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Re: Plasma



It is a pleasure to see the questions below so obviously carefully
written.

Dan Crowe asks:

Leigh has presented very interesting arguments,
but I have a few questions and comments.

1. Why is the ionization channel Y + H -> p + e
ignored? Photons of appropriate energies are
emitted (1) during recombination and (2) in
nearby galaxies.

More distant galaxies can be seen though nearby clusters (e.g. the Coma
cluster). The cluster gas is optically thin; almost all photons are
transmitted, so the process is not important, and each photon only gets
one trip through. The particles, on the other hand, stay in the
cluster's gravitational well for billions of years even if they undergo
few interactions in a trip through.

I think Dan originally suggested that ultraviolet radiation from the
galaxies in the cluster might be responsible for ionizations. The fact
is that galaxies are just not bright enough to matter. To get an idea
of how bright galaxies are, go outside on a dark night and look at the
Milky Way. The galaxies in a cluster have comparable surface
brightness, but they do not cover as much of the sky when viewed from a
point in the gas. You might also try looking at the nearby galaxy M31
in Andromeda.

2. Energy must be added to an ideal gas during
an isothermal expansion, but Leigh does not
describe the addition of any energy during
the expansion, implying that the expansion
is adiabatic. The temperature of an ideal
gas decreases during an adiabatic expansion.
Would the decrease in temperature result in
a net decrease in degree of ionization?

John Denker suggested that he knew no relatively simple explanation for
the fact that highly ionized plasmas existed at relatively low
temperatures. These plasmas have very small particle densities. What I
am trying to demonstrate is that if the particle density of a gas is
decreased, a greater degree of ionization will result.

I said:

Now consider what happens if the volume of the box is suddenly
doubled.
("Suddenly" means that the wall or walls of the box move faster than
any of the particles during the expansion.) The kinetic energies of
the
particles in the box, and therefore the temperature of the system,
remains constant.

This describes an adiabatic expansion, but it is an irreversible
adiabatic expansion, usually called a "free expansion". No work is done
on or by the gas during the expansion, therefore its internal energy is
unchanged during the expansion. One might say that its temperature is
unchanged, too, but as the gas is not in an equilibrium state until a
few more ionizations take place, strictly it doesn't have a
temperature. Still, the statement is "approximately correct" if the
volume is only doubled. The temperature will actually decrease by an
infinitessimal amount when the additional ionizations have occured

3. Why is the expansion of an ideal gas important
anyway? Is Leigh saying that the degree of
ionization of intergalactic hydrogen is
affected by the expansion of the universe?
But the expansion of the universe is not
sudden, as he has defined it, and it is not
applicable in the cores of the rich galaxy
clusters he discussed in his earlier posts
on this subject.

The argument I was making had nothing to do with an astrophysical
problem.

The physical state of this system in equilibrium depends solely upon
two parameters, its temperature and volume. It is common practice in
thermodynamics to construct such hypothetical processes in discussions
such as this since the state of the system does not depend upon its
history; it doesn't matter how the system got to a state characterized
by temperature and volume.

4. Three-body recombination has a much smaller
probability than two-body recombination at
the low concentrations in intergalactic
media; therefore, its effect on the degree
of ionization should be small even in the
case of isothermal expansion.

You are quite correct in your observation if you say that three-body
recombination has a much smaller *frequency* than two-body
recombination at sufficiently low density. It is that low density
improbability of three-body recombinations that is the point of my
explanation. That is why the degree of ionization is higher in a lower
density gas.

The two-body recombination process ( e + p -> H + Y ) is hindered
because the constraints (conservation laws) make recombination
relatively unlikely*. Bremsstrahlung
( e + p -> e + p + Y ) is the very much more probable result of e-p
interactions. The important point is that three-body recombinations are
significant, and that they become improbable more rapidly than two-body
recombinations with decreasing particle density. (That's sort of a left
handed way of saying that three-body recombinations become more
probable relatively faster than the rate at which two-body
recombinations do with increasing particle density.) The effect on the
degree of ionization is significant precisely because the cluster gas
has such an incredibly low density.

I hope this discussion has been useful to some members of this group. I
do believe it has clarified my own understanding of the intracluster
gas, for which enlightenment I thank the other participants.

Leigh

*This is where the golden rule of which I spoke comes in. Technically,
the volume of the phase space of final states for the two-body
recombination reaction is relatively small. The golden rule says that
the probability of the reaction is proportional to that phase space
volume.