UKC

Tried to find answers to this online but I can't find anything convincing.

Why is tritium - tritium fusion not preferrable to deuterium - tritium fusion?
Intuitively I would assume that the greater average mass:charge ratio of the particles would make it energetically easier to achieve. It should also result in a faster reaction because every collision in the plasma would have the potential to result in fusion (as opposed to a deuterium - tritium situation where only half the collisions could possibly result in deuterium - tritium fusion).

It clearly doesn't work better than deuterium - tritium in practice. Can anyone explain why?

In reply to henwardian:

The simple answer is the maximum possible reaction rate for the T-T reaction is about 25x lower than the D-T reaction. See this graph which shows the reaction rates for various types of fusion reaction versus the temperature of the system (measured in keV):

http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_4b.html

This means that it is more difficult to achieve a self-sustaining T-T fusion against the energy losses from the plasma, especially when you take into account that each T-T fusion releases less energy than each D-T fusion (the ratio of energy released is about 60%).

But you also ask why the T-T reaction rate is slower than the D-T rate. This is a difficult question and one I couldn't find a perfect answer for. To answer it you need to delve into the theory for fusion reaction rates.

For the linked reaction rates graph, the curves can be approximated by the third formula (<sigma v> = 0.8052...) in the section on 'Fusion reaction rates' on this page:

http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_4.html

The most important term in the equation to answer the question is A, and then to a lesser extent R. A is 56 times larger for the D-T reaction, hence it contributes a factor of 56 to the difference in D-T and T-T reaction rates.

A is part of something known as the astronomical S-factor, which describes all the nuclear physics of the fusion reaction. It describes the quantum physics of the nuclear binding under the strong force, and the probability that D-T or T-T nuclei fuse if they come into contact inside the Coulomb barrier.

It looks like the S-factor is something that physicists don't have a complete theory for, and hence A is measured by experiment rather than predicted using an equation in fundamental physical constants. Thus the best answer we may have is that D-T fusion is more preferable than T-T fusion just because it is.

R is the square root of something called the Gamow energy, which describes the probability of the two nuclei quantum tunnelling through the Coulomb barrier. R is similar for the D-T and T-T reactions, but the fact its in an exponential leads to a factor 1 to 5 in favour of D-T fusion reaction rate than T-T fusion.

R is related to the number of protons in each of the fusing nuclei, and the reduced mass of the nuclei. The consequence of R is the probability of tunnelling decreases rapidly as the atomic number and mass increase, and is one reason why only the lightest nuclei are real fusion candidates.

m in the equation (the reduced mass) in this case is equivalent to the mass charge ratio that you asked about. You're right, it does favour the T-T reaction over the D-T reaction, by about 10%. This is nowhere near enough to offset the differences caused by A and R however.

I didn't understand your point about why D-T fusions are 50% less probable than T-T fusions - can you elaborate?

As it happens there are some fusion scientists working down the corridor from me, so I'll ask them to explain the astronomical S factor.

In reply to henwardian:

Ahh sorry I get your point now about D-T collision only being 50% of the collisions in a D-T plasma, versus 100% T-T collisions in a T-T plasma. That must come in somewhere, but again it's only a factor of 2 so won't change the story.

I'll have a think about where it fits in.

In reply to camalins:

Ok, so <sigma v> is not the reaction rate but something called the averaged reactivity. It needs to be multiplied by the factor n_i n_j / (1+delta_ij) to give the actual reaction rate, i.e. number of i-j fusions per unit volume per second.

The factor results in twice the reaction rate for T-T fusions in a purely tritium plasma than for D-T fusions in a mixed 50/50 D-T plasma. That's assuming the same plasma density, temperature, etc...

So again, your two reasons for thinking T-T fusion should be easier than D-T fusion are correct. However the driving force behind the actual difference in reality, such that D-T is massively more favourable, is the astrophysical S factor.

I'll ask an expert about this perhaps poorly-understood quantity.

In reply to camalins:


Ha!

In reply to Removed UserBwox:

Ok, point well made.

In reply to camalins:


Ah, that is interesting. I remember learning about electron tunneling and rapidly relegating it to mental area reserved for "things I need to regurgitate in an exam but seem far to complicated to properly assimilate". Had not heard about tunneling (aka cheating!) in larger particles.
I can get on board with a theory of tunneling decreasing with size so this makes sense to me.


That would be good to hear. I know very little about the strong force to begin with though.
In a standard chemical reaction the reactants often need to approach at just the right angle to form an activated complex before the reaction can proceed. Is the S factor a sort of similar correction for a nuclear reaction? - where a wider variety of orientations of the colliding nuclei will result in a reaction with D-T than with T-T.
If so, I would intuitively assume that it would be much harder to calculate than measure empirically.

Your second link is a bit too advanced for me. I think I would need to do some background learning before I can understand it properly.

In reply to henwardian:

I think you should read this:

http://rationalwiki.org/wiki/Fusion_woo