Gordeyev integrals

[jswoboda]

The Gordeyev integral are not being evaluated properly. The function doesn't seem to evaluate it at all.

[jsemeter]

Did you write the function or grab from somewhere? Early on in this project I think I forwarded a spectrum calculator Diaz coded up from the Sheffield book (which should be same as Chapter 1 of this book: http://www.eiscat.com/groups/Documentation/BlueBooks/Cargese%20book.pdf He includes a small side function to deal with Gordeyev integral. I’ve attached the script here. This is for no magnetic field effects (ok for ~B_parallel observations) and no collisions (ok for F-region). Could be worth to check your spectrum model against this.

I modified this version to allow for non-zero bulk ion motion, but it shifts the spectrum outside the limits so needs a bit more work. E.g.,

[Spec w ACF t]=isr_20Aug2008(450,3000,3000,1e12,16,1,5e-5,2000,2000); plot(w,Spec)

On Apr 20, 2016, at 10:39 PM, John Swoboda notifications@github.com<mailto:notifications@github.com> wrote:

The Gordeyev integral are not being evaluated properly. The function doesn't seem to evaluate it at all.

— You are receiving this because you are subscribed to this thread. Reply to this email directly or view it on GitHubhttps://github.com/jswoboda/ISRSpectrum/issues/3

[jswoboda]

I wrote this function based off of whats in the Kudeki paper. I've been noticing some odd behavior when I'm trying to resolve the gyro lines. I think its probably an issue with the way the bounds of the integration are chosen.

[jswoboda]

I've gone through the code pretty carefully. First off I've been able to get some agreement between Asti Bhatt's electron line program and my own. I think she's doing a similar process but her dissertation, from which figure one is taken from, predates the 2011 Kudeki, Milla paper this repository is derived from.

To get the agreement I have changed the software. The sampling rate of tau, the lag parameter for the single particle ACF, is driven by the largest frequency component desired for the ISR spectrum. The numerical integration algorithm will basically keep integrating over tau until the difference is smaller then the desired setting. I have run into memory issues when I would use too many samples. I will need to make some sort of setting to keep this from happening in the future.

There are a couple of extra aspects that I will need to address. First off the ion line will have components that are larger in frequency than should be physically possible. I'm thinking of adding a piece of code to see the ion line to zero after a certain frequency. Otherwise I think I'm just going to put a note that the ion line acts unphysically after a certain frequency. This frequency is on the order of plasma frequency so it should impact anything I'm doing right now.

On other aspect is that the single particle ACF used to calculate the Gordeyev integral for the case with a magnetic field and no collisions is slightly different between Hagafor's publications and the Kudeki and Milla publication. I'm not sure how much of difference this makes and need to investigate it further.

I'm going to keep this open for now and will hopefully close this issue soon.

[jswoboda]

Tried killing the Gordeyev integrals for the ions at a set frequency. This caused there to be a discontinuity in the electron line at the cut off. I also only applied this to the thermally driven density spectra, the <|ni|^2> terms in equation 41 (Kudeki 2011). This only impacted the ion line and not the electron line where I was seeing some odd behavior.