Plotting Reaction Rate vs Temperature with MATLAB

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Discussion Overview

The discussion revolves around plotting the reaction rate as a function of temperature using MATLAB, specifically focusing on integrating cross section data obtained from the exfor website. Participants explore the relationship between cross sections and reaction rates under Maxwellian conditions.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant seeks guidance on how to integrate cross section data to plot reaction rates in MATLAB.
  • Another participant confirms the need for numerical integration and clarifies the relationship between temperature and the average energy of nuclei in plasma.
  • A participant mentions using pb11 cross section data and notes that textbooks often explain the difference between cross section and reaction rate without detailing the integration steps.
  • Multiple participants inquire about the availability of raw data versus plots of cross sections, emphasizing the need for a table of values for integration.
  • There is a discussion about whether the cross sections are evaluated at energy "E" or if they are differential cross sections, with a suggestion to convert them if necessary.
  • A participant corrects their earlier statement regarding the treatment of cross sections, asserting that they are always evaluated at "E" and that dividing by "delta-E" is not required, but rather it is the flux that may depend on "E".
  • A participant expresses a desire to edit their previous post due to the confusion caused by their earlier claim.

Areas of Agreement / Disagreement

Participants generally agree on the need for numerical integration and the importance of having the correct form of cross section data. However, there is some disagreement regarding the treatment of cross sections and whether they need to be converted to differential form.

Contextual Notes

Limitations include potential missing assumptions about the nature of the cross section data and the specific integration methods to be used in MATLAB. The discussion does not resolve whether the cross sections should be treated as differential or not.

Rhony
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TL;DR
I know how to get fusion cross section plots from the exfor website but now I need to plot the reaction rate as a function of temperature. According to the image, I have sigma and E values as x and y data. How do I integrate using matlab .
I know how to get fusion cross section plots from the exfor website but now I need to plot the reaction rate as a function of temperature. According to the image, I have sigma and E values as x and y data. How do I integrate using MATLAB .
 

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It would seem this is a MATLAB numerical integration problem.

So one has a nuclear (nuclei) energy spectrum, and I assume T is the average temperature (related to <E>) of the nuclei in the plasma. Is this correct?
 
Yes that's correct. I had got pb11 cross section data points from exfor. Now using maxwellian conditions, I wanted to use those to plot reaction rate. Its done in many textbooks where the explain the difference between cross section and reaction rate, but they never mention the steps followed.
 
Do you have a plot of the cross sections, or a table of the cross section values? You will need the table of values.
If you only have the plot, check the website again to see if there is a way to download the raw data.

Next, check to see if the cross sections are evaluated at "E", are are they differential cross sections as a function of E? (sigma(E)). I've seen it both ways.
If they are not differential cross sections, you will need to divide the cross section by the appropriate "delta-E" to put it in differential form.

Now you have:
  • Values of sigma(E)
  • T is a constant value
  • You can evaluate E*exp()
It is just a matter of performing the numerical integration.
 
rpp said:
Do you have a plot of the cross sections, or a table of the cross section values? You will need the table of values.
If you only have the plot, check the website again to see if there is a way to download the raw data.

Next, check to see if the cross sections are evaluated at "E", are are they differential cross sections as a function of E? (sigma(E)). I've seen it both ways.
If they are not differential cross sections, you will need to divide the cross section by the appropriate "delta-E" to put it in differential form.

Now you have:
  • Values of sigma(E)
  • T is a constant value
  • You can evaluate E*exp()
It is just a matter of performing the numerical integration.
I just realized my last post was incorrect, and I don't see a way to edit it. The cross sections are always going to be evaluated at "E", you should never have to divide by "delta-E". It is the flux that can be a function of E. Sorry for the confusion.

Mentors: is there a way to edit my previous post?
 

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