Nuclear Fusion Rate: Calculating Reaction Speed & Energy

[Nivek Writer]

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).

 

[mfb]

There are calculations, sure. Fusion rate depends on both temperature and pressure (or particle density).
Wikipedia, as usual, has details.

 

[Nivek Writer]

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?

 

[mfb]

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.

 

[Nivek Writer]

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.

 

[Nivek Writer]

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?

 

[mfb]

You can check the websites, publications and other pages of/about various reactors. You are supposed to do the research.