is similar to coupled oscillators via the collective behav-

iour. Basic characteristic oscillation frequency of plasma is the plasma
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2
frequency  (= (4  ) 2 ),where   is the electron mass. A condition
for ionized gas to be a plasma is that,   is much smaller than the sys-

tem dimension  i.e.    . Debye shielding is valid only for enough

particles in Debye sphere. The number   of particles in “Debye sphere”

is
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  =(43)   (1.1)

then we demand that

   1 (1.2)

For collisions, a third condition is    1;  is the mean interval time

between any collision with the neutral atoms. Thus the conditions for

plasma must satisfy:

  ¿  (1.3)

  À 1 (1.4)

and

   1 (1.5)

1.3 Fluid Description of Plasma

In fluid theory, plasma is described by macroscopic time and space

functions. By neglecting viscosity and collisions, normalized electron fluid

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