Introduction to Plasma Theory (Plasma Physics), by Dwight R. Nicholson

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Introduction to Plasma Theory (Plasma Physics), by Dwight R. Nicholson

Introduction to Plasma Theory (Plasma Physics), by Dwight R. Nicholson

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Introduction to Plasma Theory (Plasma Physics), by Dwight R. Nicholson

Provides a complete introduction to plasma physics as taught in a 1-year graduate course. Covers all important topics of plasma theory, omitting no mathematical steps in derivations. Covers solitons, parametric instabilities, weak turbulence theory, and more. Includes exercises and problems which apply theories to practical examples. 4 of the 10 chapters do not include complex variables and can be used for a 1-semester senior level undergraduate course.

  • Sales Rank: #1388620 in Books
  • Published on: 1983-03-25
  • Original language: English
  • Number of items: 1
  • Binding: Hardcover
  • 292 pages

Most helpful customer reviews

5 of 7 people found the following review helpful.
A Brilliant Textbook That Ought to be More Readily Available!
By PHILIP A. STAHL
I had been searching for this particular plasma physics text since taking a Ph.D. course in space plasma physics (with only a few library copies avaialable) in 1985 at the Univ. of Alaska- Fairbanks, because Nicholson’s approach is so well adapted to the space physics domain. I finally managed to obtain it on amazon.com. meaning I no longer had to go to assorted libraries – which was good.

I felt it incumbent on myself to write a detailed review of the book, if I ever could get hold of it, and this is what I present here. (Knowing in advance some potential readers may not relish the level of detail, including the mathematical inclusions and hence not find it “useful” to them – which likely means to me they wouldn’t have purchased it anyway and probably are better suited to getting a basic text like ‘The Fourth State of Matter’)

Nicholson begins with a rigorous attending to essential definitions, quantitatively given in Chapter 1. Then in Chapter 2 ‘Single Particle Motion’ he sets into high gear, tackling E X B drifts (p. 17), Grad B drift (p. 20) along with gyro-motion and guiding center approximation (21-22) and curvature drifts (p. 22), then polarization drift and magnetic moments – finishing with the adiabatic invariants, ponderomotive force and diffusion.

The treatment of mirror machines and mirror confinement in the context of magnetic moment and the adiabatic invariants is also particularly applicable to the space physics arena.

For example, In space physics, one uses the sine of *the loss cone angle* to obtain the mirror ratio (where
B(min) , B (max) refer to minimum and maximum magnetic induction respectively). This requires minor adjustments to Nicholson’s formalism, leading to:

sin(Θ_L) = ± [ (B(min) / B (max)]^½

If one finds that there are particles within the “mirrors” for which the “pitch angle” (φ) has:

sin (φ) > [ (B(min) / B (max )]^½

then these will be reflected within the tube, On the other hand, those particles for which the “less than” condition applies will be lost, on transmission out of the mirror configuration.

Since the adiabatic invariant u for particle motion is a constant of the motion:

u= ½ [mv ^2 /B]

we have (with the v’s the perpendicular and parallel components of velocity, i.e. relative to the B-field):

[v⊥^2 /B(max)] = [v ‖ ^ 2 /B_z] = const. or [v⊥^2 /v ‖ ^ 2 ] = B_z /B(max)

where we take B_z = B(min)

that is, the minimum of the magnetic field intensity, say occurring at the apex of a solar coronal loop.

Probably chapters 3 and 4 (Plasma Kinetic Theory 1 and II) will be the toughest bars to cross for most students, but again, Francis Chen’s ‘Introduction to Plasma Physics’, is a good augmenting and support text. (See also my review of Chen’s book).

The Vlasov equation (Chapter 6) is also critical material and most Ph.D. courses will include it in a first semester course. What the potential reader needs to bear in mind, of course, is that classification of differing fluid regimes is at the heart of most plasma physics and progresses via consideration of different ‘moments’.

For example, consider the Boltmann eqn.: @f/ @t + v*grad f + F/m*@f/@t = (@f/@t)_C

(where @ denotes partial derivative, and (@f/@t)_C is the time rate of change in f due to collisions.)

The first moment, then yields a ‘two-fluid’ (e.g. electron-ion) medium, obtained by integrating the above eqn. with F = q/m (E + v X B). If one then assumes a sufficiently hot plasma so it’s collisionless, the term on the RHS, (@f/@t)_C -> 0.

This is the Vlasov equation:

@f/@t + v*grad f + q/m (E + v X B)*@f/@t = 0

The 2nd moment is obtained by multiplying the original eqn. (Boltzmann) by mv then integrating it over dv.

Anyway, the progression by using this procedure is that one gets in succession:

Two -fluid theory (e.g. ions and electrons treated as a separate fluids)

!
!
V

One fluid theory (introducing low frequency, long wave length and quasi -neutral approximations, e.g. n_e ~ n_i
!
!
V

MHD Theory (proceeds from 1-fluid theory with further assumptions, simplifications)

This is basically the same progression followed in Nicholson, ending up (roughly) at Magnetohydrodynamics (MHD) in Chapter 8 (with two further chapters on discrete particle effects and weak turbulence theory to clear up finer details, e.g. to do with debye shielding.

I especially have always liked Nicholson’s treatment of Landau damping (sec. 6.5, page 80) and the way it follows on from the treatment of the Landau contour.(p. 76)

the case below, for the upper right half-plane for plotting velocities u on the imaginary (vertical) and real (horizontal) axis.

For some Laplace transform function E1(w) one has:

E1(w) ~ INT du {(df/du) / [u – w/k])}

And at certain value of u (= w/k) what do we find? Well, w/k – w/k = 0 so

E1(w) -> oo

Of course, this is verboten! It is an infinity! A singularity! As you can see they don’t merely arise with naked singularities!

To avoid this (E1(w) -> oo) in obtaining what we call the inverse transform, one then performs (as shown below with arrows) an “analytical continuation” process which escapes the singularity and arrives at a rational and reasonable solution.

Plotting the graph on the axes:

u(i)
!
!
! pole x
!
!
!
!—–>-!———-!—>—–>u(r)
(x) Res
Landau contour

This Landau contour – after the contour integral, wends its way around the singular pole (infinity) and going along the horizontal axis, then downwards (picking up what we call a “residue” (2 pi(i)) and then back up and further along to the right of real axis u(r).

Further note: When I took the Space Plasma Physics course, I was concurrently taking Mathematical Physics (Ph.D. level) with it. My suggestion is that perhaps students can get more out of Nicholson’s text if they take the Mathematical physics as a prerequisite. Especially useful in this case, is greater exposure to the calculus of residues.

Nicholson’s book belongs on the shelves of every serious graduate level plasma physics student, or space physics researcher – but as I noted- I just wished it was more widely available!

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