I know that nuclear fusion reactions takes place in the core of the Sun
where the temperature and density are highest. But why are high
temperatures and high density needed?
Most of our work on Earth, in plasma physics labs, shows that you can't
just have fusion reactions in ordinary physical conditions. You need
temperatures of at least 10 million degrees to start, and you need to
confine your plasma magnetically (to ensure it won't disperse or diffuse).
Right now, the most we can achieve here on Earth ( e.g. in Tokamaks), is a few
One of the inherent physics problems is that atomic nuclei have enormous
energy barriers that must be overcome to allow fusion.
Think of it. You are trying to fuse together, at the most basic initial
level, two protons (hydrogen nuclei) with the SAME electric charge (+). A
powerful Coulomb barrier exists that makes it extremely difficult. (Recall,
unlike charges attract, like charges repel from Gen. Science).
This sort of combining simply can't be accomplished in low density
conditions. You need billions and billions of protons packed into a small
confined volume to:
a) ensure that the protons come close enough to permit what we call
quantum tunneling - through the Coulomb potential barrier, which I have
with the "barrier" at height V, so we can visualize the particle of lesser energy
K, moving from the left side of the E-axis "tunneling" through to the right side
where it may have wave function, U(x) ~sin (kx + φ), where φ denotes a phase angle
b) ensure the high temperatures (via kinetic energy proton collisions) to
sustain nuclear reactions.
In respect of (a) researcher Martin Schwarzschild once calculated that the
probability of the Coulomb potential barrier being overcome (by
tunneling) is about 1 in 10 to the 57 power. That's one in 10 followed by
In temporal terms, we'd expect about one proton-proton fusion ever 14
billion years (or more than the age of the universe) on this basis.
Clearly, an offset is required to reduce the probabilities, since clearly
stars are shining by fusion.
This 'offset' arrives via enormously high density which: i) increases the
probability for (a) enormously, since so many more protons are in
extremely close proximity, and ii) enhances temperatures to the point they
can be sustained, and continue - thereby building up *other* fusion
reactions to finish the initial one.
In the Sun, for example, this leads to the most basic set of three fusion
reactions for the proton-proton cycle, viz.
1H + 1H + e- ® 2 H + n + 1.44 MeV
2 D + 1H ® 3 He + g + 5.49 MeV
3 He + 3 He ® 4 He + 1H + 1H + 12.85 MeV
These reactions are illustrated in the graphic below:
In the first, H1 denotes the proton (hydrogen nucleus), e is an electron,
D2 is deuterium - an isotope of hydrogen- and n is the neutrino, and
1.44 MeV of energy given off.
This leads to the next reaction, with deuterium fusing with a proton to
yield the isotope helium 3, a gamma ray and 5.49 MeV energy given off.
Finally, this leads to the end stage reaction, with the helium 3 combining
with another helium 3 nucleus to give helium 4, two more protons (to start
the cycle anew) and energy given off.
Thus we see the key is not merely getting a fusion reaction, but
sustaining it. We need to sustain it so a particular energy cycle can be
completed, in the case above - the fusion of 4 protons effectively
yielding helium, with the differential in mass coming off as radiant
energy. (In an amount defined by Einstein's famous, E = m c2 )
high temperatures and density in the core - which initiated the reactions.