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Thread: Questions on Plasma Physics & Kinnetic Theory of Gases

  1. #1
    Join Date
    Oct 2016

    Questions on Plasma Physics & Kinnetic Theory of Gases

    A two-parter, if that's okay?

    As is often the case, I find myself debunking pseudoscience! Currently on the radar is one Pierre-Marie Robitaille. Yep, him of the liquid metallic hydrogen (LMH) Sun, and the oceans being responsible for the CMB. What's not to believe?

    Two questions that have arisen in discussions with his fanboys that are not necessarily easy to find in the literature. They are at such a low-level that they would most likely be found in textbooks. I think I know the answers, but let's assume for the sake of the aforementioned fanboys, that I need it spelling out in terms that even an idiot could understand. Any references would be a bonus.

    1) In the Kinetic Theory of Gases (KToG), the gas pressure is calculated assuming a 2D surface from which we can work out the pressure from P = F/A. Robitaille claims that a real solid surface is required! Otherwise the gas just expands into the vacuum. I kid you not. Pointing out that the Sun proves this to be wrong is pointless, as he thinks it is a giant ball of LMH! I have even found and linked a good paper saying that this surface can be 'imaginary'. However, the retort is that it is an imaginary surface within an already bound (by solid surfaces) gas!
    So, the question is - can the KToG be applied to a totally unbound mass of gas? For the sake of this question, let us assume a giant molecular cloud that is in virial equilibrium.

    2) Another of Robitaille's claims is that his liquid Sun is proven by the observation of ripples in the photosphere. This was seen for the first time in 1996. I'm not sure on the rules re posting links, so if anybody is interested in this, look for this paper by Kosovichev & Zharkova (1998); 'X-ray flare sparks quake inside Sun'.

    The claim is that such transverse waves cannot exist in plasma, and that they require conditions that are not present in the photosphere. I beg to differ, but an explanation from an actual plasma (astro)physicist might be handy!

    Many thanks.

  2. #2
    Join Date
    Aug 2002
    Hi JD

    Usually, in textbooks like "Allonso & Finn" you are getting the derivation of pressure through an example particle with mass m and velocity v that hits a surface A and then bounces back and then you have the change in momentum and you get a force on the wall. And then it is said that to get to pressure, which is force per area, P = F/A, can then be obtained. It then also says that this only works with a large number of particles, because pressure is a macroscopic quantity.

    The only way of treating a large number of particles is through kinetic theory, as in general you cannot assume that all the particle have the same velocity in the gas. If they have the same mass and speed, but different angles wrt the wall, it is kind of easy to calculate, but there still is a wall.

    Assuming a cloud of particles with a distribution of velocities, in the kinetic theory you describe these with a particle distribution function f(v), which can be extended to phase space to also put in the location and time but that needlessly makes things more complicated than they need to be.

    Now the cloud gets split up into small cells, where there are many particles and their velocities can only be described by f(v).
    The total number of particles in the cell is then the integral:

    This is called the zero order moment. (And if all the particles have the same mass then you get the regular density ρ = m n, for the fluid description)

    You then get the so-called fluid velocity in the cell, i.e. the mean velocity of the particles in the cell as the first moment:

    and this is related to the fluid momentum density p = ρ u.

    You can go on like this, take higher order moments, the second order is pressure, the third order is heat flux, but this is usually done in a "co-moving frame" with velocity u, this way the quantities are independent of the reference frame, so you get

    and that gets put into the second moment

    which is a 3x3 pressure tensor, where each component (i,j) is to be understood as the flux of momentum m δvi transported by velocity δvj

    So, how does this relate to the fluid model of scalar pressure? Well there are symmetries in a fluid, and assuming isotropy you will get that the perssure tensor is diagonal and only dependent on a scalar value P

    where I is the identity matrix. That is how you get to pressure without assuming a physical wall. And indeed, as you say a star or a molecular cloud or whatever, would be a good example of a gas (plasma) without physical walls. (Not that that is going to be believed.) And of course this is all only a lot of mathemajics.

    For problem 2, this is of course nonsense, there can be waves and "tsunamis" on the surface of the Sun.
    There is no problem with posting links to papers, here is the link to ADS for the mentioned paper, but you don't have enough posts yet to get links through.
    Don't have time at this point, but will try to come back.

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  3. #3
    Join Date
    Oct 2016
    Many thanks for that. Bookmarked. As for the transverse waves, they were actually predicted as far back as Wollff (1972). And by Zharkova and A. N. Other, a year before the observation, iirc.

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