pp reaction cross section

[RemDelaporteMathurin]

Hi! thanks for that great package. Very useful!

I'd like to plot cross sections with the pp reaction. Do you think there's a way of adding this to fusion_cross_sections.py ?

I've come up with that script so far but must've messed up something with the units...

import numpy as np
import matplotlib.pyplot as plt
from scipy.constants import e, atomic_mass, hbar


ev_to_joule = 1.60218e-19  # J/eV
barn_to_m2 = 1e-28  # m2/b

E = np.logspace(0, 6)  # eV


A1 = A2 = 1.0072765
mu = atomic_mass*A1*A2/(A1+A2)
vel = (2*E*ev_to_joule/mu)**0.5

eta = e**2/hbar/vel
S_0 = 4e-25*1e6  # eV b
S_prime_0 = 11.2  # b
S = S_0 + S_prime_0 * E
cross_section = S/E*np.exp(-2*np.pi*eta)
cross_section *= barn_to_m2

plt.plot(E, cross_section)
plt.xscale("log")
plt.yscale("log")
plt.show()

[alfkoehn]

Thanks for your kind words, greatly appreciated!

Concerning your request: I have actually done that in a lecture I gave 2 month ago and I wanted to add that to the plot-script here. I will have a close look at your code and compare it with my code over the next days (somewhat busy these days, sorry) and then come back to you here - I'm curious to see if there are any difference :)

[alfkoehn]

Well, I've just realized that I have already added that to the fusion_reactivity plot :)

Is that what you were looking for?

[RemDelaporteMathurin]

hi @alfkoehn thanks for reaching out!

This is indeed what I was looking for 😄 I had similar results for pp cross sections (waaayy lower than DD, DT...). Shall I start a PR to add this to fusion_cross_sections.py ?

[alfkoehn]

hi @RemDelaporteMathurin, sorry for my extremely late answer! Isn't this what you are looking for: https://github.com/alfkoehn/fusion_plots/tree/master/fusion_reactivity , i.e. in my understanding your suggestion is already part of the package?

[RemDelaporteMathurin]

hi @alfkoehn , no probs

You are right it is included in fusion_reactiviy, but not in cross sections (which are a bit different). I know that the pp cross section would be way lower, but maybe users could have the possibility to add it.

It's a nice comparison sometimes required to show why we cannot simply burn H-H plasmas

[alfkoehn]

Ah, you're right of course. I'm just wondering now why I haven't included them... will look into it and comment here as soon as I have added them.

[RemDelaporteMathurin]

I'm just wondering now why I haven't included them..

One reason might be that the pp cross section is so low, it would squish all the curves and we wouldn't see anything. But that's the point in a way. I find it useful to say: "this is the cross sections of DD DT etc. Why don't we use HH? well here it is, down below"

[jhillairet]

I was also looking for the pp cross section, but according to:

Adelberger, E.G., et al.., 1998. Solar fusion cross sections. Rev. Mod. Phys. 70, 1265–1291. https://doi.org/10/ftx3j3

However, the rate for the fundamental p + p -> 2D + e+ + nu_e reaction is too small to be measured in the laboratory. Instead, the cross section for the p-p reaction must be calculated from standard weak-interaction theory.

And indeed I didn't manage to find experimental values for p-p in any paper. I didn't try to make it from the analytical expression presented in the paper.