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The PP Hydrogen Fusion Simulator

The PP hydrogen fusion simulator evolves a gas of hydrogen and helium over one-trillion years. This simulator illustrates how the processes of the proton-proton (PP) fusion chains change the composition of a gas and generate the power dumped into the core of a main-sequence star. As discussed in an earlier page of the “Stars” path, the PP processes are the processes that convert hydrogen into helium-4 in present-day main-sequence stars that are the size of the Sun or smaller, and they are the only hydrogen fusion processes at work in the first stars created in our universe, when the universe consisted of little more than hydrogen and helium.

The simulator only follows the binary fusion processes. Decay processes, such as the decay of boron-8 into beryllium-8, occur on a time scale much shorter than time scales for the binary fusion reactions, such as the fusion of beryllium-7 with hydrogen to produce boron-8. Recapping the binary fusion processes, with the decay processes made implicit, of the PP fusion chains, hydrogen is converted into deuterium, and then into helium-3. Along the PP 1 chain, the helium-3 interacts with other helium-3 to directly create helium-4. On the PP 2 and PP 3 chains, the helium-3 interacts with helium-4 to create beryllium-7. Along the PP 2 chain, the beryllium-7 combines with electrons to form lithium-7, which combines with a proton to form helium-4. Along the PP 3 chain, the beryllium-7 combines with a proton to produce helium-4.

The simulator evolves a gas of hydrogen and helium-4 until all of the hydrogen is consumed through the PP process. This is simulated for a constant temperature and a constant nucleon (proton and neutron) density. The simulator calculates the gas composition, the total power, the power in neutrinos, and the relative contribution of the PP 1, PP 2, and PP 3 chains, plus the loss of helium-4 through the creation of Be7, as functions of time. These results are displayed in three plots. The plot of composition shows the fraction of nucleons in each isotope. The plot of the relative contribution of each process to the creation of helium-4 is normalized so that all processes that create hydrogen sum to unity; the loss of hydrogen through the creation of beryllium-7 is normalized to the sum of the helium-4 creation rates.

The results from the simulator are discussed on a separate page, so that the reader may place the page in a separate window or tab. The link to this page opens the page into the current window, so the reader must take special action to place the page in a new window. Go to the results page.

Simulator Notes

Parameters

The initial hydrogen and helium-4 composition of the gas can be set by the reader. Other isotopes from the PP processes are set to 10-20 times the nucleon density.

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.

Usage

The reader can change three variables in the simulator. The temperature can be change using the slider on the simulator. Valid temperatures are between 5 and 50 million degrees. The initial hydrogen and helium-4 composition of the gas can be changed. The values are expressed as “nucleon parts,” by which I mean the fraction of protons and neutrons tied up in helium versus the number of free protons. The values placed in these slots must be between 10-7 and 1. At this time, the simulator does not understand exponential notation, so the values must be entered in decimal notation. The fraction of nucleons in each constituent is determined by dividing each value by the sum of the two values, so values of 0.8 and 0.2 for hydrogen and helium nucleon parts give the same composition as 0.4 and 0.1 for these values.

The simulator is run by pressing the “Burn” button. Once a simulation has run, this button is disabled until at least one variable is modified.

The button marked “Reset” sets the values of the simulation to their default values of 15 million degrees for the temperature and 0.8 and 0.2 for the nucleon parts of hydrogen and helium.

The reader can choose the plot with the radio buttons on the left side of the simulator. The “Composition” button shows a plot of the nucleon fraction of each isotope. The “Power” button shows a plot of the total power and the power in neutrinos. The “Processes” button shows a plot of each process's contribution to the creation of helium-4.

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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