In my previous post, Plasma Physics: "E Orientation" or "B Orientation"?
, I presented the basic justification for the superiority of the "B" (magnetic field) orientation over the "E" (electric field) orientation when dealing with astrophysical plasmas. I want to complete that task in this post by presenting in more detail the physics involved. In this way we can go beyond any sense of relying solely on the assertion of individuals, even if their expertise is unquestioned, and have in place for ourselves an understanding for why the assertion is valid, based on sound physical principles. In that previous post I include a passage from the book Conversations on Electric and Magnetic Fields in the Cosmos
by Eugene Parker, one of the foremost living plasma astrophysicists. In that comment he says, "As already noted, the difficulty is that there are no tractable dynamical equations for E
". His "As already noted
" refers to the passage I now quote first below. As before, any hilight
emphasis is mine, but all other emphasis is carried over from the original.
Originally Posted by Eugene Parker, "Conversations on Electric and Magnetic Fields in the Cosmos", Introduction, page 2
Here Parker makes a point that we have not emphasized in this thread, but will now. A plasma is a collection of charged particles and those particles have mass as well as charge, so they are not only affected by electric & magnetic fields as by Maxwell's equations, but they also have momentum and kinetic energy as by Newton's equations, and we have to respect all of the physics that counts, not just the parts we like. There is no overlap between the E
paradigm and classical Newtonian mechanics; Newton's equations do not include either E
. However, there is an overlap between the B
paradigm and classical Newtonian mechanics; the velocity, v
, of the particles shows up in both, which immediately connects the Newtonian energy & momentum to Maxwell's equations. Hence the obvious preference for the B
paradigm: It makes the difference between tractable and intractable physics.
Parker says above that "we will come back to specific aspects of the misunderstanding ...
". I want to do that now so we can see exactly what is happening.
Originally Posted by Eugene Parker, "Conversations on Electric and Magnetic Fields in the Cosmos", chapter 7 "Moving Reference Frames", pages 69-70
In this passage above the notation "O(v2/c2
)" means "on the oder of v2/c2
" and shows an approximate order of magnitude. Also note that the papers by Vasyliunas (retired director of the Max Planck Institute for Solar System Research
) are particularly interesting and reinforce what Parker tells us quite nicely.
Parker's reference to equation 1.8 is this:
E'/B = c/4πσl = (10-4
which equates the electric field in the moving reference frame of the plasma (E') and the magnetic field (B) (σ is the electrical conductivity). This is all found in Parker's Conversations
on page 8. The upshot is that E'/B is likely never greater then 10-9
, and since the stresses induced by the fields are proportional to (E'/B)2
, the stress induced on the plasma by E' must be ~ 10-18
compared to the stress induced by B.
Parker's reference to equation 7.2 is this:
, t) = [-v
, t) X B
, t)] / c
This is the electric field E
, t) in the laboratory frame of reference when the electric field in the plasma frame of reference (E
') is zero. It is found in Parker's Conversations
at the bottom of page 68.
What it all boils down to is this: One cannot construct physically meaningful equations to describe the dynamics of a plasma in the "electric" paradigm favored by Mozina. One can do so only in the "magnetic" paradigm, increasingly favored by plasma physicists
. This post and my previous post detail the physical reasoning behind this choice of "B" over "E". It is not as simple as Mozina
claims, it's not simply a prejudice for one over the other, and it certainly is not "putting the magnetic cart before the electric horse
", as Mozina
has said it. The physical horse is in fact the magnetic field in almost all astrophysical cases. It is important to note the distinction that astrophysical plasmas and laboratory plasmas, despite both being plasmas, are not the same; astrophysical spatial scales cannot be reproduced in a laboratory, and that is significant. The relationship between electric and magnetic fields in the two plasmas are not the same, as a direct result of the difference in spatial scales, and that affects plasma dynamics. One should not blindly apply the paradigm of one unto the other. As is often the case in physics, each situation is like a position in a chess game: While there are general principles one can apply, each must be considered carefully on its own merits for its own proper solution.