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The CNO Hydrogen Fusion Simulator

The CNO fusion simulator shows the binary fusion processes of the CNO cycles. The simulator gives insight into two important questions: At what rate does nuclear fusion occur in the CNO cycle, and what is the equilibrium density of nitrogen-14 relative to carbon-12 and oxygen-16?

The CNO reactions form a pair of coupled cycles. The first cycle, generally referred to as CNO 1, transmutes carbon-12 through the sequence C12→C13→N14→N15→C12; the second cycle, CNO 2, transmutes nitrogen-15 through the sequence N14→N15→O16→O17→N14. The two cycles are joined by the nitrogen-15 stage.

The simulator follows the nuclear fusion of hydrogen into helium-4 in a gas composed of hydrogen, helium, and isotopes of carbon, nitrogen, and oxygen under the condition that both the temperature and the nucleon density of the gas are constant. The only fusion processes occurring in this simulation are those of the CNO cycles. The simulator calculates the gas composition, the total power, the power in neutrinos, and the relative contribution of the CNO 1 and CNO 2 cycles in producing helium-4 as functions of time. These results are displayed in three plots. The “Composition” plot gives the nucleon fraction for all isotopes. The “Power” plot gives the total power generated in the fusion cycles and the power carried away by neutrinos. The “Processes” plot gives the relative contribution of the CNO 1 and CNO 2 processes to the production of helium-4.

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 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


While there are eight isotopes followed in the simulation, only five can have their initial contribution to the composition of the gas set by the reader: hydrogen, helium-4, carbon-12, nitrogen-14, and oxygen-16; the remaining elements each initially constitute 10-7 of the nucleon density of the gas.

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 given.

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 25 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 over all eight isotopes of their nucleon fraction values equals 1. 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 CNO 1 and CNO 2 cycles; the sum of these values is normalized to 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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