The Astrophysics Spectator



Interactive Pages


Other Pages



The Hydrogen Fusion Simulator

This simulator calculates the evolution of a gas subject to the thermonuclear fusion of hydrogen. The gas is composed initially of hydrogen, helium-4, carbon-12, nitrogen-14, and oxygen-16, and the thermonuclear fusion processes of the proton-proton (PP) chains and the carbon-nitrogen-oxygen (CNO) cycles convert the hydrogen into helium-4. This simulator shows the evolution of seven isotopes: hydrogen, helium-3, helium-4, carbon-12, carbon-13, nitrogen-14, and oxygen-16. While the evolution of the remaining isotopes in the PP and CNO processes are calculated within the simulator, they are not displayed in the plot of results, because they are present in such small quantities.

Two other simulators on the “Stars” survey path allow the reader to study the PP fusion processes and the CNO hydrogen fusion processes as independent sets of processes. The simulator on this page shows the effect of temperature on the relative contribution of the CNO cycles and the PP chains to the generation of energy and helium-4. The simulator also demonstrates that the CNO cycle is important in converting carbon-12 and oxygen-16 into nitrogen-14 even in small stars.

The Sun has a core temperature of about 15 million degrees Kelvin, which is the default temperature of the simulator. The abundances in the Sun of carbon, nitrogen, and oxygen by nucleon fraction relative to hydrogen are 0.0043, 0.0016, and 0.014. Helium is much more abundant, with a nucleon fraction relative to hydrogen of 0.39. These values translate to the nucleon fractions given as the default values in the nucleon part table.

Notes on the results found with the simulator are collected on a second page. This is so that the reader can pull this results page into a second window or a tabbed pane (for those using FireFox). The link pulls the new page into the current window unless it is explicitly sent to a new window by the reader. Go to notes on simulator results.

Simulator Notes


The simulator follows the evolution of 12 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. Of the remaining isotopes, the isotopes deuterium, helium-3, beryllium-7, and lithium-7 have their initial nucleon fractions set to 10-20, and the isotopes carbon-13, nitrogen-15, and oxygen-17 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 total nucleon density is fixed at one 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, hydrogen and helium nucleon parts of 0.8 and 0.2 means that for every 8 nucleons that are in hydrogen nuclei, there are 2 that are in helium nuclei.

The temperature is given in units of millions of degrees Kelvin, and can be set from 5 million degrees to 50 million degrees.


The simulator comes up unexecuted and with a set of default values for the temperature and the nucleon parts. The temperature of the gas can be set by the reader with the slider. The nucleon parts can be changed by the reader by double-clicking with the mouse in the relevant table box. The nucleon part value must be between 1 and 10-7. The table does not accept exponential notation at this time; this shortcoming will be repaired in a future release.

The simulation is executed by pressing the “Burn” button. Once executed, this button is disabled until new initial values are set.

If the reader changes any parameters from their initial values, the “Reset” button is enabled. This button sets values back to their default values. The default value for the temperature is 15 million degrees Kelvin.

The three radio buttons to the left of the simulator allow the reader to choose among the three plots that give results of the simulation. The “Composition” plot gives the nucleon fraction; the sum of nucleon fraction over all twelve isotopes within the simulator equals 1; because the nucleon fraction for only seven of these isotopes is plotted, the sum of nucleon fraction over the plotted lines is slightly less than unity. The “Power” plot shows the total power released in the nuclear reactions and the power carried by neutrinos. The “Processes” plot shows the relative contribution to the creation of helium-4 of the PP 1 chain, PP 2 chain, PP 3 chain, CNO 1 cycle, and CNO 2 cycle; the sum of these values is normalized to 1. The rate of destruction of helium-4 through the creation of beryllium-7, which is listed as “PP 23 Loss,“ is normalized by the sum of the creation processes.

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.

Ad image for The Astrophysics Spectator.