# Rate of nuclear fusion

1. Feb 21, 2016

### 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).

2. Feb 21, 2016

### Staff: Mentor

3. Feb 21, 2016

### Nivek Writer

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?

4. Feb 21, 2016

### Staff: Mentor

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.

5. Feb 21, 2016

### Nivek Writer

Thanks for the explanation. I understand it now.

6. Feb 22, 2016

### Nivek Writer

Is there a formula or a website where you can find the number density of plasma?

7. Feb 22, 2016

### Staff: Mentor

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