Collisions, Plasma, Ionization

[Dancing David]

Hello,

I am mainly hoping to get Iantreman here, this is to continue my pedantic argument with him about his statement that

According to Hannes Alfven plasma/gases with 1% ionization may be considered to be highly ionised.

Hi Ian.
Alfven quote

".. it is convenient to discuss separately the properties of weakly ionized gases, where the collisions of the charged particles with the neutral gas molecules are the most important, and those of highly ionized gases, where collisions between charged particles play a dominant role. It must then be observed that due to the large effective cross-section for collisions between charged particles, such collisions can be dominant even at a relatively low degree of ionization. Thus, as far as collision processes are concerned, plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized." (emphasis in original) Hannes Alfvén and Carl-Gunne Fälthammar, Cosmical Electrodynamics, 2nd Edition, 1963 (p.145)


So where we were, I had stated that i felt that this was a statement about the mechanical collisions of the particles in the plasma, and that it should be limited to consideration of the collisions in the plasma gas, to which you responded
http://forums.randi.org/showpost.php?p=3560972&postcount=88


Originally Posted by Dancing David
here is Alfven, from a post of yours.

Originally Posted by Dancing David
It must then be observed that due to the large effective cross-section for collisions between charged particles, such collisions can be dominant even at a relatively low degree of ionization. Thus, as far as collision processes are concerned, plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized."

This is what you said right here:

"I quoted Alfvén as saying that a 1% ionized gas may be treated as fully ionized"

No he said that you may treat it as fully ionised in terms of the collision processes. Which I take to mean the mechanical bumping of particles as opposed to the EM scattering and magnetic effects of a plasma.

.
This is my understanding. There are two types of collision in a partially ionized gas/plasma; (1) Collision of charged particles with charged particles (2) Collision of charged particles with neutrals. The latter is what I think you would call "mechanical" collisions, whereas ion collisions are what you are describing as EM..., which I think are called Coulomb collisions due to Coulomb's Law.

By saying that 1% ionized gas can be treated as a fully-ionized plasma, I think Alfvén is saying that Coulomb collisions dominate. I note that:

"Collisions between charged particles in a plasma differ fundamentally from those between molecules in a neutral gas because of the long range of the Coulomb force." -- Richard Fitzpatrick1, Introduction to Plasma Physics: A graduate level course, "Collisionality"
.
Or a better clarification:
".. Coulomb collisions will dominate over collisions with neutrals in any plasma that is even just a few percent ionized. Only if the ionization level is very low (<10-3) can neutral collisions dominate." -- Robert J. Goldston, Paul Harding Rutherford, Introduction to Plasma Physics, "Fully and Partially Ionized Plasmas" (page 164)




Okay, so I said that make some sense. But here is where I think that there maybe a disctinction made:

Now Alfven in the quote states

It must then be observed that due to the large effective cross-section for collisions between charged particles, such collisions can be dominant even at a relatively low degree of ionization


So I think that we agree on that, the collisions of the charged partciles, through Coloumb interactions will have a higher impact in a kinetic sense than those of the charged/neutral and neutral/neutral collisions.

But here is where I am asking for clarification

When the phrase
", plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized"

What is it referencing?

-the collision processes through any of the three possible combinations of partciles (ingnoring electron)

- the more 'plasma' effects, such as collective response, expanded interactions through the deybe shpere, magnetic interaction and electrical current

So when Alfven states:
"Thus, as far as collision processes are concerned, plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized."

Is he making reference to the
-(mechanical collisions plus Coloumb collisions) in other words normal 'gas' behavior plus the Coloumb interactions

or

-the plasma effects which differentiate plasma (minus the Coloumb collisions) from gas

Thanks .

:)

[sol invictus]

So when Alfven states:
"Thus, as far as collision processes are concerned, plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized."

Is he making reference to the
-(mechanical collisions plus Coloumb collisions) in other words normal 'gas' behavior plus the Coloumb interactions

or

-the plasma effects which differentiate plasma (minus the Coloumb collisions) from gas

He says, "as far as collision processes are concerned" - so only the first.

The second certainly does not hold. For example, as you cool the plasma (with density held fixed) the Debye length goes to zero, so no matter what the degree of ionization is it will no longer behave as a plasma below some temperature.

[Dancing David]

Thanks Sol, I am just trying to parse out certain concepts that perhaps have been over generalised. Ian does seem to want his web site to be accurate, so we shall see.

[iantresman]

Unfortunately I haven't been able to detail the characteristics of a partially ionized gas/plasma, and suspect that it as varied as there are plasmas.

As and when I find some relevant references, I'll post them.

[Dancing David]

Okay, thanks for your attention, I know I kind of posted this and it fell to the second page. I was just interested in the Alfven quote that is referenced above. But the more the merrier!

Thanks. :)

[iantresman]

I think it is worth investigating specific plasma regimes, rather than hypothetical plasmas with hypothetical characteristics. And since we're most interested in space plasmas, here is what I've found:

Magnetosphere and ionosphere
The ionosphere has a degree of ionization of 2x10-3(ref (http://books.google.co.uk/books?id=WbkLRSNB3uwC&pg=PA13&dq=%22degree+of+ionization%22+altitude+layer+ionos phere&sig=FT03x2evnPDFEhi_ZZmxJ9R-oEU#PPA13,M1)) but I'm not entirely sure whether the ionosphere is part of the magnetosphere, or bounds it.
.. when we leave the Earth's surface, and encounter an ionized atmosphere, the ionosphere, already at altitudes above 80km. Further exploration of the whole environment of the Earth shows that the neutral atmosphere occupies only a tiny fraction of the magnetosphere, defined as the region where the Earth's magnetic field dominates all plasma behavior (my emphasis). -- Frank Verheest, Waves in Dusty Space Plasmas, (2001) Springer, (page 1 (http://books.google.co.uk/books?id=jzDlr6ijHhUC&pg=PT17&dq=%22partially+ionized%22+%22space+plasmas%22+dom inates&num=100&sig=LD44YwpTVII0ZaLwtlfEf-W8HnM#PPT17,M1))

Sun's photosphere
The degree of ionization is around 10-4(ref (http://books.google.co.uk/books?id=DCcA44Zj8ukC&pg=PA76&lpg=PA76&dq=photosphere+%22degree+of+ionization%22&source=web&ots=ZGII4FwAp6&sig=EjUqL9ALAmqx75BkxWBqxfL06Nc&hl=en)), and sometimes referred to as "photospheric plasma"(ref (http://www.google.co.uk/search?num=100&hl=en&c2coff=1&safe=off&q=%22photospheric+plasma%22&btnG=Search&meta=)) whose dynamics is dominated by the plasma (Ref (http://books.google.co.uk/books?id=76zLv_CKah8C&pg=PA150&dq=photosphere+dominated+magnetic+dynamics&num=100&sig=1wa7hVOEEd6gUUBZ7wWWAtmtkGc)); this source then implies that modelling of the photosphere with the corona is with magnetohydrodynamics, suggesting that magnetic fields dominate; on the other hand, one references note that "the dynamics of the solar photosphere is dominates by its velocity"(Ref (http://books.google.co.uk/books?id=8Y2lsHYEJH4C&pg=PA348&dq=photosphere+dominated+magnetic+dynamics&num=100&sig=LEf_HeDrTrdrvujRN8hHmNNrEbs)), but I don't know what this is, nor whether that suggests magnetic or non-magnetic influences.

More if and when I find it.

[Dancing David]

Um, okay but my questions were very specidifc to the quote from Alfven that "Thus, as far as collision processes are concerned, plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized", what is the word collision processes reffering to?

-the mechanical collision between neutral/charged, neutral/neutral plus the Coloumb collision of same charged particles

-the 'plasma' effect minus the Coloumb collision

Which is in reference to the statment of being regarded as 'highly ionised' for 1% ionization in regards the collision processes.

I will try to look at the other references as well.

[iantresman]

Now Alfven in the quote states

So I think that we agree on that, the collisions of the charged partciles, through Coloumb interactions will have a higher impact in a kinetic sense than those of the charged/neutral and neutral/neutral collisions.
.
Unfortunately I don't know.

[iantresman]

OK, I've done some homework. I contacted Alfvén's co-author, Carl-Gunne Fälthammar, and another plasma expert. I wrote:
In your book, Cosmical Electrodynamics, you write (p.145):

".. it is convenient to discuss separately the properties of weakly ionized gases, where the collisions of the charged particles with the neutral gas molecules are the most important, and those of highly ionized gases, where collisions between charged particles play a dominant role. It must then be observed that due to the large effective cross-section for collisions between charged particles, such collisions can be dominant even at a relatively low degree of ionization. Thus, as far as collision processes are concerned, plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized." (emphasis in original) Hannes Alfvén and Carl-Gunne Fälthammar, Cosmical Electrodynamics, 2nd Edition, 1963

Why do you qualify "as far as collision processes are concerned", that "ionization larger than 1 per cent are to be considered as highly ionized".
Carl-Gunne S Fälthammar replied:
"Highly ionized as far as collisions are concerned" means that collisions between the charged particles themselves dominate over other collisions (i.e. between charged and uncharged particles and among uncharged particles themselves). The actual percentage of ionization that marks the border between high an low ionization in this sense depends of course also to some extent on temperature.

The qualification "as far as …." only means that I do not exclude the possibility that there may be other aspects of a plasma in which it could be meaningful to give "high" and "low" ionization a different meaning. But I do not know of such an example.

And another plasma expert responded:
Transitions between the ordinary three states of matter (solid, liquid, gas) occur by adding heat. By heating further, you can also reach a plasma (the atoms and molecules will be split into their electrically charged constituents), but there are other methods of ionizing particles in a plasma, like collisions and by the influence of electromagnetic radiation. The particles are affected by each other due to their charge, and this influence their trajectories. What Alfvén and Fälthammar did is that they introduced an equivalent collisional cross section, by which the interaction between the charged particles could be treated as ordinary collisions. In the text, when they say 'as far as collision processes are concerned', they then mean that they are ignoring ionization due to heating or electromagnetic radiation.

A plasma which is 1% ionized consists mainly of neutrals, but at a high electron temperature, collisions between electrons and ions are dominating over collisions with neutrals, since the collisions are Coulumb collisions, where the particles are always influenced by other charged particles in the surrounding region. The cross section (i.e. probability) is thus much larger for collisions between charged particles than with neutrals, also at a very low ionization. So, even though the ionization is low in the sense that only a few percent of the particles are charged particles, it is still the charged particles that determine the characteristics, and the plasma is better described as highly ionized.

[Dancing David]

So Ian, calling a 1% ionization rate 'highly ionised' applies to the mechanical and pseudo mechanical collision between partciles in the plasma, not the 'plasma' aggregate effects that are the hallmark of plasmas?

Yes or no.

[robinson]

This is making my brain hurt.

[iantresman]

So Ian, calling a 1% ionization rate 'highly ionised' applies to the mechanical and pseudo mechanical collision between partciles in the plasma, not the 'plasma' aggregate effects that are the hallmark of plasmas?
.
I'm not sure it is a yes/no answer (or I'm not entirely sure what you're asking). I asked the plasma expert the following: "And presumably that implies that electromagnetic forces dominates its dynamics.", and the reply was:

Well, basically that is true, since the collisions are coulumb collisions, which is a collision between two charged particles and the collisional parameters are determined by their charge (the force between the two particles is given by Coulombs law, which takes the charges into account and falls of as 1/r^2, which means that they still reach quite far). So a plasma dominated by collisions still is in fact dominated by electromagnetic forces. In many cases the density of the plasma is so low that there might not be enough particles for collisions to dominate, and instead the dynamics are determined by electric and magnetic fields. One example is how particles (electrons mainly) are guided along magnetic field lines in Earth's magnetic field down to the ionosphere, where they excite particles and cause aurora!

I then asked:
I've seen mention that intergalactic H I neutral hydrogen has a degree of ionization of about 10^-4, but that this is sufficient to treat it as a plasma. Does this mean that electromagnetic forces, rather than gravity, dominates its dynamics?

And the reply:

I've seen a number of 10^-3 as example of when a plasma can be considered a highly ionized plasma, with a 10^3 times larger cross section for electrons than for neutrals. Have you heard of frozen-in magnetic field lines? Basically, it means that under certain conditions, the plasma has to move with the magnetic field lines, so that the field-lines are frozen-in, in the plasma. If the magnetic field is directed in a specific direction (like the Sun's magnetic field), the plasma has to move with the field (you can see this in solar flares etc., where you can actually see the magnetic field lines since they are frozen into the plasma!). This is very typical for cosmic plasma, and has to do with the magnetic Reynolds number that is (almost) always much larger than 1 in interplanetary space (this is the criteria). So electromagnetic forces dominates its dynamics, the H I is forced to move with the magnetic field lines that are present (this is also what I'm talking about in my paper that you found).

As for the other hallmark characteristics of a plasma, I believe that a plasma that is already only 1% ionized is already considered highly electrically conductive. What other characteristics do you have in mind?

[Dancing David]

So, my point is that these very general statements " a plasma with 1% ionization " "may be" "considered" "highly ionised" is a generalization and perhaps not accurate.

In the Alfven quote above it is about mechanistic and psuedo mechanistic collisions. It is not a statement about conduction, scattering, magnetism and debye length interactions.

In other cases it varies upon the free electrons, the density, energetic inputs, degrees of ionization and the temperature. And that all the factors are imporatant if deciding is this bunch of atoms display mechanistic gas properties or plasma properties.

So I would say that the best practice would to be very carefull about general statements. So in regards to the Alfven quote above the most accurate statement would be "for mechanistic and electrical collisions a plasma with 1% ionization is considered 'highly ionised' "?
To say that Alfven states that plasmas of 1% ionization may be considered to be "highly ionised" may be perhaps and possibly considered misleading, as it refers to qualites that are similar to gas motion and not to qualities that define plasma.

[iantresman]

So, my point is that these very general statements " a plasma with 1% ionization " "may be" "considered" "highly ionised" is a generalization and perhaps not accurate.
.
I agree. And as I have shown, even degrees of ionization as low a 10-4 may be sufficient to be considered a plasma. I have given some actually examples where this is accurate (ionosphere, Sun's photosphere), and I have not yet found any examples of space plasmas where this is not a fair generalization.

So I would say that the best practice would to be very carefull about general statements. So in regards to the Alfven quote above the most accurate statement would be "for mechanistic and electrical collisions a plasma with 1% ionization is considered 'highly ionised' "?
.
Sorry, I still don't know whether it is telling us that a 1% partially ionized plasma is considered full ionized ONLY as far as collisional processes are concerned, or whether other characteristics are included or excluded.

[Dancing David]

I agree that there are other conditions where the ionization could be lower and still have plasma behaviors.

Yet, in the Alfven statements it seems rather clear what he said, where would the extra meanings come from?


it is convenient to discuss separately the properties of weakly ionized gases, where the collisions of the charged particles with the neutral gas molecules are the most important, and those of highly ionized gases, where collisions between charged particles play a dominant role.

this sets the stage, it is convinient to discuss two seperate types of collisions
-weak ionization where charged particles with the neutral gas molecules are the most important
-highly ionized gases, where collisions between charged particles play a dominant role


It must then be observed that due to the large effective cross-section for collisions between charged particles, such collisions can be dominant even at a relatively low degree of ionization.


sets up the mechanism, it states that the collisions of charged partciles dominate at low ionization


Thus, as far as collision processes are concerned, plasmas with degrees of ionization larger than 1 per cent are to be considered as highly ionized

draws the conclusion.

And you are right, this statement makes no reference to any of the other properties defined to plasmas that are commonly used to differentiate them from gases.


Yet here is the point that i have been headed to,

So if the statement is talking about collisions and how the collsions may set a parameter where we say that the plasma is highly ionised regarding collisions and the transition from mechanic to electrical repulsive collisions,

Is it appropriate to ascribe this quote of Alfven to having meaning about the non-collisions apsects of a plasma and rates of ionization?

Does this quote of Alfvens make any statements about the relative strength of plasma properties like magnetism, conduction, scattering and debye length in regards to rates of ionization.

And therefore can it be used to support information about 'plasma' defining characteristics such as like magnetism, conduction, scattering and debye length in regards to rates of ionization?

It is a poor blade that does not cut both ways. the statement is neither inclusive nor exclusive, it is a statement about mechanical collisions and electrical repulsive collisions and that a 1% ionization will make a difference in collsion being dominated by electrical repulsive collisions.

So it does not exclude the 'plasma' properties nor does it include 'plasma' properties.

Ergo tyhe quote of Alfvens may not be used to exclude 'plasma' properties at 1% ionization nor may it be used to include 'plasma' effects at 1% except for the transition from mechanical collisions to electrical repulsive collisions.

And the crucial part of the quote is not that '1% ionization may be considered highly ionised' but that EM forces are important in defining the difference between gas and plasma. And that EM forces are part of the defining characteristics of plasmas.