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enroger0

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Can anyone name it? Or even better point me to some nice materials on it? Thanks.

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- Thread starter enroger0
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In summary: Thermal fluctuations lead to "vaporising" some particles and/or neutral clasters,2) Atomic recombinations create neutral atoms that are not affected with binding forces and leave the plasma volume.3) After recombination of all electrons and nuclei, you obtain a hot gas with pressure which should expand anyway.In summary, the theorem states that a system of charged particles (plasma) cannot be bound without the presence of an external field.

- #1

enroger0

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Can anyone name it? Or even better point me to some nice materials on it? Thanks.

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Phrak

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http://www.iop.org/EJ/abstract/0305-4470/25/15/005

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enroger0

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Vanadium 50

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enroger0

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http://en.wikipedia.org/wiki/Virial_theorem

It's a general theory that deal with any force interaction, EM interaction takes special treatment.

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Vanadium 50 said:

The theorem that states that a system of EM particles can't be bound is a classical theorem; it doesn't apply to a qm system. I think the OP is mistaken about its being the same theorem as the virial theorem.

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enroger0

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enroger0 said:but as Vanadium 50 point out: how about a pair of proton and electron?

The theorem is classical. Classically, a hydrogen atom isn't stable. It collapses by radiation.

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Bob_for_short

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enroger0 said:

Can anyone name it? Or even better point me to some nice materials on it? Thanks.

If you speak of "hot" plasma - it has pressure inside and no pressure outside so it should expand.

If you speak of "cold" plasma, then it can be quasi-stable for some time but:

1) Thermal fluctuations lead to "vaporising" some particles and/or neutral clasters,

2) Atomic recombinations create neutral atoms that are not affected with binding forces and leave the plasma volume.

3) After recombination of all electrons and nuclei, you obtain a hot gas with pressure which should expand anyway.

In other words, plasma is a too energetic system to be in a "condensed" state.

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arivero

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Bob_for_short

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arivero

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Bob, forget gravity.

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arivero

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Bob_for_short

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arivero said:Bob, forget gravity.

I did no mean gravity (stars) as an attractive force. I spoke of far inter-stellar space. Sorry, I was not clear.

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arivero said:

Right. I know the theorem exists, but I don't know the exact statement of the theorem, and I don't know exactly what's involved in the proof. You would have to worry about things like cases where the particles are moving without accelerating, so that they don't radiate. You could also have cases where the particles are accelerating, but they cancel out each other's radiation, etc. And I'm not sure what the theorem actually claims happens. I think it probably states that, e.g., the system decomposes into pointlike, electrically neutral pieces, which then fly off without any further interactions.

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Bob_for_short

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If we speak of hot plasma, there are two regimes of its radiation: from its volume and from its surface. When the plasma is dense and thick, it reabsorbs its own volume radiation so it radiates only from its surface (black body radiation determined with T).bcrowell said:...You could also have cases where the particles are accelerating, but they cancel out each other's radiation, etc.

It is very important in laboratory conditions to pass quickly the first regime while ionizing the neutral gas in order to decrease the radiative losses from volume. It's a question to be transparent or non transparent for radiation. But a hot plasma has pressure and a lot of instabilities even when confined.

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There seems to be a family of theorems of this general flavor.

Earnshaw's theorem: http://en.wikipedia.org/wiki/Earnshaw's_theorem , http://www.everything2.com/index.pl?node_id=1449752 http://math.ucr.edu/home/baez/physics/General/Levitation/levitation.html

optical Earnshaw's theorem: http://www.everything2.com/title/magneto-optical%20trap

Some of the links also discuss the magnetic versions of the theorem.

The form of the theorem that I'm think of doesn't seem to fit with any of these. I seem to recall that Prof. Rich Muller told my Physics H7 class at Berkeley about such a theorem ca. 1983, saying that someone he knew (possibly Purcell, the author of the text we were using?) had proved it, but hadn't published the proof.

Earnshaw's theorem: http://en.wikipedia.org/wiki/Earnshaw's_theorem , http://www.everything2.com/index.pl?node_id=1449752 http://math.ucr.edu/home/baez/physics/General/Levitation/levitation.html

optical Earnshaw's theorem: http://www.everything2.com/title/magneto-optical%20trap

Some of the links also discuss the magnetic versions of the theorem.

The form of the theorem that I'm think of doesn't seem to fit with any of these. I seem to recall that Prof. Rich Muller told my Physics H7 class at Berkeley about such a theorem ca. 1983, saying that someone he knew (possibly Purcell, the author of the text we were using?) had proved it, but hadn't published the proof.

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enroger0

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The argument (Virial) I'm reading is ignoring anything about radiation and collision.

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takeTwo

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If there are enough electrons or ions such that the number of them in a "Debye sphere" = { 740 * SQRT[ T(degrees K) / n(cm^-3) ] }^3 >1, then collective phenomena (non-local EM forces) occur and thus the problem with fusion energy! The components of the hydrogen atom fail this test of "plasma or not". Systems of not-plasma must be common, say, in interstellar space (as Bob for short mentioned), but in laboratories, I can't think of any (maybe electron traps, but they are not self-constrained).

However, there is "ball lightning". This is the one (supposedly) self-constrained system of charged particles that I've ever hear of.

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arivero

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So at the end the question is about the stability of "ball lightning". Uff.

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enroger0

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crap, you caught me.

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Bob_for_short

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arivero said:So at the end the question is about the stability of "ball lightning".

AFAIK, the ball lightning is not really stable but actively decaying. Some chemical reaction like fire or so.

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takeTwo said:Our solar system is many-bodied. When it formed, it had billions more bodies.

We're talking about specific mathematical theorems here. For instance, Earnshaw's theorem refers to classical systems in stable, static equilibrium. The solar system is a nonclassical system (the atoms have nonclassical properties) that is not in static equilibrium.

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takeTwo

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bcrowell said:We're talking about specific mathematical theorems here. For instance, Earnshaw's theorem refers to classical systems in stable, static equilibrium. The solar system is a nonclassical system (the atoms have nonclassical properties) that is not in static equilibrium.

OK. I was just thinking out loud. I like analogies: here is another many-bodied, classical system. In any case, doesn't the theorem refer to the

The long-range gravitational forces of the (classical) clumps of rocks (not molecules) of our solar system during, say, only the last millions of years is still not in any kind of equilibrium. Doesn't this agree with Earnshaw's theorem? Why did comet Shoemaker-Levy collide with Jupiter? Whatever perturbation it experienced sent it into a different orbit; the 1/r^2 forces are not restorative.

The impossibility of self constrained system of charged particles refers to the fact that a system of charged particles cannot exist in a stable equilibrium solely due to their own electrostatic forces.

This is due to the fact that the electrostatic forces between the particles will cause them to either repel or attract each other, leading to an unstable equilibrium. This means that the system will eventually break apart or collapse.

There are some special cases where a self constrained system of charged particles can exist. For example, in a plasma, the charged particles are constantly moving and interacting with each other, which can create a stable equilibrium.

The impossibility of self constrained system of charged particles is a result of the second law of thermodynamics, which states that entropy (disorder) in a closed system will always increase over time. In this case, the unstable equilibrium of the charged particles leads to an increase in entropy as the system breaks apart or collapses.

While it is not possible for a self constrained system of charged particles to exist in a stable equilibrium, it is possible to artificially create such a system using external energy sources or constantly adjusting the particles' positions. However, this is not a natural occurrence and requires constant maintenance to sustain the system.

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