Can this fusion cycle work in practice?

[Casian]

Hello
I would like to ask here because I couldn't find an answer anywhere on the internet. I recently noticed that two fusion equations have a very good reciprocal cycle, namely the equation: 1H + 2H = 3He, and the equation 3He + 2H = 4He + 1H. I understand that it may have practical limitations, each of the reactions has a different temperature of maximum efficiency and in terms of fuel they would be mostly deuterium which would lead to unwanted mutual fusion of D + D, even so I think it is definitely interesting. Additionally, one such cycle would produce 23.8 MeV which is close to one P + P cycle in the sun. So what is your opinion on it? (I also attach my own graphic for understanding)

 

[mfb]

The first reaction is far less common than D+D at all temperatures with relevant fusion rates (should be something like 6-8 orders of magnitude difference). You basically build a deuterium fusion reactor that has some unreactive protons mixed in. And that's another 1-2 orders of magnitude worse than deuterium-tritium.

 

[snorkack]

The first reaction is far less common than D+D at all temperatures with relevant fusion rates (should be something like 6-8 orders of magnitude difference).

The first reaction is also the prevalent fate of D in the world. But then the problem is keeping both the steps the main branch.

You basically build a deuterium fusion reactor that has some unreactive protons mixed in. And that's another 1-2 orders of magnitude worse than deuterium-tritium.

From
https://en.wikipedia.org/wiki/Deuterium_fusion
the reaction
1) d+p=³He+γ
is the prevalent fate of d not only in Sun (where d concentration is kept low by the rapidity of reaction 1) - lifetime quoted as 1 s!), but also in brown dwarfs (that start with primordial d concentration). Since the primordial d/p ratio is just 4,6 magnitudes, it should not be a 6-8 magnitudes difference of cross-section?
Other d reactions include
2) d+d=³He+n
3) d+d=t+p
these require high d concentrations to compete with 1)
4) d+t=α+n
this requires availability of t
5) d+³He=α+p
this of course requires availability of ³He. What kind of ³He concentrations would have it as the major fate of ³He?
Also, I understand that the temperature dependence of thermonuclear reactions depends on Coulomb barrier. Which is proportional to (z₁z₂/r). All the reactions 1) to 4) have the same z₁z₂ (1), though r may differ. Reaction 5) has the bigger z₁z₂ (2).

 

[mfb]

The first reaction is also the prevalent fate of D in the world.

Yes, in stars that don't have enough deuterium to make D-D fusion relevant, and where the power density only matches a compost heap. Fusion reactors don't have the same conditions.

Since the primordial d/p ratio is just 4,6 magnitudes, it should not be a 6-8 magnitudes difference of cross-section?

The cross section has nothing to do with the concentration.

D-D fusion ends up with a neutron directly or indirectly, which produces another deuterium nucleus in a star (but not in a fusion reactor), so stars are doing p-D fusion with extra steps.