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2. Vector nonlinearities (vortices, etc.)

3. Chaotic behavior.

1.2 Plasma as the Fourth State of Matter

Plasma is a quasineutral gas of charged and neutral particles which

exhibits collective behavior. Here, we will define "quasineutral" and "col-

lective behavior". Firstly, quasineutral means that, the density of positive

ions   approximately equals to the density of electrons  ,   ≈   ≡ 
where  is a plasma density, but not all the electromagnetic forces vanish.

Now, "collective behavior" means that, the motions depend not only on

local conditions but also on plasma state [4, 5]. With few exceptions, dis-
crete particle interactions, i.e. collisions, are omitted from these analysis,

[6, 7], and collective interactions are assumed to dominate on the time and

length scales of interest. In this case, the plasma may be described within

the framework of the Vlasov-Maxwell equations [8, 9].

1.2.1 Another Definition of Plasma

The study of charged particles collected in a sufficient number so
that, the long-range Coulomb force is a factor determining their statistical

properties [5].

1.2.2 Plasma Parameters

The charged particles in a plasma rearrange their positions to effec-
tively shield electrostatic fields within a small distance characterized by

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the Debye length  (= (   4 ) 12 ) where   and   are the electron
temperature, the electronic charge and Boltzmann constant, respectively.

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