Talk:Electron cyclotron resonance

Untitled

Should this article be classified as a stub? I've worked on Fermi surface and effective mass and haven't really thought through which material should be in which article. Obviously each article should be self-contained although we'd like them to avoid unnecessary repetition. Is electron cyclotron resonance still too short? If "Landau level," "Shubnikov-de Haas" and "de Haas-van Alphen" all existed, we'd have a pretty good collection of articles on this general topic. Alison Chaiken 19:34, 29 December 2005 (UTC)

Looks ok to de-stub it to me, though if you want second opinions, maybe add this page to Wikipedia:Pages needing attention/Physics. It could still use fleshing out; in particular, you might want to add a couple of equations showing how the derivation is performed (equating lorentz force and centripetal force), and a brief explanation of why Fermi surface is related to cyclotron resonance, but even as-is it looks decent. --Christopher Thomas 19:44, 29 December 2005 (UTC)

The article is a curious mixture of plasma physics and solid state physics. The first word of the article is plasma, but effective mass and Landau levels are concepts not used in plasma physics. I can help assure that the plasma physics remains correct, but I don't know anything about the significance and application of ECR in solid state physics. --Art Carlson 20:49, 29 December 2005 (UTC)

I reformatted the article to separate the plasma and condensed-matter content. This makes the plasma-specific content look a bit skimpy but should be less confusing to the neophyte. Most of the condensed-matter content on this topic is actually in effective mass and Fermi surface. Alison Chaiken 22:01, 29 December 2005 (UTC)

That's an improvement. I'll try to flesh out the plasma physics. --Art Carlson 13:26, 30 December 2005 (UTC)

edits by 129.93.123.197

Actually I think it's a good idea to write formulas in SI units. Is there a general solution in Wikipedia to the question of what units to use, or at least to make clear which set apply to a given formula? --Art Carlson 08:13, 28 March 2006 (UTC)

If the change was valid, go ahead and reinsert it. That IP just had at least one instance of subtly mangling data, and I wasn't in a position to determine if the edit to this article was valid or not. Some mention of units should probably be added anyways. --Christopher Thomas 17:16, 28 March 2006 (UTC)

formula

omega = e*B/m = (1.602e-19 C)*(0.0875 T)/(9.109e-31 kg) = 1.539e10 rad/s

f = omega/(2*pi) = (1.539e10 rad/s)/(2*3.14159) = 2.45 GHz

--Art Carlson 16:31, 14 February 2007 (UTC)

The distinction of "angular frequency" rather than traditional frequency is invaluable. However, I'd like to point out that the elementary charge(e) of an electron is -1, not 1.602e-19, and it is an Atomic unit, not an SI unit.

omega = e*B/m = (1 e)*(0.0875 T)/(9.109e-31 kg) = ??e29 rad/s

f = omega/(2*pi) = (??e29 rad/s)/(2*3.14159) = ???e19 GHz

which is nowhere near 2.45 GHz. Kevin Baas^talk 21:38, 18 February 2007 (UTC)

The elementary charge is defined as a positive quantity, so you get a positive frequency. e is less ambiguous than q when we are talking about electron cyclotron resonance. The numerical value of the elementary charge in atomic units is one. The numerical value of the elementary charge in SI units is 1.602e-19. The formula is correct - and yields 2.45 GHz - in SI units. I think it is enough to specify SI units, but to make you happy I have now detailed the units of every variable. --Art Carlson 21:22, 21 February 2007 (UTC)

Neither e nor q is ambiguous. e means "the numerical value of the charge of a body (or space) in atomic units". q means "the numerical value of the charge of a body (or space) in SI units." It is a scientific mathematical formula, and in scientific mathematical formulas, letters stand for very specific things. In this case, we are using SI units, and the "q" of an electron is -1.602e-19, whereas in AMU, the "e" of an electron is -1. The formula, w=1.602e-19eB/m.

q is often used as a general symbol for a charge, whether elementary or not; e is only used for the elementary charge. The elementary charge is a particular quantity of electrical charge, independent of the units used to express that quantity. If you have a problem with the definition of e as a positive quantity, take it up on Elementray charge, where the first line is "The elementary charge (symbol e or sometimes q) is ... the negative of the electric charge carried by a single electron." (my emphasis) --Art Carlson 12:39, 27 February 2007 (UTC)

I do not have a problem with e being defined as a positive quantity. The first line of elementary charge reads "The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton...", not an electron. This is not "proton cyclotron resonance". An electron has the opposite charge: -1 "unit[s] of electric charge in the system of atomic units". (Expressed in the system of SI units, this is -1.602e-19 coulombs.) So when that e is there, what you do, by convention (because this is what it means), is substitute the quantity of units of electric charge in AMU, which, in this case, is -1. Just as, with the B, you substitute the magnetic field strength in teslas (as opposed, for instance, to gauss), and with the m, you substitute the mass in kilograms (as opposed, for instance, to pounds), and just as w means angular velocity, as opposed to frequency, as you pointed out. So the formula, substituting the signifiers for their values, comes out to a negative quantity. This is where you contradicted yourself mathematically. You said it comes out positive. You also just emphasized "the negative of an electric charge carried by a single electron. So, since e represents the charge of a particle in AMU, and we are considering an electron, which is the negative of the unit of electric charge in AMU, the e in this equation represents -1; the charge of an electron in AMU. Kevin Baas^talk 19:35, 3 March 2007 (UTC)

And you mathematically contradicted yourself: "The elementary charge is defined as a positive quantity, so you get a positive frequency...the numerical value of the elementary charge in SI units is 1.602e-19." elementary charge is defined as the charge of a proton, not an electron. It is a fundamental physical constant and the unit of electric charge in the system of atomic units. An electron has an elementary charge of -1, which is not a positive quantity. One look at the second sentence of the article on electrons validates this: "It is a spin-½ lepton that participates in electromagnetic interactions, and its mass is less than one thousandth of that of the smallest atom. Its electric charge is defined by convention to be negative, with a value of −1 in atomic units." (emphasis added) The sign of the angular speed tells us if the particle is revolving clockwise or counterclockwise. When we are concerned with frequency, we use the absolute value; the speed rather than the velocity, so to speak, because the direction of rotation is not important.

I don't see what you consider to be a mathematical contradiction. I know that the electron has (by convention) a negative charge. --Art Carlson 12:39, 27 February 2007 (UTC)

Ergo, the formula w=eB/m, where e is the charge of the particle in question, an electron, which as you know, is negative. and B and m are both positive, yields a negative w. You said that w was positive definite. Therein lies the contradiction. Kevin Baas^talk 19:35, 3 March 2007 (UTC)

The formula for cyclotron resonance is not just for electron cyclotron resonance, it is a physical relationship between charge, mass, and magnetic field, that holds for any charge of any particle of any mass in any field. and the relationship is: radians per second equals coulomb teslas per kilogram, which is mathematically expressed: rad/s=qB/m. The expression rad/s=eB/m means radians per second equals elementary charge teslas per kilogram, which, besides giving incorrect results, mixes two unit systems (atomic and standard). And by mixing two unit systems, it clearly makes the sentence "given in SI units" incorrect, as the formula is given in a combination of SI units and atomic units (elementary charge being an atomic unit). Kevin Baas^talk 01:55, 27 February 2007 (UTC)

This article is about electron cyclotron resonance, not cyclotron resonance in general. I can't make any sense out of the rest of this paragraph. --Art Carlson 12:39, 27 February 2007 (UTC)

I get it now, you're using e as one would use c, the speed of light in vacuum. c represents a physical constant in relativity formulas because it represents a scale relationship between the time dimension and space dimensions of minkowski space; it is a constant of a metric, and when used in a formula, it elucidates a physical/geometric relationship. When e is used as a constant in an equation such as w=eB/m, rather than elucidating a relationship like c in the lorentz transformation elucidates the space-time geometry of special relativity, using a constant e in the formula for electron cyclotron resonance unnecessarily hides a physical/geometric relationship. w=eB/m, where e is a constant, is as different from w=qB/m as 4x=2y is from 4x=yz. when you replace a variable with a constant, you lose information about the relationship that the formula represents. electron cyclotron resonance is a phenomena that exists due to a physical/geometric relationship. the purpose of the formula should be to express that relationship.

talking about ambiguity again, e is much more ambiguous than q, as one doesn't know whether it represents the physical constant 1.602e-19 coulombs or the charge of the particle in AMU, which is -1.

• if the former is the case, then the charge of the particle is conspicuously absent from the equation, and the equation looks like a relationship between the magnetic force and the gravitational force that produces angular velocity (one might as well replace e with G.). This is surprising. One would expect it to be a relationship between the electric and magnetic force, as is usually the case in electromagnetics. However surprising, i'm sure the reader will digest just fine from the formula that ECR is a relationship between the magnetic force and the gravitational force that produces angular velocity. Nevermind the fact it's actually a relationship between the magnetic and electric forces that produces angular momentum.
• if the latter is the case, where e is interpreted as "electric charge in the system of atomic units", the formula gives a result that doesn't match physical experiment, by about 19 orders of magnitude. furthermore, the formula uses both SI units (B and M) and atomic units (e), which is bad enough, nevermind the fact that the article clearly states that it is given in SI units only.

So in conclusion, as ambiguous as w=eB/m is, both interpretations lead to serious conceptual and/or quantitative problems. In comparison, w=qB/m has only one interpretation, which is both conceptually straightforward and quantitatively accurate. Kevin Baas^talk 19:35, 3 March 2007 (UTC)

You have to expect confusion if you mix SI units and atomic units. Elementary charge: "The elementary charge (symbol e or sometimes q) ... has a value of 1.602 176 53(14) × 10^-19 C". Use that (positive!) value in the equation and everything is fine. I disagree that anyone except you will be confused by the formula. (One could consider a separate article on cyclotron motion in general, where, of course, the formula would be qB/m. Other articles, such as Cyclotron and Guiding center would then have to be rewritten a bit. I think it would be hard to make such an article more than a stub.) --Art Carlson 20:55, 3 March 2007 (UTC)

I don't think we'd really need to rewrite Cyclotron and Guiding center. :-) Kevin Baas^talk 22:48, 3 March 2007 (UTC)

Those articles use q. Kevin Baas^talk 20:09, 8 March 2007 (UTC)

They also apply in principle to multiply charged ions, not just elementary charges. --Art Carlson 20:30, 8 March 2007 (UTC)

ECR Ion Sources

I think a section on ECR ion source needs to be in a sub-section on its own. I will try to add something.Scaler1112 10:01, 11 July 2007 (UTC)

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