Nuclear Fusion Rate: Calculating Reaction Speed & Energy

In summary, the conversation revolves around a question about the rate of nuclear fusion in a deuterium-tritium mixture. The experts explain that the fusion rate depends on temperature and pressure, and there are calculations and formulas available to determine it. They also mention that Wikipedia has more information on this topic. The conversation ends with a suggestion to check various websites and publications for the number density of plasma.
  • #1
Nivek Writer
7
0
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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  • #3
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?
 
  • #4
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
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.
 
  • #6
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?
 
  • #7
You can check the websites, publications and other pages of/about various reactors. You are supposed to do the research.
 

FAQ: Nuclear Fusion Rate: Calculating Reaction Speed & Energy

What is nuclear fusion rate?

Nuclear fusion rate is the measure of how fast nuclear fusion reactions occur in a given amount of time. It is typically measured in reactions per second.

How is nuclear fusion rate calculated?

Nuclear fusion rate is calculated by multiplying the number of reactants by the reaction speed. The reaction speed is determined by factors such as temperature, pressure, and the types of nuclei involved in the fusion reaction.

What factors affect nuclear fusion rate?

The factors that affect nuclear fusion rate include temperature, pressure, the types of nuclei involved in the reaction, and the presence of any catalysts or inhibitors.

How does nuclear fusion rate impact energy production?

Nuclear fusion rate directly impacts energy production, as it determines the amount of energy that can be generated by nuclear fusion reactions. A higher fusion rate means more energy can be produced in a given amount of time.

What challenges are involved in accurately calculating nuclear fusion rate?

Accurately calculating nuclear fusion rate can be challenging due to the complex nature of the reactions involved. Factors such as temperature and pressure can vary greatly in a fusion reactor, making it difficult to predict and control the rate of fusion reactions. Additionally, the behavior of plasma, which is the state of matter in which fusion reactions occur, can be unpredictable and difficult to model accurately.

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