# What is the key parameter in fusion: momentum or energy?

• A
The released products of a transmutation reaction (I say transmutation when 2 particles reacts to generate more than one) follows the conservation of kinetic energy law. Also particles moving in opposite direction can have equal speed one with respect the other than rather if one of them is static.
In other ways almost all the fusion cross section data are taken using a static target.

(In other way when a charge that goes again a nucleous it follows integral of E*q/r^2 with respect distance that is F*x that is energy, but that is true for large distance due short range forces are not present)

It is possible that the cross section horizontal axe should be the kinetic momentum instead of energy?
It is useful as long as accordingly kinetic momentum is better to accelerate both particles one again other due less energy is involved.

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mfb
Mentor
It doesn't matter which reference frame you use, and kinetic energy and momentum have a fixed relation for given particle types.
In the lab frame you reach the same center of mass energy with less energy if you accelerate both particles, but that can be less practical (you can't accelerate a solid target that fast, and collider schemes have much lower luminosity than fixed target experiments).

I do not agree at all, E=.5*m*v^2 of one particle needs a lot more energy for the same approaching speeds than accelerate one again other.
As example if both particles have the same weight E1=.5*m*v1^2 with one of them fixed
And if both cames in opposite direction at v1/2 we have: E2=m*v1^2/4, that is a half of the energy E1
The problem as you said is that the "collider" system is a lot more difficult to achieve.
If there is a bigger difference between a particle and the other the advantage is less

mfb
Mentor
I do not agree at all, E=.5*m*v^2 of one particle needs a lot more energy for the same approaching speeds than accelerate one again other.
A factor 2 for symmetric reactions. Yes. So what?

A car crash test needs less energy if you make the wall move as well. That doesn't mean it would be useful to do so, moving the wall adds so much overhead to the test that it becomes much more expensive, and you probably don't even save energy in the end due to all this overhead.