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The Helium Fusion Simulator

The next thermonuclear fusion stage following the fusion of hydrogen into helium in the core of a star is the fusion of helium into carbon. This process is known as the triple-alpha process, because it converts three helium-4 nuclei (α particles) into a single carbon-12 nucleus. This process operates efficiently above 100 million degrees Kelvin; its strong temperature-dependence means that it can convert all the helium within the core of a star into carbon and heavier elements in less than a year for temperatures above 200 million degrees Kelvin.

At the temperatures where the triple-alpha process is effective, other fusion processes efficiently combine helium-4 with carbon-12 into heavier elements. The principal processes step through the sequence of nuclei that are multiples of the He4 nucleus: C12→O16 → Ne20 →Mg24 → Si28 → S32 → Ar36.

Two secondary fusion chains occur if hydrogen, carbon-13, or nitrogen-14 is present in the gas. One normally expects the last-two elements to be present if the star underwent the CNO hydrogen-burning process. One process combines C13 and He4 to give O16 and a neutron, which can decay into a proton and an electron. The second combines N14 with He4 to give O18 and a positron. The oxygen-18 undergoes fusion with helium-4 to produce neon-21 and neon-22, with the production of neon-21 accompanied by the production of a neutron. These processes produce hydrogen, which is burned to helium-4 through the CNO processs.

The helium fusion simulator on this page shows the change in composition of a gas experiencing the nuclear fusion of helium-4. The default initial composition is pure helium-4, although this can be modified by the reader. The simulation follows the nuclear fusion until all of the helium-4 is consumed. While many more elements than those shown on the composition plot are generated during the fusion of helium-4 fusion, only those elements with nucleon fractions above the lower bound of the plot are displayed. The power generated by the various fusion processes and the total power generated through nuclear fusion are presented in the power plot.

The end products depend on the temperature of the gas. For the highest temperatures allowed by the simulator, the end product of fusion is primarily carbon-12, but for the lowest temperatures allowed in the simulation, it is primarily oxygen-16.

Simulator Notes

Parameters

The simulator follows the evolution of 21 isotopes, but only five of these can have the initial values of their nucleon part set by the reader: hydrogen, helium-4, carbon-12, nitrogen-14, and oxygen-16. The remaining isotopes have their initial nucleon fractions set to 10-15.

The nucleon density is defined to be the total number of protons and neutrons per unit volume. For instance, the contribution of helium-4 to the nucleon density is 4 times the number of helium nuclei per unit volume. Nucleon density is used because the number of nucleons in conserved in a fusion reaction. The the simulation the total nucleon density is fixed at 105 g-mole (an Avogadro's number of 6.022169×1023 nucleons) per cubic centimeter.

The initial composition is expressed as nucleon parts, meaning a ratio relative to the other nucleons. For instance, in the table of initial composition, if the hydrogen and helium nucleon parts were 0.8 and 0.2, then for every 8 nucleons that are in hydrogen nuclei, there would 2 that are in helium nuclei.

The temperature is given in units of tens of millions of degrees Kelvin, and can be set from 100 million degrees to 350 million degrees.

Usage

The simulator comes up unexecuted and with a default value for the temperature. The temperature of the gas can be set by the reader with the slider.

The simulation is executed by pressing the “Burn” button. Once executed, this button is disabled until a new temperature is given.

If the reader changes the temperature from its initial values, the “Reset” button is enabled. This button sets the temperature back to its default values. The default value for the temperature is 120 million degrees Kelvin. The default value for the composition is pure helium-4.

The plot gives the composition of the gas as the fraction of all nucleons (protons and neutrons) that are contained in each nucleus. This will be close to the mass fraction in each nucleus; the difference is that the density of nucleons in the gas is constant with time, while the mass density of the gas falls slightly with time as the rest-mass energy of the nuclei is converted into thermal energy. The values are limited to between 10-7 and 1.

The keyboard navigation of the simulator's controls is described in the Applet Usage Guide.

I would appreciate hearing from you if you encounter an error while running the simulator or if you have suggestions for improvement. Send your e-mail to the editor of the website.

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