Talk:Guiding center

New Introductory paragraph?
Do you think that the following introductory paragraph, may help beginners? I've tried to base it on a practical, rather than purely mathematical description. It is rewritten from information found in Hannes Alfvén's Cosmic Plasma, p.43-44.

In plasma physics, the presence of a perfectly uniform magnetic field, would make charged particles (electrons and positive ions), move in a perfect circle, the center of which can be thought of as the guiding center. In practice, additional forces such as gravity, an electric field, non-uniform magnetic fields, and inertia, will change this perfect circle into distorted spirals and helixes, and the guiding center may move, and ions will appear to drift.

Since most of these drifts depend on the sign of the charge on an ion, they also produce an electric current (the exception is electric field drift). It is also worth noting that:


 * since the gravitational drift depends on the mass of the ion, it can produce chemical separation.
 * magnetic drift can also result in chemical separation if the perpendicular temperatures of different ions is different
 * inertia drift transfers kinetic energy into electromagnetic energy, and vice versa.

Mathematically, the guiding center of a charged particle in a magnetic field...

--Iantresman 14:07, 5 August 2005 (UTC)


 * I tried to incorporate these ideas and more of my own. I realized that some of what I had written before was wrong, and that it is rather tricky to develop the ideas in a way which is both didactic and rigorous. I hope the present version is better in both regards. --Art Carlson 15:07, 2005 August 8 (UTC)


 * Sounds good. Is inertia drift mentioned, perhaps under a different name? --Iantresman 17:24, 8 August 2005 (UTC)


 * I assume that is what I call the polarization drift.--Art Carlson 19:22, 2005 August 8 (UTC)

Inertial Drift vs Polarisation Drift
I don't think that the intertial drift is the same as the polarisation drift, though I can't figure out which (if any) it is similar to. A pages mentions them as different drifts:

http://farside.ph.utexas.edu/teaching/plasma/lectures/node17.html


 * You're right, although I don't know how standard this nomenclature is. The inertial drift (in this sense) is a generalization of the curvature drift. I have made appropriate changes. --Art Carlson 21:49, 2005 August 22 (UTC)

Confusion
This article is very confusing. The fluid and particle pictures are mixed up. The diamagnetic drift is not a particle drift in a straight and homogeneous B field. it is merely a fluid drift. Read chapter 7 in Goldston rutherfor introduction to plasma physics......

Article should at least include remarks about guiding centre theory and gyro center theory...


 * The fluid picture is only used where the diamagnetic drift is mentioned. That is only twice, and both times it is pointed out that it should not be confused with a guiding center drift. What elements of guiding center theory are missing? Are you using "gyro center theory" to mean something different than "guiding center theory"?
 * The article is very dense, but I don't immediately see how the material can be presented more clearly without making it much longer. Concrete suggestions are welcome. Better yet, try to improve it yorself! --Art Carlson 15:16, 8 November 2006 (UTC)

Grad-B Drift Formula

 * $$\vec{v}_{\nabla B} = \frac{\epsilon_\perp}{qB} \frac{\vec{B}\times\nabla B}{B^2}$$

This is ambiguous, because the second vector of the cross product ($$\nabla B$$). I'd change it myself, but the reason I came to this page was to check a formula from my class notes. The expression I have is


 * $$\vec{v}_{\nabla B} = \frac{2\epsilon_\perp}{q}

\frac{\vec{B}\times\vec{\nabla}|\vec{B}|}{B^2} $$

I guess the cross product is right, but I'm scrounging around for the numerical factors now: I'm not sure where my extra $$2B$$ comes from. Warrickball (talk) 14:14, 3 May 2008 (UTC)

Derivation of the equation
I wonder if some book contains a direct derivation by perturbation expansion of the drift terms on the generalised first-order equation of the particle dynamics in the case witha a Lorentz force:

$$m \frac {\operatorname d \vec v}{\operatorname dt} = \vec F + q \vec v \times \vec B $$

at the present time in this page as I found in some introductory books like Freidberg's one there is only a list that doesn't show which ones are the zero order ones, which ones the first order, and so on. For convenience, I purpose to do this by putting it in the elementary form:

$$\frac {\operatorname d \vec v}{\operatorname dt} + \vec \omega_c \times \vec v = \vec a $$

where a is the acceleration and ωc is the Larmor frequency. --79.52.61.80 (talk) 19:55, 26 July 2014 (UTC)