Nuclear Fusion Rate: Calculating Reaction Speed & Energy

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Discussion Overview

The discussion revolves around calculating the rate of nuclear fusion reactions, specifically focusing on Deuterium-Tritium fusion. Participants explore how temperature and particle density influence the fusion rate, seeking formulas and examples for practical calculations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant inquires about the formula for calculating the fusion reaction rate and its dependence on temperature, specifically at 100 million Kelvin.
  • Another participant notes that the fusion rate is influenced by both temperature and pressure (or particle density), suggesting that Wikipedia contains relevant details.
  • A participant requests an example calculation to better understand the formula, indicating uncertainty about its application.
  • One participant provides a hypothetical calculation using assumed densities of Deuterium and Tritium, yielding a reactivity rate and discussing the implications for reactor viability.
  • A later reply asks for resources or formulas to find the number density of plasma, indicating a need for further research.

Areas of Agreement / Disagreement

Participants generally agree on the factors affecting fusion rate, but there is no consensus on the specific formulas or calculations, as some express uncertainty and seek clarification.

Contextual Notes

Limitations include the reliance on assumed plasma density values and the lack of a definitive formula presented in the discussion. Some participants express uncertainty about their understanding of the calculations involved.

Who May Find This Useful

High school students and individuals interested in nuclear fusion research, particularly those looking for foundational understanding and practical calculation examples.

Nivek Writer
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Hello everyone,

I have a question about nuclear fusion.
Deuterium-Tritium fusion generates 3.4 * 1014 J/kg when you have a
mixture of around 400 grams of deuterium and 600 grams of tritium.
My question is: what is the rate at which this fusion reaction takes place?
Is there a formula for the fusion rate and what is the reaction speed at, for example, 100 million Kelvin?
I am in high school and I am doing research on nuclear fusion. I was able to calculate the amount of energy released per kg, but I don't know how to calculate the rate at which this reaction takes place depending on the temperature (in kg per m^3 per second).
 
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mfb said:
There are calculations, sure. Fusion rate depends on both temperature and pressure (or particle density).
Wikipedia, as usual, has details.
I have read the Wikipedia page, but I don't know for sure if I fully understand how the formula works.
Could you please give an example of a calculation?
 
If you know densities and temperature, you can just plug in numbers.
Let's say we have 1015/m3 D and 1015/m3 T at a temperature of 100 million K. The reactivity rate, from the plot, is about 10-22 m3/s.
Multiply everything together, and you get 1015/m3 * 1015/m3 * 10-22 m3/s = 108/(m3*s) reactions. Not enough for a reactor, but I just made up those plasma density numbers.
 
mfb said:
If you know densities and temperature, you can just plug in numbers.
Let's say we have 1015/m3 D and 1015/m3 T at a temperature of 100 million K. The reactivity rate, from the plot, is about 10-22 m3/s.
Multiply everything together, and you get 1015/m3 * 1015/m3 * 10-22 m3/s = 108/(m3*s) reactions. Not enough for a reactor, but I just made up those plasma density numbers.

Thanks for the explanation. I understand it now.
 
mfb said:
If you know densities and temperature, you can just plug in numbers.
Let's say we have 1015/m3 D and 1015/m3 T at a temperature of 100 million K. The reactivity rate, from the plot, is about 10-22 m3/s.
Multiply everything together, and you get 1015/m3 * 1015/m3 * 10-22 m3/s = 108/(m3*s) reactions. Not enough for a reactor, but I just made up those plasma density numbers.

Is there a formula or a website where you can find the number density of plasma?
 
You can check the websites, publications and other pages of/about various reactors. You are supposed to do the research.
 

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