3 ms·

Ok what is F sub N and F sub L in the last paragraph of this page? http://imgur.com/a/bRFFE http://imgur.com/a/bRFFE

yorwba 10y ago
Also sent you an email, putting my response here for posterity. First of all I'm sorry for responding so late, HN comments are somewhat of a fire-and-forget for me. Second, I'm not much of a plasma physicist (or any kind of physicist, really). In fact, I was mostly interested in your example because I wanted to see how well I could understand it without the relevant background. Turns out, not very well. But I think I figured out what the fs are, so maybe that will help you. Looking at the paragraph in your photo, I noticed that it mentions three kinds of frequencies: of the whistlers, of the plasma and the electron gyrofrequency. Since f is frequently used to denote frequencies in physics, I guess that f, f_N and f_L are these three. (The units of Hertz are another hint.) Based on the description, the whistler frequency should be the smallest one. In the example, that is f. It remains to determine f_N and f_L. Unfortunately, the names are definitely not mnemonic, so I needed some other source. Turns out Wikipedia has an article on the Appleton-Hartree equation that defines all the variables it uses. (https://en.wikipedia.org/wiki/Appleton%E2%80%93Hartree_equation https://en.wikipedia.org/wiki/Appleton%E2%80%93Hartree_equat...) There, f_0 and f_H are used for plasma frequency and gyro frequency. Also not mnemonic, but at least explained. I guess the relevant equation is in the section on quasi-longitudinal propagation. I simplified it even further by using the assumption that the angle theta = 0, which means that the sine is 0 and the cosine is 1. Then the equation becomes n^2 = 1 - X/(1 ± Y) and since the book assumes that X and Y are much larger than unity, this can be approximated by n^2 = 1 ± X/Y = 1 ± (f_0^2/f^2)/(f_H/f) = 1 ± f_0^2/(f*f_H) Further assuming that the ratio is so large that the 1 can be dropped, this gives an expression for the refractive index n = f_0/sqrt(f*f_H) Matching terms with the equation in the book, f_N appears to denote the plasma frequency (f_0 on Wikipedia) and f_L is the gyro frequency (f_H on Wikipedia). Mystery solved! Now I completely agree with you that this kind of detective work shouldn't have been necessary and the full derivation should have been in an appendix or in a cited reference.

Also sent you an email, putting my response here for posterity. First of all I'm sorry for responding so late, HN comments are somewhat of a fire-and-forget for me. Second, I'm not much of a plasma physicist (or any kind of physicist, really). In fact, I was mostly interested in your example because I wanted to see how well I could understand it without the relevant background. Turns out, not very well. But I think I figured out what the fs are, so maybe that will help you. Looking at the paragraph in your photo, I noticed that it mentions three kinds of frequencies: of the whistlers, of the plasma and the electron gyrofrequency. Since f is frequently used to denote frequencies in physics, I guess that f, f_N and f_L are these three. (The units of Hertz are another hint.) Based on the description, the whistler frequency should be the smallest one. In the example, that is f. It remains to determine f_N and f_L. Unfortunately, the names are definitely not mnemonic, so I needed some other source. Turns out Wikipedia has an article on the Appleton-Hartree equation that defines all the variables it uses. (https://en.wikipedia.org/wiki/Appleton%E2%80%93Hartree_equation https://en.wikipedia.org/wiki/Appleton%E2%80%93Hartree_equat...) There, f_0 and f_H are used for plasma frequency and gyro frequency. Also not mnemonic, but at least explained. I guess the relevant equation is in the section on quasi-longitudinal propagation. I simplified it even further by using the assumption that the angle theta = 0, which means that the sine is 0 and the cosine is 1. Then the equation becomes n^2 = 1 - X/(1 ± Y) and since the book assumes that X and Y are much larger than unity, this can be approximated by n^2 = 1 ± X/Y = 1 ± (f_0^2/f^2)/(f_H/f) = 1 ± f_0^2/(f*f_H) Further assuming that the ratio is so large that the 1 can be dropped, this gives an expression for the refractive index n = f_0/sqrt(f*f_H) Matching terms with the equation in the book, f_N appears to denote the plasma frequency (f_0 on Wikipedia) and f_L is the gyro frequency (f_H on Wikipedia). Mystery solved! Now I completely agree with you that this kind of detective work shouldn't have been necessary and the full derivation should have been in an appendix or in a cited reference.