# Lawson Parameter for Sustained Deuterium-Deuterium Fusion

1. Mar 19, 2013

### accidentprone

1. The problem statement, all variables and given/known data

Calculate the minimum Lawson parameter for sustained deuterium-deuterium fusion in a plasma with an energy of 10 keV.

2. Relevant equations

The Lawson parameter is given as $$n \tau > \frac{12 k T}{<\sigma v> Q}$$

where $\sigma$ is the fusion cross-section.

3. The attempt at a solution

I think that Q for d-d reaction is 4 MeV when a proton is produced and 3.3 MeV when a neutron is produced so I assume for the minimum Lawson parameter I should use the larger value of 4 MeV?

Also if the energy of the plasma is 10 MeV should I use this to calculate the temperature of the reaction $T$ using $\frac{3}{2} k T$ or somehow the velocity $v$ using $\frac{1}{2} m v^2$?

Last edited: Mar 19, 2013