Figure 1.3: Charged slab
This results in a force on the charges tending to expel whichever species is in excess. That
is, if ni > ne , the E ﬁeld causes ni to decrease, ne to increase tending to reduce the charge.
This restoring force is enormous!
Consider Te = 1eV , ne = 1019 m−3 (a modest plasma; c.f. density of atmosphere nmolecules ∼
3 × 1025 m−3 ). Suppose there is a small diﬀerence in ion and electron densities Δn = (ni − ne )
so ρ = Δn e
Then the force per unit volume at distance x is
Fe = ρE = ρ2
= (Δn e)2
Take Δn/ne = 1% , x = 0.10m.
Fe = (1017 × 1.6 × 10−19 )2 0.1/8.8 × 10−12 = 3 × 106 N.m−3
Compare with this the pressure force per unit volume ∼ p/x : p ∼ ne Te (+ni Ti )
Fp ∼ 1019 × 1.6 × 10−19 /0.1 = 16N m−3
Electrostatic force >> Kinetic Pressure Force.
This is one aspect of the fact that, because of being ionized, plasmas exhibit all sorts of col
lective behavior, diﬀerent from neutral gases, mediated by the long distance electromagnetic
forces E, B.
Another example (related) is that of longitudinal waves. In a normal gas, sound waves are
propagated via the intermolecular action of collisions. In a plasma, waves can propagate
when collisions are negligible because of the coulomb interaction of the particles.