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3 Plasmas


Existence of plasma

In a gas in thermal equlibrium at temperature T , the number of neutral molecules nn and free elec-

trons ne are related by the Saha equation

n e = n n 2 π K T h 2


1 nn


V KT i


w h e r e K a n d h a r e B o l t z m a n n s a n d P l a n c k s c o n s t a n t s , a n d V i i s t h e i o n i z a t i o n e n e r g y f o r t h e n e u t r a particles. For ordinary air at room temperature, one gets a ridiculously small number, ne/nn 10120. For the gas to become a plasma, ne/nn must obviously reach much higher values. Looking at the Saha equation, we can identify three possibilities: l

H i g h t e m p e r a t u r e ( K T V i ) . T h i s g i v e s h i g h k i n e t i c e n e r g y t o t h e p a r t i c l e s , s o t h a t m o l e c u l e may be ionized in collissions. s

  • Low density. This makes the probability of recombination low: once an atom is ionized, it is hard to find an electron to recombine with in such a way that both energy and momentum are conserved in the recombination.

  • Non-equilibrium. In this case, the Saha equation is no longer valid. For space plasmas, colli- sion mean free paths are usually long and collision frequencies low. This means that it takes a very long time for the plasma to come into equilibrium, and many interesting things may happen before the plasma comes to equilibrium.

3.2 Interactions in plasmas

In a gas of neutral particles (henceforth called a ”neutral gas”), the particles interact with each other only through collisions.

In a plasma, the particles interact with each other at all times through the electromagnetic forces. Thus, the dynamics of a plasma is inherently more complicated than that of a neutral gas.


Particle description of plasmas

The equation of motion for a particle k in a classical non-relativistic plasma (Newton’s second law)


dvk dt

= qk(E + vk × B) + other forces.


The ”other forces” may include for example the gravitational force. Thus, if the electromagnetic (EM) fields E and B are given, we can, at least in principle, get the particle motion vk(t) and position rk(t) by integration. To calculate the EM fields E(r, t) and B(r, t), we have Maxwell’s


∇·E = ∇·B = 0


(3) (4)

∇ × E = B ∂t



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