E.5.1 Nuclear fusion in stars

Nuclear Fusion: The Power Behind Stars

1. Imagine standing outside on a warm, sunny day.
2. The sunlight you feel on your skin has traveled millions of kilometers from the Sun, powered by a process that has been ongoing for billions of years: nuclear fusion.
3. This process not only fuels stars but is also responsible for the creation of many elements in the universe.

Deuterium-Tritium Fusion

1. Consider the fusion of deuterium (${}^2\text{H}$) and tritium (${}^3\text{H}$): $${}^2\text{H}{+}^3\text{H}{\to }^4\text{He}{+}^1\text{n}$$
2. In this reaction, a helium nucleus (${}^4\text{He}$) and a neutron (${}^1\text{n}$) are produced.
3. The mass of the reactants is slightly greater than the mass of the products, and this mass difference ($\mathrm{\Delta }m$) is converted into energy: $$Q=\mathrm{\Delta }m{c}^2$$
4. For this reaction, the energy released is approximately 17.6 MeV (million electron volts) per fusion event—an immense amount of energy at the atomic scale.

Conditions for Fusion to Occur

Fusion requires extreme conditions to overcome the Coulomb repulsion between positively charged nuclei. Let’s break down the three key conditions:

1. High Temperature

At high temperatures (millions of kelvin), nuclei move at very high speeds.

$⟹$ This increases the likelihood that they will collide with enough energy to overcome the repulsive electrostatic force between them.

2. High Density

A high density of nuclei ensures that there are enough collisions happening per second to sustain a chain of fusion reactions.

3. Confinement Time

The conditions of high temperature and density must be maintained for a sufficiently long time to allow significant fusion to occur.

4. High Pressure

• High pressure plays a crucial role in fusion by forcing nuclei closer together, increasing the probability of collisions.
• In stars, gravitational pressure compresses the plasma, ensuring a high density of nuclei and sustaining fusion reactions.

5. Quantum Tunneling

• Even at extreme temperatures, classical physics suggests that most nuclei do not have enough energy to overcome the Coulomb barrier.
• However, due to quantum mechanics, there is a small probability that nuclei can "tunnel" through the energy barrier instead of going over it.

This effect allows fusion to occur at lower energies than expected and is essential for sustaining fusion reactions in stars.

Why Does Fusion Release Energy?

The energy released in fusion comes from the binding energy of atomic nuclei.

1. Heavier nuclei like helium have a higher binding energy per nucleon than lighter nuclei like hydrogen.
2. When light nuclei fuse to form a heavier nucleus, the total binding energy increases, and the excess energy is released.

Fusion in Stars: The Energy Source of the Universe

1. Stars are nature’s perfect fusion reactors.
2. In their cores, immense gravitational pressure creates the high temperatures and densities needed for fusion.
3. Let’s examine how this works:

The Proton-Proton Chain

• In stars like our Sun, the dominant fusion process is the proton-proton chain, which converts hydrogen nuclei (${}^1\text{H}$) into helium (${}^4\text{He}$):
  1. ${}^1\text{H}{+}^1\text{H}{\to }^2\text{H}+e^{+}+{\nu }_e$
  2. ${}^2\text{H}{+}^1\text{H}{\to }^3\text{He}+\gamma$
  3. ${}^3\text{He}{+}^3\text{He}{\to }^4\text{He}+2^1\text{H}$
• The net result is the fusion of four hydrogen nuclei into one helium nucleus, releasing energy in the form of photons, positrons, and neutrinos.

Reflection

While stars achieve fusion naturally, replicating this process on Earth is challenging. The main obstacles include achieving and maintaining the required high temperatures and densities, containing the hot plasma, and sustaining the reaction long enough to produce more energy than consumed.