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Board game contains BP spill scenario

Tar balls found on Lake Pontchar…2:01


Added On July 6, 2010
Parts of the lake, near New Orleans, are now off-limits for fishing. CNN’s Brooke Baldwin reports.



Added On July 6, 2010

CNN’s Randi Kaye tracks the movement of the Gulf oil spill and the areas that it has affected.



If every one of us in America – and even around the world – send a note with a dollar that says, “I am an American (or whatever) and I want to see this produced – here is what I can do to help.” to each of these two guys below – the one who used his own money to work on nuclear fusion and the one who has created the air lithium battery and JTEC engine – then we wouldn’t have to put up with oil companies owning everybody and wouldn’t have to watch some big companies take over these inventions and shelve them. We could all send even a dollar each to them and if millions of us did that – these things could go into production whether investors, or bankers or anybody else decided to get off the dime or not.

Wouldn’t it be about time that we decided that these things to benefit all of us – go forward, instead of leaving it to somebody else who doesn’t care about us and our future at all? I’m going to do it and I will see what can be done to encourage everyone to do it. A million one dollars or thirty million one dollars would take care of what these brave inventors need to put their inventions into production so we can all benefit from them. Let’s do it. Why not? Somebody has to get on with it and it might as well start right now, right here.

I’m going to figure out where they are and send them a dollar each with my little note – I encourage everyone else to do the same and let others know what we are doing and why – so maybe they will send a dollar each to them also. It could be very interesting to see the choices for what goes forward coming from the rest of us rather than Wall Street and corporate players who only want the same old, same old game to our detriment.

We joined together to create airplanes in World War II when it was necessary for our world’s safety and protection. It is time to get going on things that matter by walking around those who are playing by rules that do not serve our greater good.

– cricketdiane, 07-07-10

Homemade Nuclear Fusion –

Added On July 5, 2010

CNN’s Carol Costello talks with an amateur physicist who built a nuclear fusion reactor in a New York warehouse.



Engineer’s life mission3:49


Added On July 6, 2010

An engineer looks to find a way to phase out gas and coal and harness the sun. CNN’s Tony Harris reports.


On bloomberg a few minutes ago, they showed Tony Hayward boarding a plane to leave Abu Dhabi after his twenty-four hour visit which they stated included talks with the Prince in charge of the largest sovereign wealth fund. Damn the board of directors and executives of BP for their business practices – how could anyone be sure of anything loaning money to them or purchasing assets from them when their methods for handling everything is to lie, mislead, deny the facts, alter the facts, distort the facts and play with extremely loose interpretations of reality. If they get an influx of loaned money, how can they be trusted with it? How could anyone believe anything the BP executives, board of directors and representatives of the company might say or any numbers they might produce about anything? They aren’t simply failing to be “forthcoming” with information, because the evidence on a continuing basis is nothing short of lying and working to hide the true facts of any given situation where BP is involved. I know we don’t need businesses that are like that and they are not the only game in town anyway. Let their contracts and leases go to companies that are more decent and honorable in their business practices and more appropriately interested in doing business at the same time providing safe business work environments and protection for the environment and communities surrounding their operations.

– cricketdiane

I have some questions that I want to find answers to understand.

Earlier on CNN and on bloomberg, I had the opportunity to hear President Obama speak today (11.55 am EDT, 07-07-10) about exports and business generally, the establishment of a team to work for a more level playing field in our export opportunities and other matters about creating jobs, stimulating an innovative, educated and inventive environment of research and development support, upgrades to our critical infrastructures and clean energy initiatives today forward. It was very powerful and interesting. Some of it has already been done or the foundations laid for us to go forward and some is yet to do.

But, the questions I have are about the information I have posted above this note about the JTEK engine, the air lithium battery and the fusion set-up in the videos from CNN I found last night.

And, the other questions I have are about the A Whale ship that is being tested in the Gulf of Mexico that is supposed to take millions of gallons of crude oil out of the waters and separate it from the ocean waters. There have been a passing mention in news stories about the ship being created by a businessman in Taiwan who had it modified in Portugal for this purpose from what uses carrying iron ore and coal or something before that. How much is this ship going to cost to put into use? Is that why the Coast Guard and EPA and BP are hesitant about using it in the Gulf of Mexico? It looks more like they are striving to prove it can’t work, doesn’t work, won’t work and to establish enough paperwork to provide reasons to send it away without using it at all to take the oil from the water. I can only guess that many of the decision-makers are still ascribing to the belief that the oil will magically disappear from the Gulf of Mexico by weathering, wave washing, and bacteria eating it. Do they not realize that the quantity of volume, concentration of that volume and the short time in which those concentrated volumes have occurred make that “magical” dissolution of the crude oil very unlikely and that those studies supporting any of those things naturally occurring do not account for these massive quantities, nor the spread of these quantities through vast 3-dimensional fields, nor the concentrations of crude oil in mass quantities of extremely short periods of time nor do they suggest the degree of years required for those natural processes to resolve any of it nor at what cost to the aquatic eco-system within that time.

The other question I want to find answers to understand is about the idea which is demanded of alternative energy systems including fusion – that more energy comes out than goes in – for it to be considered viable. However, the lie that supports and propagates is the concept that any of the energy sources in use now are doing that because they aren’t. More gasoline and crude oil to make gasoline is going into the systems than energy comes out and that in spite of it being an energy dense product. The coal that goes in is simply converted to another energy form we like better to have heat or electricity or steam to power turbines. The hydro-electric systems are also converting one energy form to another with more going in to the system than any of the energy coming from it despite the massive turbines that are being turned and the massive reservoir systems being used to harness that power to convert it from falling or moving water. The demand that any other sources provide something more out than what energy goes into the system is an unreasonable expectation and an unreasonable demand that isn’t even being placed on the more traditional sources in use now.

Also, I noted the other day, that we really don’t need “alternative” energy and “alternative” fuels – we need primary ones that aren’t dependent on the traditional sources. It has been a misnomer to say we are “addicted” to oil. We are fully dependent on oil without reasonable other choices. That is a national security nightmare in progress which undermines national and international security at any of thousands of given points and event horizon potentialities. It has too much place, power and position in our economies across the USA and the world – and it has too much potential to be devastating at any given point for too many of the smallest magnifying reasons. That has to change. We need  new primary energy sources and new primary fuel sources such that petroleum provides the other things it can be used to do from plastics to fertilizers maybe and as a backup possibility rather than our prime energy choice.

So, the question I have is how many other energy choices and fuel choices were abandoned or denied because they were required to meet this demand for more energy to come from it than was put into it when the only real thing it needs to do is convert energy from one form to another one that is needed in as efficient, safe and reliable a manner as possible.

Let’s see what I can find about these questions . . .

– cricketdiane

I still believe we could all send a dollar each to each of those two inventors in the videos listed above about fusion and about the JTEC engine with a note and make that investment in the future being closer to now than any banker could make it. I’m going to do it and email the people I know to encourage them to do it.





Here’s how it works –



Johnson Thermo-Electrochemical Converter System

Until now, thermodynamic engines that use compressible working fluids have generally been mechanical devices. These devices have inherent difficulties in achieving high compression ratios and in achieving the near constant temperature compression and expansion processes needed to approximate Carnot equivalent cycles. Solid-state thermoelectric converters that utilize semiconductor materials have only been able to achieve single digit conversion efficiency. Extensive resources have been applied toward Alkali Metal Thermoelectric Converters (AMTEC), which operate on a modified Rankine cycle and on the Stirling engine. However, because of inherent limitations, these systems have not achieved envisioned performance levels.

The JTEC is an all solid-state engine that operates on the Ericsson cycle. Equivalent to Carnot, the Ericsson cycle offers the maximum theoretical efficiency available from an engine operating between two temperatures. The JTEC system utilizes the electro-chemical potential of hydrogen pressure applied across a proton conductive membrane (PCM). The membrane and a pair of electrodes form a Membrane Electrode Assembly (MEA) similar to those used in fuel cells. On the
high-pressure side of the MEA, hydrogen gas is oxidized resulting in the creation of protons and electrons. The pressure differential forces protons through the membrane causing the electrodes to conduct electrons through an external load. On the low-pressure side, the protons are reduced with the electrons to reform hydrogen gas. This process can also operate in reverse. If current is passed through the MEA a low-pressure gas can be “pumped” to a higher pressure.

The JTEC uses two membrane electrode assembly (MEA) stacks. One stack is coupled to a high temperature heat source and the other to a low temperature heat sink. Hydrogen circulates within the engine between the two MEA stacks via a counter flow regenerative heat exchanger. The engine does not require oxygen or a continuous fuel supply, only heat. Like a gas turbine engine, the low temperature MEA stack is the compressor stage and the high temperature MEA is the power stage. The MEA stacks will be designed for sufficient heat transfer with the heat source and sink to allow near constant temperature expansion and compression processes. This feature coupled with the use of a regenerative counter flow heat exchanger will allow the engine to approximate the Ericsson cycle.

The engine is scaleable and has applications ranging from supplying power for Micro Electro Mechanical Systems (MEMS) to power for large-scale applications such as fixed power plants. The technology is applicable to skid mounted, field generators, land vehicles, air vehicles and spacecraft. The JTEC could utilize heat from fuel combustion, solar, low grade industrial waste heat or waste heat from other power generation systems including fuel cells, internal combustion engines and combustion turbines. As a heat pump, the JTEC system could be used as a drop in replacement for existing HVAC equipment in residential, commercial, or industrial




CNN right now – just 2.49 pm (07-07-10) is showing Aquamarine Power which uses tidal and wave power in a system in Scotland? Wowsa – I thought they’d never get around to saying anything about that – Amazing.
Let’s do that here in the US – I want one. or a thousand of them. or eighty thousand of them. let’s do that.
who is this moron reporter – that is not unsightly – oil rigs are unsightly you moron.


Continuing – later –

Reactor types

NC State‘s PULSTAR Reactor is a 1 MW pool-type research reactor with 4% enriched, pin-type fuel consisting of UO2 pellets in zircaloy cladding.


Nuclear Reactors are classified by several methods; a brief outline of these classification schemes is provided.

Classification by type of nuclear reaction



Let’s Dance



CNN did a web writeup: Man builds web pages by day and nuclear fusion reactors by night.

CNN TV: Nuclear fusion the ‘Holy Grail’ of green energy?

CNN live interview.

My friend Olivia Koski was on this story from the start: Amateur Fusioneer Dreams of Clean Energy.




In 1931 Walther Bothe and Herbert Becker in Germany found that if the very energetic alpha particles emitted from polonium fell on certain light elements, specifically beryllium, boron, or lithium, an unusually penetrating radiation was produced. At first this radiation was thought to be gamma radiation, although it was more penetrating than any gamma rays known, and the details of experimental results were very difficult to interpret on this basis. The next important contribution was reported in 1932 by Irène Joliot-Curie and Frédéric Joliot in Paris. They showed that if this unknown radiation fell on paraffin, or any other hydrogen-containing compound, it ejected protons of very high energy. This was not in itself inconsistent with the assumed gamma ray nature of the new radiation, but detailed quantitative analysis of the data became increasingly difficult to reconcile with such a hypothesis.

In 1932, James Chadwick performed a series of experiments at the University of Manchester, showing that the gamma ray hypothesis was untenable. He suggested that the new radiation consisted of uncharged particles of approximately the mass of the proton, and he performed a series of experiments verifying his suggestion.[4] These uncharged particles were called neutrons, apparently from the Latin root for neutral and the Greek ending -on (by imitation of electron and proton).

The discovery of the neutron explained a puzzle involving the spin of the nitrogen-14 nucleus, which had been experimentally measured to be 1 ħ. It was known that atomic nuclei usually had about half as many positive charges as if they were composed completely of protons, and in existing models this was often explained by proposing that nuclei also contained some “nuclear electrons” to neutralize the excess charge. Thus, nitrogen-14 would be composed of 14 protons and 7 electrons to give it a charge of +7 but a mass of 14 atomic mass units. However, it was also known that both protons and electrons carried an intrinsic spin of 12 ħ, and there was no way to arrange 21 particles in one group, or in groups of 7 and 14, to give a spin of 1 ħ. All possible pairings gave a net spin of 12 ħ. However, when nitrogen-14 was proposed to consist of 3 pairs of protons and neutrons, with an additional unpaired neutron and proton each contributing a spin of 12 ħ in the same direction for a total spin of 1 ħ, the model became viable. Soon, nuclear neutrons were used to naturally explain spin differences in many different nuclides in the same way, and the neutron as a basic structural unit of atomic nuclei was accepted.

Intrinsic properties

Stability and beta decay

The Feynman diagram for beta decay of a neutron into a proton, electron, and electron antineutrino via an intermediate heavy W boson

Under the Standard Model of particle physics, because the neutron consists of three quarks, the only possible decay mode without a change of baryon number is for one of the quarks to change flavour via the weak interaction. The neutron consists of two down quarks with charge −13 e and one up quark with charge +23 e, and the decay of one of the down quarks into a lighter up quark can be achieved by the emission of a W boson. By this means the neutron decays into a proton (which contains one down and two up quarks), an electron, and an electron antineutrino.

Outside the nucleus, free neutrons are unstable and have a mean lifetime of 885.7±0.8 s (about 14 minutes, 46 seconds); therefore the half-life for this process (which differs from the mean lifetime by a factor of ln(2) = 0.693) is 613.9±0.8 s (about 10 minutes, 14 seconds).[2] Free neutrons decay by emission of an electron and an electron antineutrino to become a proton, a process known as beta decay:[5]



Classification by use



In nuclear physics, an energy amplifier is a novel type of nuclear power reactor, a subcritical reactor, in which an energetic particle beam is used to stimulate a reaction, which in turn releases enough energy to power the particle accelerator and leave an energy profit for power generation. The concept has more recently been referred to as an accelerator-driven system (ADS).




The concept is credited to Carlo Rubbia, a Nobel Prize nuclear physicist and former director of Europe’s CERN international nuclear physics lab. He published a proposal for a power reactor based on a proton cyclotron accelerator with a beam energy of 800 MeV to 1 GeV, and a target with thorium as fuel and lead as a coolant.

Principle and feasibility

The energy amplifier uses a synchrotron or other appropriate accelerator (e.g. cyclotron, fixed-field alternating-gradient) to produce a beam of protons. These hit a heavy metal target such as lead, thorium or uranium and produce neutrons through the process of spallation. It might be possible to increase the neutron flux through the use of a neutron amplifier, a thin film of fissile material surrounding the spallation source; the use of neutron amplification in CANDU reactors has been proposed. While CANDU is a critical design, many of the concepts can be applied to a sub-critical system.[1][2] Thorium nuclei absorb neutrons, thus breeding fissile uranium-233, an isotope of uranium which is not found in nature. Moderated neutrons produce U-233 fission, releasing energy.

This design is entirely plausible with currently available technology, but requires more study before it can be declared both practical and economical.


The concept has several potential advantages over conventional nuclear fission reactors:

  • Subcritical design means that the reaction could not run away — if anything went wrong, the reaction would stop and the reactor would cool down. A meltdown could however occur if the ability to cool the core was lost.
  • Thorium is an abundant element — much more so than uranium — reducing strategic and political supply issues and eliminating costly and energy-intensive isotope separation. There is enough thorium to generate energy for at least several thousand years at current consumption rates.[3]
  • The energy amplifier would produce very little plutonium, so the design is believed to be more proliferation-resistant than conventional nuclear power (although the question of uranium-233 as nuclear weapon material must be assessed carefully).
  • The possibility exists of using the reactor to consume plutonium, reducing the world stockpile of the very-long-lived element.
  • Less long-lived radioactive waste is produced — the waste material would decay after 500 years to the radioactive level of coal ash.
  • No new science is required; the technologies to build the energy amplifier have all been demonstrated. Building an energy amplifier requires only some engineering effort, not fundamental research (unlike nuclear fusion proposals).
  • Power generation might be economical compared to current nuclear reactor designs if the total fuel cycle and decommissioning costs are considered.
  • The design could work on a relatively small scale, making it more suitable for countries without a well-developed power grid system
  • Inherent safety and safe fuel transport could make the technology more suitable for developing countries as well as in densely populated areas.


  • General technical difficulties.
  • Each reactor needs its own facility (particle accelerator) to generate the high energy proton beam, which is very costly. For example the Spallation Neutron Source facility cost 1.1 Billion dollars, although it has a lot of research equipment not needed for a commercial reactor.
  • Apart from linear accelerators, which are very expensive, no proton accelerator of sufficient power and energy (> ~12 MW at 1GeV) has ever been built. Currently, the Spallation Neutron Source utilizes a 1.44 MW proton beam to produce its neutrons, with upgrades envisioned to 5 MW.[4]

See also


External links

Search Wikimedia Commons Wikimedia Commons has media related to: Thorium
Search Wiktionary Look up thorium in Wiktionary, the free dictionary.




More about Neutrons –


An article published in 2007 featuring a model-independent analysis concluded that the neutron has a negatively charged exterior, a positively charged middle, and a negative core.[7] The negatively charged exterior of the neutron gives an intuitive explanation for why more neutrons are required in atoms with large numbers of protons, as the neutrons’ negatively charged surfaces attract the positively charged protons to stay clumped together in the atom.

Neutron compounds

Dineutrons and tetraneutrons

Main articles: Dineutron and Tetraneutron

The existence of stable clusters of four neutrons, or tetraneutrons, has been hypothesised by a team led by Francisco-Miguel Marqués at the CNRS Laboratory for Nuclear Physics based on observations of the disintegration of beryllium-14 nuclei. This is particularly interesting because current theory suggests that these clusters should not be stable.

The dineutron is another hypothetical particle.

Neutronium and neutron stars

Main articles: Neutronium and Neutron Star

At extremely high pressures and temperatures, nucleons and electrons are believed to collapse into bulk neutronic matter, called neutronium. This is presumed to happen in neutron stars.




Neutron flux is a term referring to the number of neutrons passing through an area over a span of time. It is most commonly measured in neutrons/(cm²·s).[1] This is drawn from the mathematical definition of flux. The neutron fluence is defined as the neutron flux integrated over a certain time period and represents the number of neutrons per unit area that passed during this time.

Both within natural processes and in the experimental laboratory, neutron flux may be applied to atomic nuclei, in which nuclei are bombarded with neutrons at a steady rate. This can be used to produce different isotopes, including unstable, radioactive ones, of a given chemical element.



Natural neutron flux

Neutron flux in asymptotic giant branch stars and in supernovae is responsible for most of the natural nucleosynthesis producing elements heavier than iron. In stars there is a relatively low neutron flux on the order of 105 to 1011 neutrons per cm2 per second, resulting in nucleosynthesis by the s-process (slow-neutron-capture-process). By contrast, after a core-collapse supernova, there is an extremely high neutron flux, on the order of 1022 neutrons per cm² per second, resulting in nucleosynthesis by the r-process (rapid-neutron-capture-process).

Artificial neutron flux

Artificial neutron flux refers to neutron flux which is man-made, either as byproducts from weapons or nuclear energy production or for specific application such as from a research reactor or by spallation. A flow of neutrons is often used to initiate the fission of unstable large nuclei. The extra neutron(s) pushes the nuclide over the edge, causing it to split to form more stable products. This effect is essential in fission reactors and nuclear weapons.

Within a nuclear fission reactor the neutron flux is primarily the form of measurement used to control the reaction inside. The flux shape is the term applied to the density or relative strength of the flux as it moves around the reactor. Typically the strongest neutron flux occurs in the middle of the reactor core, becoming lower toward the edges. The higher the neutron flux the greater the chance of a nuclear reaction occurring as there are more neutrons going through an area.

In popular culture

In James Cameron‘s Avatar, a ‘neutron flux’ is responsible for the floating mountains, and is the location of the ‘Tree of Souls’.


  1. ^ Neutron flux from the United States Nuclear Regulatory Commission, retrieved 05/30/2008

See also

v • d • e

Fusion power

Core topics
v • d • e

Nuclear fusion methods

Magnetic confinement
Inertial confinement
Other forms
v • d • e

Fusion experiments by confinement method

EAST (China) · ADITYA (India) · JT-60 and the Large Helical Device (Japan) · KSTAR (South Korea) · H-1NF (Australia)
JET (UK) · Tore Supra and TFR (France) · ASDEX Upgrade and Wendelstein 7-X (Germany) · T-15 (Russia) · FTU, IGNITOR and RFX-mod (Italy) · TCV (Switzerland) · MAST and START (UK)
HiPER (EU) · Asterix IV (Czech Republic) · LMJ, LIL and LULI2000 (France) · ISKRA (Russia) · Vulcan (UK)
NIF · OMEGA · Nova · Nike · Shiva · Argus · Cyclops · Janus · Long path
International Fusion Materials Irradiation Facility




The neutron plays an important role in many nuclear reactions. For example, neutron capture often results in neutron activation, inducing radioactivity. In particular, knowledge of neutrons and their behavior has been important in the development of nuclear reactors and nuclear weapons. The fissioning of elements like uranium-235 and plutonium-239 is caused by their absorption of neutrons.

Cold, thermal and hot neutron radiation is commonly employed in neutron scattering facilities, where the radiation is used in a similar way one uses X-rays for the analysis of condensed matter. Neutrons are complementary to the latter in terms of atomic contrasts by different scattering cross sections; sensitivity to magnetism; energy range for inelastic neutron spectroscopy; and deep penetration into matter.

The development of “neutron lenses” based on total internal reflection within hollow glass capillary tubes or by reflection from dimpled aluminum plates has driven ongoing research into neutron microscopy and neutron/gamma ray tomography.[8][9][10]

A major use of neutrons is to excite delayed and prompt gamma rays from elements in materials. This forms the basis of neutron activation analysis (NAA) and prompt gamma neutron activation analysis (PGNAA). NAA is most often used to analyze small samples of materials in a nuclear reactor whilst PGNAA is most often used to analyze subterranean rocks around bore holes and industrial bulk materials on conveyor belts.

Another use of neutron emitters is the detection of light nuclei, particularly the hydrogen found in water molecules. When a fast neutron collides with a light nucleus, it loses a large fraction of its energy. By measuring the rate at which slow neutrons return to the probe after reflecting off of hydrogen nuclei, a neutron probe may determine the water content in soil.


Because free neutrons are unstable, they can be obtained only from nuclear disintegrations, nuclear reactions, and high-energy reactions (such as in cosmic radiation showers or accelerator collisions). Free neutron beams are obtained from neutron sources by neutron transport. For access to intense neutron sources, researchers must go to specialist facilities, such as the ISIS facility in the United Kingdom, which is currently the world’s most intense pulsed neutron and muon source.[citation needed]

The neutron’s lack of total electric charge makes it difficult to steer or accelerate them. Charged particles can be accelerated, decelerated, or deflected by electric or magnetic fields. These methods have little effect on neutrons beyond a small effect of an inhomogeneous magnetic field because of the neutron’s magnetic moment. Neutrons can be controlled by methods that include moderation, reflection and velocity selection.




Neutron transport refers to determination of the neutron flux, observed from an efflux of neutrons from a neutron source. In relation to this, beams of free neutrons can be obtained via extraction from neutron sources.

Neutron sources

The source can be considered as a volume filled with a very low pressure neutron gas (density up to 1024 n/m³), which has an energy distribution corresponding to the temperature of the volume. By inserting a beam tube into the volume, a current of neutrons can be observed flowing out through the tube, much like water flowing out from a tube that is stuck into a volume of wet sand. The current density (in n/m²s) depends on the solid angle formed by the aperture and the length of the tube, and also on the reflecting properties of the inner wall of the tube. Neutrons are indeed reflected at a wall, but usually at an extremely low rate, which is a function of the wall’s nature and surface quality, the neutron energy, and the angle of incidence.

Characteristics of neutron beams

The moving neutron has a kinetic energy E = ½·m·v² (m = mass, v = velocity). The SI unit for energy is the joule (J), but for particles the energy unit of electronvolts (eV) is usually used (1 J = 6.24\cdot1018 eV). The energy can also be expressed in temperature (unit: kelvins) by the relation E = k·T (k = 1.38·10-23 J/K). Furthermore, a moving particle can be considered a matter wave with the de Broglie wavelength λ = h/(2k·T·m)1/2 (h = 6.6·10-34 J·s). The corresponding wavelength for the neutron is generally expressed in nanometers (nm) or sometimes in angstroms (Å), where 1 Å = 0.1 nm.

A thermal neutron, for instance, with a temperature of 293 K (corresponding to E = 0.0253 eV) travels with a speed of 2210 m/s, and has a wavelength of .18 nm.

Neutron Transport Equation

The neutron transport equation is as follows:

\frac{1}{v(E)}\frac{\partial\varphi(\mathbf{r},E,\mathbf{\hat{\Omega}},t)}{\partial   t}+\mathbf{\hat{\Omega}}\cdot\nabla\varphi(\mathbf{r},E,\mathbf{\hat{\Omega}},t)+\Sigma_t(\mathbf{r},E,t)\,\varphi(\mathbf{r},E,\mathbf{\hat{\Omega}},t)=\quad
\quad\int_{4\pi}d\Omega^\prime\int^{\infty}_{0}dE^\prime\,\Sigma_s(\mathbf{r},E^\prime\rightarrow  E,\mathbf{\hat{\Omega}}^\prime\rightarrow  \mathbf{\hat{\Omega}},t)\varphi(\mathbf{r},E^\prime,\mathbf{\hat{\Omega}^\prime},t)+s(\mathbf{r},E,\mathbf{\hat{\Omega}},t)


Symbol Meaning Comments
\mathbf{r} Position vector (i.e. x,y,z)
 \mathbf{v}(E) Neutron velocity vector
\mathbf{\hat{\Omega}}=\frac{\mathbf{v}(E)}{|\mathbf{v}(E)|}=\frac{\mathbf{v}(E)}{{v(E)}} Unit vector in direction of motion
t Time
E Energy
\varphi(\mathbf{r},E,\mathbf{\hat{\Omega}},t)dr\,dE\,d\Omega Angular neutron flux
Number of neutrons in a differential volume dr about r, with a differential energy in dE about E, moving in a differential solid angle in dΩ about \mathbf{\hat{\Omega}}, at time t.
Note integrating over all angles yields Neutron Scalar Flux
\phi \ = \ \int_{4\pi}d\Omega\varphi
\Sigma_t(\mathbf{r},E,t) Macroscopic total cross section
\Sigma_s(\mathbf{r},E'\rightarrow  E,\mathbf{\hat{\Omega}}'\rightarrow \mathbf{\hat{\Omega}},t)dE^\prime  d\Omega^\prime Double differential scattering cross section
Characterizes scattering of a neutron from an incident energy E and direction \mathbf{\hat{\Omega}} to a final energy E^\prime in dE^\prime and direction \mathbf{\hat{\Omega}}^\prime in d\Omega^\prime.
s(\mathbf{r},E,\mathbf{\hat{\Omega}},t) Source term

Neutron transport calculations

Usually the neutron transport calculations can be divided into two categories: shielding and criticality search.


In the case of shielding calculation, there are three important things which must be modeled: neutron source, shield, and detector. Shielding calculation usually yields the neutron flux in the region of space occupied by the detector. Based on the flux in the detector, the shield thickness or source strength are optimized.

Criticality search

In criticality calculation, a fissile or fissionable material is part of the modeled geometry. Neutron source is the part of the modeled geometry which contains the fissile or fissionable material. The spatial dependence of neutron source intensity is proportional to the flux, which dictates the fission reaction density, hence spatial dependence of neutron source is proportional to the fissions induced by the neutrons. The parameter which is the result of criticality calculation is k-effective (keff). This is a parameter which reflects the time dependence on neutron density in a multi-lying medium.

  • keff < 1, if the neutron density is decreasing as time passes;
  • keff = 1, if the neutron density remains unchanged; and
  • keff > 1, if the neutron density is increasing with time.

In the case of a nuclear reactor, neutron density and power density are synonymous, hence during reactor start-up keff > 1, during reactor operation keff = 1 and keff < 1 at reactor shutdown.


Both shielding and criticality calculations can be done using deterministic methods such as diffusion theory, or using stochastic methods such as Monte Carlo. Deterministic methods usually involve multi-group approaches while Monte Carlo can work with multi-group and continuous energy cross-section libraries. Multi-group calculations are usually iterative, because the group constants are calculated using flux-energy profiles, which are determined as the result of the neutron transport calculation.

See also


  • Duderstadt, J., & Hamilton, L. (1976). Nuclear Reactor Analysis. New York: Wiley. ISBN 0-471-22363-8.
  • Marchuk, G. I., & V. I. Lebedev (1986). Numerical Methods in the Theory of Neutron Transport. Taylor & Francis. p. 123. ISBN 978-3-718-60182-0.




The Lady Godiva device[1] was an unshielded, pulsed nuclear reactor[2] originally situated at the Los Alamos National Laboratory (LANL), New Mexico, U.S. It was one of a number of criticality devices within Technical Area 18 (TA-18). Specifically, it was used to produce bursts of neutrons and gamma rays for irradiating test samples, and inspired development of Godiva-like reactors. It received its name from Otto Frisch, who called it “Lady Godiva” because it was ‘naked and unshielded’.[3].



The “Six-factor formula” is the neutron life-cycle balance equation, which includes six separate factors, the product of which is equal to the ratio of the number of neutrons in any generation to that of the previous one; this parameter is called the effective multiplication factor (k), a.k.a. Keff. k = LfρLthfηЄ, where Lf = “fast non-leakage factor”; ρ = “resonance escape probability”; Lth = “thermal non-leakage factor”; f = “thermal fuel utilization factor”; η = “reproduction factor”; Є = “fast-fission factor”.

k = (Neutrons produced in one generation)/(Neutrons produced in the previous generation) When the reactor is critical, k = 1. When the reactor is subcritical, k < 1. When the reactor is supercritical, k > 1.

(intended for consideration in nuclear fission where critical events are discussed but all of it applies in neutron generating physics)



Oklo: a natural nuclear reactor

Modern deposits of uranium contain only up to ~0.7% 235U (and ~99.3% 238U), which is not enough to sustain a chain reaction moderated by ordinary water. But 235U has a much shorter half-life (700 million years) than 238U (4.5 billion years), so in the distant past the percentage of 235U was much higher. About two billion years ago, a water-saturated uranium deposit (in what is now the Oklo mine in Gabon, West Africa) underwent a naturally occurring chain reaction that was moderated by groundwater and, presumably, controlled by the negative void coefficient as the water boiled from the heat of the reaction. Uranium from the Oklo mine is about 50% depleted compared to other locations: it is only about 0.3% to 0.7% 235U; and the ore contains traces of stable daughters of long-decayed fission products.


Natural fission chain-reactors on Earth

Criticality in nature is uncommon. At three ore deposits at Oklo in Gabon, sixteen sites (the so-called Oklo Fossil Reactors) have been discovered at which self-sustaining nuclear fission took place approximately 2 billion years ago. Unknown until 1972 (but postulated by Paul Kuroda in 1956[18]), when French physicist Francis Perrin discovered the Oklo Fossil Reactors, it was realized that nature had beaten humans to the punch. Large-scale natural uranium fission chain reactions, moderated by normal water, had occurred far in the past and would not be possible now. This ancient process was able to use normal water as a moderator only because 2 billion years before the present, natural uranium was richer in the shorter-lived fissile isotope 235U (about 3%), than natural uranium available today (which is only 0.7%, and must be enriched to 3% to be usable in light-water reactors).



Typical fission events release about two hundred million eV (200 MeV) of energy for each fission event. By contrast, most chemical oxidation reactions (such as burning coal or TNT) release at most a few eV per event, so nuclear fuel contains at least ten million times more usable energy per unit mass than does chemical fuel. The energy of nuclear fission is released as kinetic energy of the fission products and fragments, and as electromagnetic radiation in the form of gamma rays; in a nuclear reactor, the energy is converted to heat as the particles and gamma rays collide with the atoms that make up the reactor and its working fluid, usually water or occasionally heavy water.

When a uranium nucleus fissions into two daughter nuclei fragments, an energy of ~200 MeV is released. For uranium-235 (total mean fission energy 202.5 MeV), typically ~169 MeV appears as the kinetic energy of the daughter nuclei, which fly apart at about 3% of the speed of light, due to Coulomb repulsion. Also, an average of 2.5 neutrons are emitted with a kinetic energy of ~2 MeV each (total of 4.8 MeV). The fission reaction also releases ~7 MeV in prompt gamma ray photons. The latter figure means that a nuclear explosion or criticality accident emits about 3.5% of its energy as gamma rays, less than 2.5% of its energy as fast neutrons, and the rest as kinetic energy of fission fragments (“heat”). In an atomic bomb, this heat may serve to raise the temperature of the bomb core to 100 million kelvin and cause secondary emission of soft X-rays, which convert some of this energy to ionizing radiation. However, in nuclear reactors, the fission fragment kinetic energy remains as low-temperature heat which causes little or no ionization.

The total prompt fission energy amounts to about 181 MeV, or ~89% of the total energy. The remaining ~11% is released in beta decays which have various half-lives, but begin as a process in the fission products immediately; and in delayed gamma emissions associated with these beta decays. For example, in uranium-235 this delayed energy is divided into about 6.5 MeV in betas, 8.8 MeV in antineutrinos (released at the same time as the betas), and finally, an additional 6.3 MeV in delayed gamma emission from the excited beta-decay products (for a mean total of ~10 gamma ray emissions per fission, in all).

The 8.8 MeV/202.5 MeV = 4.3% of the energy which is released as antineutrinos is not captured by the reactor material as heat, and escapes directly through all materials (including the Earth) at nearly the speed of light, and into interplanetary space. Almost all of the remaining radiation is converted to heat, either in the reactor core or its shielding.

Some processes involving neutrons are notable for absorbing or finally yielding energy — for example neutron kinetic energy does not yield heat immediately if the neutron is captured by a uranium-238 atom to breed plutonium-239, but this energy is emitted if the plutonium-239 is later fissioned. On the other hand, so called “delayed neutrons” emitted as radioactive decay products with half-lives up to a minute, from fission-daughters, are very important to reactor control because they give a characteristic “reaction” time for the total nuclear reaction to double in size, if the reaction is run in a “delayed-critical” zone which deliberately relies on these neutrons for a supercritical chain-reaction (one in which each fission cycle yields more neutrons than it absorbs). Without their existence, the nuclear chain-reaction would be prompt critical and increase in size faster than it could be controlled by human intervention. In this case, the first experimental atomic reactors would have run away to a dangerous and messy “prompt critical reaction” before their operators could have manually shut them down (for this reason, designer Enrico Fermi included radiation-counter-triggered control rods, suspended by electromagnets, which could automatically drop into the center of Chicago Pile-1). If these delayed neutrons are captured without producing fissions, they produce heat as well.[1]

While, in principle, all fission reactors can act in all three capacities, in practice the tasks lead to conflicting engineering goals and most reactors have been built with only one of the above tasks in mind. (There are several early counter-examples, such as the Hanford N reactor, now decommissioned). Power reactors generally convert the kinetic energy of fission products into heat, which is used to heat a working fluid and drive a heat engine that generates mechanical or electrical power. The working fluid is usually water with a steam turbine, but some designs use other materials such as gaseous helium. Research reactors produce neutrons that are used in various ways, with the heat of fission being treated as an unavoidable waste product. Breeder reactors are a specialized form of research reactor, with the caveat that the sample being irradiated is usually the fuel itself, a mixture of 238U and 235U. For a more detailed description of the physics and operating principles of critical fission reactors, see nuclear reactor physics. For a description of their social, political, and environmental aspects, see nuclear reactor.




The trefoil symbol is used to indicate radioactive material.

The neutrons and protons that constitute nuclei, as well as other particles that may approach them, are governed by several interactions. The strong nuclear force, not observed at the familiar macroscopic scale, is the most powerful force over subatomic distances. The electrostatic force is almost always significant, and in the case of beta decay, the weak nuclear force is also involved.

The interplay of these forces produces a number of different phenomena in which energy may be released by rearrangement of particles. Some configurations of the particles in a nucleus have the property that, should they shift ever so slightly, the particles could rearrange into a lower-energy arrangement and release some energy. One might draw an analogy with a snowfield on a mountain: while friction between the ice crystals may be supporting the snow’s weight, the system is inherently unstable with regard to a state of lower potential energy. A disturbance would thus facilitate the path to a state of greater entropy: the system will move towards the ground state, producing heat, and the total energy will be distributable over a larger number of quantum states. Thus, an avalanche results. The total energy does not change in this process, but because of the law of entropy, avalanches only happen in one direction and that is towards the “ground state” – the state with the largest number of ways in which the available energy could be distributed.

Such a collapse (a decay event) requires a specific activation energy. For a snow avalanche, this energy comes as a disturbance from outside the system, although such disturbances can be arbitrarily small. In the case of an excited atomic nucleus, the arbitrarily small disturbance comes from quantum vacuum fluctuations. A radioactive nucleus (or any excited system in quantum mechanics) is unstable, and can thus spontaneously stabilize to a less-excited system. The resulting transformation alters the structure of the nucleus and results in the emission of either a photon or a high-velocity particle which has mass (such as an electron, alpha particle, or other type).

Types of decay

As for types of radioactive radiation, it was found that an electric or magnetic field could split such emissions into three types of beams. For lack of better terms, the rays were given the alphabetic names alpha, beta and gamma, still in use today. While alpha decay was seen only in heavier elements (atomic number 52, tellurium, and greater), the other two types of decay were seen in all of the elements.

In analyzing the nature of the decay products, it was obvious from the direction of electromagnetic forces that alpha rays carried a positive charge, beta rays carried a negative charge, and gamma rays were neutral. From the magnitude of deflection, it was clear that alpha particles were much more massive than beta particles. Passing alpha particles through a very thin glass window and trapping them in a discharge tube allowed researchers to study the emission spectrum of the resulting gas, and ultimately prove that alpha particles are helium nuclei. Other experiments showed the similarity between beta radiation and cathode rays; they are both streams of electrons, and between gamma radiation and X-rays, which are both high energy electromagnetic radiation.

Although alpha, beta, and gamma are most common, other types of decay were eventually discovered. Shortly after discovery of the neutron in 1932, it was discovered by Enrico Fermi that certain rare decay reactions yield neutrons as a decay particle. Isolated proton emission was eventually observed in some elements. Shortly after the discovery of the positron in cosmic ray products, it was realized that the same process that operates in classical beta decay can also produce positrons (positron emission), analogously to negative electrons. Each of the two types of beta decay acts to move a nucleus toward a ratio of neutrons and protons which has the least energy for the combination. Finally, in a phenomenon called cluster decay, specific combinations of neutrons and protons other than alpha particles were spontaneously emitted from atoms on occasion.

Still other types of radioactive decay were found which emit previously seen particles, but by different mechanisms. An example is internal conversion, which results in electron and sometimes high energy photon emission, even though it involves neither beta nor gamma decay.



In nuclear physics and nuclear chemistry, nuclear fusion is the process by which multiple atomic nuclei join together to form a single heavier nucleus. It is accompanied by the release or absorption of large quantities energy. Large scale fusion processes, involving many atoms fusing at once, must occur in matter which is at very high densities.

The fusion of two nuclei with lower mass than iron (which, along with nickel, has the largest binding energy per nucleon) generally releases energy while the fusion of nuclei heavier than iron absorbs energy; vice-versa for the reverse process, nuclear fission. In the simplest case of hydrogen fusion, two protons have to be brought close enough for the weak force to convert either of the identical protons into a neutron forming deuterium. In more complex cases of heavy ion fusion involving many nucleons, the reaction mechanism is different, but we achieve the same result of assembling larger nuclei from smaller nuclei.

Nuclear fusion occurs naturally in stars. Artificial fusion in human enterprises has also been achieved, although it has not yet been completely controlled as an energy source; successful nuclear physics experiments have been performed involving the fusion of many different nuclear species, but the energy output is negligible in these studies. Building upon the nuclear transmutation experiments of Ernest Rutherford done a few years earlier, fusion of light nuclei (hydrogen isotopes) was first observed by Mark Oliphant in 1932; the steps of the main cycle of nuclear fusion in stars were subsequently worked out by Hans Bethe throughout the remainder of that decade.

Research into fusion for military purposes began in the early 1940s as part of the Manhattan Project, but was not successful until 1952. Research into controlled fusion for civilian purposes began in the 1950s, and continues to this day.



Generally cold, locally hot fusion

Accelerator-based light-ion fusion is a technique using particle accelerators to achieve particle kinetic energies sufficient to induce light-ion fusion reactions. Accelerating light ions is relatively easy, and can be done in an efficient manner—all it takes is a vacuum tube, a pair of electrodes, and a high-voltage transformer; fusion can be observed with as little as 10 kV between electrodes. The key problem with accelerator-based fusion (and with cold targets in general) is that fusion cross sections are many orders of magnitude lower than Coulomb interaction cross sections. Therefore the vast majority of ions ends up expending their energy on bremsstrahlung and ionization of atoms of the target. Devices referred to as sealed-tube neutron generators are particularly relevant to this discussion. These small devices are miniature particle accelerators filled with deuterium and tritium gas in an arrangement which allows ions of these nuclei to be accelerated against hydride targets, also containing deuterium and tritium, where fusion takes place. Hundreds of neutron generators are produced annually for use in the petroleum industry where they are used in measurement equipment for locating and mapping oil reserves. Despite periodic reports in the popular press by scientists claiming to have invented “table-top” fusion machines, neutron generators have been around for half a century. The sizes of these devices vary but the smallest instruments are often packaged in sizes smaller than a loaf of bread. These devices do not produce a net power output.

Sonofusion or bubble fusion, a controversial variation on the sonoluminescence theme, suggests that acoustic shock waves, creating temporary bubbles (cavitation) that expand and collapse shortly after creation, can produce temperatures and pressures sufficient for nuclear fusion.[11]

The Farnsworth–Hirsch fusor is a tabletop device in which fusion occurs. This fusion comes from high effective temperatures produced by electrostatic acceleration of ions. The device can be built inexpensively, but it too is unable to produce a net power output.

The Polywell is a concept for a tabletop device in which fusion occurs. The device is a non-thermodynamic equilibrium machine which uses electrostatic confinement to accelerate ions into a center where they fuse together.

Antimatter-initialized fusion uses small amounts of antimatter to trigger a tiny fusion explosion. This has been studied primarily in the context of making nuclear pulse propulsion, and pure fusion bombs feasible. This is not near becoming a practical power source, due to the cost of manufacturing antimatter alone.

Pyroelectric fusion was reported in April 2005 by a team at UCLA. The scientists used a pyroelectric crystal heated from −34 to 7 °C (−29 to 45 °F), combined with a tungsten needle to produce an electric field of about 25 gigavolts per meter to ionize and accelerate deuterium nuclei into an erbium deuteride target. Though the energy of the deuterium ions generated by the crystal has not been directly measured, the authors used 100 keV (a temperature of about 109 K) as an estimate in their modeling.[12] At these energy levels, two deuterium nuclei can fuse together to produce a helium-3 nucleus, a 2.45 MeV neutron and bremsstrahlung. Although it makes a useful neutron generator, the apparatus is not intended for power generation since it requires far more energy than it produces.[13][14][15][16]

Hot fusion

In hot fusion, the fuel reaches tremendous temperature and pressure inside a fusion reactor or nuclear weapon (or star).

The methods in the second group are examples of non-equilibrium systems, in which very high temperatures and pressures are produced in a relatively small region adjacent to material of much lower temperature. In his doctoral thesis for MIT, Todd Rider did a theoretical study of all quasineutral, isotropic, non-equilibrium fusion systems. He demonstrated that all such systems will leak energy at a rapid rate due to bremsstrahlung produced when electrons in the plasma hit other electrons or ions at a cooler temperature and suddenly decelerate. The problem is not as pronounced in a hot plasma because the range of temperatures, and thus the magnitude of the deceleration, is much lower. Note that Rider’s work does not apply to non-neutral and/or anisotropic non-equilibrium plasmas.

Important reactions

Astrophysical reaction chains

The proton-proton chain dominates in stars the size of the Sun or smaller.

The CNO cycle dominates in stars heavier than the Sun.

The most important fusion process in nature is that which powers the stars. The net result is the fusion of four protons into one alpha particle, with the release of two positrons, two neutrinos (which changes two of the protons into neutrons), and energy, but several individual reactions are involved, depending on the mass of the star. For stars the size of the sun or smaller, the proton-proton chain dominates. In heavier stars, the CNO cycle is more important. Both types of processes are responsible for the creation of new elements as part of stellar nucleosynthesis.

At the temperatures and densities in stellar cores the rates of fusion reactions are notoriously slow. For example, at solar core temperature (T ≈ 15 MK) and density (160 g/cm³), the energy release rate is only 276 μW/cm³—about a quarter of the volumetric rate at which a resting human body generates heat.[17] Thus, reproduction of stellar core conditions in a lab for nuclear fusion power production is completely impractical. Because nuclear reaction rates strongly depend on temperature (exp(−E/kT)), then in order to achieve reasonable rates of energy production in terrestrial fusion reactors 10–100 times higher temperatures (compared to stellar interiors) are required T ≈ 0.1–1.0 GK.

Criteria and candidates for terrestrial reactions

In man-made fusion, the primary fuel is not constrained to be protons and higher temperatures can be used, so reactions with larger cross-sections are chosen. This implies a lower Lawson criterion, and therefore less startup effort. Another concern is the production of neutrons, which activate the reactor structure radiologically, but also have the advantages of allowing volumetric extraction of the fusion energy and tritium breeding. Reactions that release no neutrons are referred to as aneutronic.




Neutron temperature

Main article: Neutron temperature

Thermal neutron

A thermal neutron is a free neutron that is Boltzmann distributed with kT = 0.024 eV (4.0×10−21 J) at room temperature. This gives characteristic (not average, or median) speed of 2.2 km/s. The name ‘thermal’ comes from their energy being that of the room temperature gas or material they are permeating. (see kinetic theory for energies and speeds of molecules). After a number of collisions (often in the range of 10–20) with nuclei, neutrons arrive at this energy level, provided that they are not absorbed.

In many substances, thermal neutrons have a much larger effective cross-section than faster neutrons, and can therefore be absorbed more easily by any atomic nuclei that they collide with, creating a heavier — and often unstableisotope of the chemical element as a result.

Most fission reactors use a neutron moderator to slow down, or thermalize the neutrons that are emitted by nuclear fission so that they are more easily captured, causing further fission. Others, called fast breeder reactors, use fission energy neutrons directly.

Cold neutrons

These neutrons are thermal neutrons that have been equilibrated in a very cold substance such as liquid deuterium. These are produced in neutron scattering research facilities.

Ultracold neutrons

Ultracold neutrons are produced by equilibration in substances with a temperature of a few kelvins, such as solid deuterium or superfluid helium. An alternative production method is the mechanical deceleration of cold neutrons.

Fission energy neutron

A fast neutron is a free neutron with a kinetic energy level close to 2 MeV (20 TJ/kg), hence a speed of 28,000 km/s. They are named fission energy or fast neutrons to distinguish them from lower-energy thermal neutrons, and high-energy neutrons produced in cosmic showers or accelerators. Fast neutrons are produced by nuclear processes such as nuclear fission.

Fast neutrons can be made into thermal neutrons via a process called moderation. This is done with a neutron moderator. In reactors, typically heavy water, light water, or graphite are used to moderate neutrons.

Fusion neutron

The fusion reaction rate increases rapidly with temperature until it maximizes and then gradually drops off. The DT rate peaks at a lower temperature (about 70 keV, or 800 million kelvins) and at a higher value than other reactions commonly considered for fusion energy.

D-T (deuteriumtritium) fusion is the fusion reaction that produces the most energetic neutrons, with 14.1 MeV of kinetic energy and traveling at 17% of the speed of light. D-T fusion is also the easiest fusion reaction to ignite, reaching near-peak rates even when the deuterium and tritium nuclei have only a thousandth as much kinetic energy as the 14.1 MeV that will be produced.

14.1 Mev neutrons have about 10 times as much energy as fission neutrons, and are very effective at fissioning even non-fissile heavy nuclei, and these high-energy fissions produce more neutrons on average than fissions by lower-energy neutrons. 14.1 MeV neutrons can also produce neutrons by knocking them loose from nuclei. On the other hand, these very high energy neutrons are less likely to simply be captured without causing fission or spallation. For these reasons, nuclear weapon design extensively utilizes D-T fusion 14.1 MeV neutrons to cause more fission.

Other fusion reactions produce much less energetic neutrons. D-D fusion produces a 2.45 MeV neutron and helium-3 half of the time, and produces tritium and a proton but no neutron the other half of the time. D-3He fusion produces no neutron.

Intermediate-energy neutrons

Transmutation flow in LWR which is a thermal-spectrum reactor

A fission energy neutron that has slowed down but not yet reached thermal energies is called an epithermal neutron.

Cross sections for both capture and fission reactions often have multiple resonance peaks at specific energies in the epithermal energy range. These are of less significance in a fast neutron reactor where most neutrons are absorbed before slowing down to this range, or in a well-moderated thermal reactor where epithermal neutrons mostly interact with moderator nuclei, not with either fissile or fertile actinide nuclides. However, in a partially moderated reactor with more interactions of epithermal neutrons with heavy metal nuclei, there are greater possibilities for transient changes in reactivity which might make reactor control more difficult.

Ratios of capture reactions to fission reactions are also worse (more captures without fission) in most nuclear fuels such as plutonium-239, making epithermal-spectrum reactors using these fuels less desirable, as captures not only waste the one neutron captured but also usually result in a nuclide which is not fissile with thermal or epithermal neutrons, though still fissionable with fast neutrons. The exception is uranium-233 of the thorium cycle which has good capture-fission ratios at all neutron energies.

High-energy neutrons

These neutrons have more energy than fission energy neutrons and are generated as secondary particles by particle accelerators or in the atmosphere from cosmic rays. They can have energies as high as tens of joules per neutron.



Photofission is a process in which a nucleus, after absorbing a gamma ray, undergoes nuclear fission (splits into two fragments of nearly equal mass).

Very high energy gamma rays have been shown to induce fission in elements as light as as tin.


Photodisintegration (also called phototransmutation) is a similar but different physical process, in which an extremely high energy gamma ray interacts with an atomic nucleus and causes it to enter an excited state, which immediately decays by emitting a subatomic particle.



Carbon burning process

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The carbon burning process or carbon fusion is a set of nuclear fusion reactions that take place in massive stars (at least 5 MSun at birth)[1] that have used up the lighter elements in their cores. It requires high temperatures (6×108 K or 50 KeV) and densities (about 2×108 kg/m3).

These figures for temperature and density are only a guide. More massive stars burn their nuclear fuel more quickly, since they have to offset greater gravitational forces to stay in (approximate) hydrostatic equilibrium. That generally means higher temperatures, although lower densities, than for less massive stars.[2] To get the right figures for a particular mass, and a particular stage of evolution, it is necessary to use a numerical stellar model computed with computer algorithms.[3] Such models are continually being refined based on particle physics experiments (which measure nuclear reaction rates) and astronomical observations (which include direct observation of mass loss, detection of nuclear products from spectrum observations after convection zones develop from the surface to fusion burning regions – known as ‘dredge-up’ events – and so bring nuclear products to the surface, and many other observations relevant to models).[4]


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Fusion reactions

The principal reactions are:[2]

126C + 126C 2010Ne + 42He + 4.617 MeV
126C + 126C 2311Na + 11H + 2.241 MeV
126C + 126C 2312Mg + n 2.599 MeV
126C + 126C 2412Mg + γ + 13.933 MeV
126C + 126C 168O + 42He –   0.113 MeV

Reaction products

This sequence of reactions can be understood by thinking of the two interacting carbon nuclei as coming together to form an excited state of the Mg-24 nucleus, which then decays in one of the five ways listed above.[5] The first two reactions are strongly exothermic, as indicated by the large positive energies released, and are the most frequent results of the interaction. The third reaction is strongly endothermic, as indicated by the large negative energy indicating that energy is absorbed rather than emitted. This makes it much less likely, yet still possible in the high-energy environment of carbon burning. But the production of a few neutrons by this reaction is important, since these neutrons can combine with heavy nuclei, present in tiny amounts in most stars, to form even heavier isotopes in the s-process.

The fourth reaction might be expected to be the most common from its large energy release, but in fact it is extremely improbable because it proceeds via the electromagnetic interaction, as it produces a gamma ray photon, rather than utilising the strong force between nucleons as do the first two reactions. Nucleons look a lot bigger to each other than they do to photons of this energy. However, the Mg-24 that is produced is the magnesium present in the oxygen-neon-magnesium white dwarfs left when the carbon-burning process ends, as Mg-23 is radioactive.

The last reaction is also very unlikely since it involves three reaction products, as well as being endothermic – think of the reaction proceeding in reverse, it would require the three products all to converge at the same time, which is less likely than two body interactions.

The protons produced by the second reaction can take part in the proton-proton chain reaction, or the CNO cycle, but they can also be captured by Na-23 to form Ne-20 plus a He-4 nucleus. In fact, almost all of the Na-23 produced by the second reaction gets used up this way.[6]

The oxygen (O-16) already produced by helium fusion in the previous stage of stellar evolution manages to survive the carbon burning process pretty well, despite some of it being used up by capturing He-4 nuclei, in stars between 4 and 8 solar masses.

So the end result of carbon burning is a mixture mainly of oxygen, neon and magnesium.

The fact that the mass-energy sum of the two carbon nuclei is similar to that of an excited state of the magnesium nucleus is known as ‘resonance’. Without this resonance, carbon burning would only occur at temperatures one hundred times higher. The experimental and theoretical investigation of such resonances is still a subject of research.[7]

Neutrino losses

Neutrino losses start to become a major factor in the fusion processes in stars at the temperatures and densities of carbon burning. Though the main reactions don’t involve neutrinos, the side reactions such as the proton-proton chain reaction do. But the main source of neutrinos at these high temperatures involves a process in quantum theory known as pair production. A high energy gamma ray which has a greater energy than the rest mass of two electrons (mass-energy equivalence) can interact with electromagnetic fields of the atomic nuclei in the star, and become a particle and anti-particle pair of an electron and positron.

Normally, the positron quickly annihilates with another electron, producing two photons, and this process can be safely ignored at lower temperatures. But around 1 in 1019 pair productions[2] end with a weak interaction of the electron and positron, which replaces them with a neutrino and anti-neutrino pair. Since they move at virtually the speed of light and interact very weakly with matter, these neutrino particles usually escape the star without interacting, carrying away their mass-energy. This energy loss is comparable to the energy output from the carbon fusion.

Neutrino losses, by this and similar processes, play an increasingly important part in the evolution of the most massive stars. They force the star to burn its fuel at a higher temperature to offset them.[2] Fusion processes are very sensitive to temperature so the star can produce more energy to retain hydrostatic equilibrium, at the cost of burning through successive nuclear fuels ever more rapidly. Fusion produces less energy per unit mass as the fuel nuclei get heavier, and the core of the star contracts and heats up when switching from one fuel to the next, so both these processes also significantly reduce the lifetime of each successive fusion-burning fuel.

Up to helium burning, the neutrino losses are negligible, but from carbon burning the reduction in lifetime due to them roughly matches that due to fuel change and core contraction. In successive fuel changes in the most massive stars, the reduction in lifetime is dominated by the neutrino losses. For example, a star of 25 solar masses burns hydrogen in the core for 107 years, helium for 106 years and carbon for only 103 years.[8]

Stellar evolution

Main article: Stellar evolution

During helium fusion, stars build up an inert core rich in carbon and oxygen. The inert core eventually reaches sufficient mass to collapse due to gravitation, whilst the helium burning moves gradually outward. This decrease in the inert core volume raises the temperature to the carbon ignition temperature. This will raise the temperature around the core and allow helium to burn in a shell around the core.[9] Outside this is another shell burning hydrogen. The resulting carbon burning provides energy from the core to restore the star’s mechanical equilibrium. However, the balance is only short-lived; in a star of 25 solar masses, the process will use up most of the carbon in the core in only 600 years.[10]

Stars with below 4 Solar masses never reach high enough core temperature to burn carbon, instead ending their lives as carbon-oxygen white dwarfs after shell helium flashes gently expel the outer envelope in a planetary nebula.[9]

Those with between 4 and 8 solar masses would theoretically accumulate enough inert reaction products of carbon burning in the core to exceed the Chandrasekhar limit of 1.4 solar masses and collapse catastrophically. This does not happen because such stars (on the Asymptotic Giant Branch) are observed to have enormous mass loss rates. Instead these stars burn carbon and their new inert core of reaction products (O, Mg, Ne) never exceeds the Chandrasekhar limit.[9]

In the late stages of carbon burning, stars with masses between 4 and 8 solar masses develop a massive stellar wind, which quickly ejects the outer envelope in a planetary nebula leaving behind an O-Ne-Mg white dwarf core. The core never reaches high enough temperature for further fusion burning of heavier elements than carbon.[9]

Stars with more than 8 solar masses proceed with the neon burning process after contraction of the inert (O, Ne, Mg) core raises the temperature sufficiently.[9]

See also


  1. ^ Girardi, L.; Bressan, A.; Bertelli, G.; Chiosi, C. (2000). “Evolutionary tracks and isochrones for low- and intermediate-mass stars: From 0.15 to 7 Msun, and from Z=0.0004 to 0.03″. Astronomy and Astrophysics Supplement 141: 371–383. doi:10.1051/aas:2000126.
  2. ^ a b c d Clayton, Donald. Principles of Stellar Evolution and Nucleosynthesis, (1983)
  3. ^ Siess L. (2007). “Evolution of massive AGB stars. I. Carbon burning phase”. Astronomy and Astrophysics 476: 893–909. doi:10.1051/0004-6361:20053043. http://adsabs.harvard.edu/abs/2006A&A…448..717S.
  4. ^ Hernandez, G. et al (dec, 2006). “Rubidium-Rich Asymptotic Giant Branch Stars”. Science 314 (5806): 1751–1754. doi:10.1126/science.1133706. PMID 17095658. http://adsabs.harvard.edu/abs/2006Sci…314.1751G.
  5. ^ Rose, William K., Advanced Stellar Astrophysics, Cambridge University Press (1998)
  6. ^ de Loore, Camiel W. H. and Doom, C.,Structure and Evolution of single and binary stars, Kluwer (1992)
  7. ^ Strandberg, E. et al (May 2008). “Mg24(α,γ)Si28 resonance parameters at low α-particle energies”. Physical Review C 77 (5): 055801-+. doi:10.1103/PhysRevC.77.055801. http://adsabs.harvard.edu/abs/2008PhRvC..77e5801S.
  8. ^ Woosley, S.; Janka, H.-T. (2006-01-12). “The Physics of Core-Collapse Supernovae”. Nature Physics 1 (3): 147–154. doi:10.1038/nphys172. http://adsabs.harvard.edu/abs/2006astro.ph..1261W. Retrieved 2009-09-10.
  9. ^ a b c d e Ostlie, Dale A. and Carrol, Bradley W., An introduction to Modern Stellar Astrophysics, Addison-Wesley (2007)
  10. ^ Anderson, Scott R., Open Course: Astronomy: Lecture 19: Death of High-Mass Stars, GEM (2001)
v • d • e

Nuclear processes

Radioactive decay
Stellar nucleosynthesis
Other processes





Main article: Allotropes of carbon

Atomic carbon is a very short-lived species and, therefore, carbon is stabilized in various multi-atomic structures with different molecular configurations called allotropes. The three relatively well-known allotropes of carbon are amorphous carbon, graphite, and diamond. Once considered exotic, fullerenes are nowadays commonly synthesized and used in research; they include buckyballs,[19][20] carbon nanotubes,[21] carbon nanobuds[22] and nanofibers.[23][24] Several other exotic allotropes have also been discovered, such as lonsdaleite,[25] glassy carbon,[26] carbon nanofoam[27] and linear acetylenic carbon.[28]

  • The amorphous form is an assortment of carbon atoms in a non-crystalline, irregular, glassy state, which is essentially graphite but not held in a crystalline macrostructure. It is present as a powder, and is the main constituent of substances such as charcoal, lampblack (soot) and activated carbon.
  • At normal pressures carbon takes the form of graphite, in which each atom is bonded trigonally to three others in a plane composed of fused hexagonal rings, just like those in aromatic hydrocarbons. The resulting network is 2-dimensional, and the resulting flat sheets are stacked and loosely bonded through weak van der Waals forces. This gives graphite its softness and its cleaving properties (the sheets slip easily past one another). Because of the delocalization of one of the outer electrons of each atom to form a π-cloud, graphite conducts electricity, but only in the plane of each covalently bonded sheet. This results in a lower bulk electrical conductivity for carbon than for most metals. The delocalization also accounts for the energetic stability of graphite over diamond at room temperature.

    Some allotropes of carbon: a) diamond; b) graphite; c) lonsdaleite; d–f) fullerenes (C60, C540, C70); g) amorphous carbon; h) carbon nanotube.

  • At very high pressures carbon forms the more compact allotrope diamond, having nearly twice the density of graphite. Here, each atom is bonded tetrahedrally to four others, thus making a 3-dimensional network of puckered six-membered rings of atoms. Diamond has the same cubic structure as silicon and germanium and because of the strength of the carbon-carbon bonds, it is the hardest naturally occurring substance in terms of resistance to scratching. Contrary to the popular belief that diamonds are forever, they are in fact thermodynamically unstable under normal conditions and transform into graphite.[12] But due to a high activation energy barrier, the transition into graphite is so extremely slow at room temperature as to be unnoticeable.
  • Under some conditions, carbon crystallizes as lonsdaleite. This form has a hexagonal crystal lattice where all atoms are covalently bonded. Therefore, all properties of lonsdaleite are close to those of diamond.[25]
  • Fullerenes have a graphite-like structure, but instead of purely hexagonal packing, they also contain pentagons (or even heptagons) of carbon atoms, which bend the sheet into spheres, ellipses or cylinders. The properties of fullerenes (split into buckyballs, buckytubes and nanobuds) have not yet been fully analyzed and represent an intense area of research in nanomaterials. The names “fullerene” and “buckyball” are given after Richard Buckminster Fuller, popularizer of geodesic domes, which resemble the structure of fullerenes. The buckyballs are fairly large molecules formed completely of carbon bonded trigonally, forming spheroids (the best-known and simplest is the soccerball-shaped structure C60 buckminsterfullerene).[19] Carbon nanotubes are structurally similar to buckyballs, except that each atom is bonded trigonally in a curved sheet that forms a hollow cylinder.[20][21] Nanobuds were first published in 2007 and are hybrid bucky tube/buckyball materials (buckyballs are covalently bonded to the outer wall of a nanotube) that combine the properties of both in a single structure.[22]
  • Of the other discovered allotropes, carbon nanofoam is a ferromagnetic allotrope discovered in 1997. It consists of a low-density cluster-assembly of carbon atoms strung together in a loose three-dimensional web, in which the atoms are bonded trigonally in six- and seven-membered rings. It is among the lightest known solids, with a density of about 2 kg/m3.[29] Similarly, glassy carbon contains a high proportion of closed porosity.[26] But unlike normal graphite, the graphitic layers are not stacked like pages in a book, but have a more random arrangement. Linear acetylenic carbon[28] has the chemical structure[28] -(C:::C)n-. Carbon in this modification is linear with sp orbital hybridization, and is a polymer with alternating single and triple bonds. This type of carbyne is of considerable interest to nanotechnology as its Young’s modulus is forty times that of the hardest known material – diamond.[30]


Graphite ore

Raw diamond crystal.

“Present day” (1990s) sea surface dissolved inorganic carbon concentration (from the GLODAP climatology)

Carbon is the fourth most abundant chemical element in the universe by mass after hydrogen, helium, and oxygen. Carbon is abundant in the Sun, stars, comets, and in the atmospheres of most planets. Some meteorites contain microscopic diamonds that were formed when the solar system was still a protoplanetary disk. Microscopic diamonds may also be formed by the intense pressure and high temperature at the sites of meteorite impacts.[31]

In combination with oxygen in carbon dioxide, carbon is found in the Earth’s atmosphere (approximately 810 gigatonnes of carbon) and dissolved in all water bodies (approximately 36,000 gigatonnes of carbon). Around 1,900 gigatonnes of carbon are present in the biosphere. Hydrocarbons (such as coal, petroleum, and natural gas) contain carbon as well—coal “reserves” (not “resources”) amount to around 900 gigatonnes, and oil reserves around 150 gigatonnes. Proven sources of natural gas are about 175 tetrillion cubic metres (representing about 105 gigatonnes carbon), but it is estimated that there are also about 900 tetrillion cubic metres of “unconventional” gas such as shale gas, representing about 540 gigatonnes carbon.[32]

Carbon is a major component in very large masses of carbonate rock (limestone, dolomite, marble etc.).

Coal is a significant commercial source of mineral carbon; anthracite containing 92–98% carbon[33] and the largest source (4,000 Gt, or 80% of coal, gas and oil reserves) of carbon in a form suitable for use as fuel.[34]

Graphite is found in large quantities in New York and Texas, the United States, Russia, Mexico, Greenland, and India.

Natural diamonds occur in the rock kimberlite, found in ancient volcanic “necks,” or “pipes”. Most diamond deposits are in Africa, notably in South Africa, Namibia, Botswana, the Republic of the Congo, and Sierra Leone. There are also deposits in Arkansas, Canada, the Russian Arctic, Brazil and in Northern and Western Australia.

Diamonds are now also being recovered from the ocean floor off the Cape of Good Hope. However, though diamonds are found naturally, about 30% of all industrial diamonds used in the U.S. are now made synthetically.

Carbon-14 is formed in upper layers of the troposphere and the stratosphere, at altitudes of 9–15 km, by a reaction that is precipitated by cosmic rays. Thermal neutrons are produced that collide with the nuclei of nitrogen-14, forming carbon-14 and a proton.


Main article: Isotopes of carbon

Isotopes of carbon are atomic nuclei that contain six protons plus a number of neutrons (varying from 2 to 16). Carbon has two stable, naturally occurring isotopes.[9] The isotope carbon-12 (12C) forms 98.93% of the carbon on Earth, while carbon-13 (13C) forms the remaining 1.07%.[9] The concentration of 12C is further increased in biological materials because biochemical reactions discriminate against 13C.[35] In 1961 the International Union of Pure and Applied Chemistry (IUPAC) adopted the isotope carbon-12 as the basis for atomic weights.[36] Identification of carbon in NMR experiments is done with the isotope 13C.

Carbon-14 (14C) is a naturally occurring radioisotope which occurs in trace amounts on Earth of up to 1 part per trillion (0.0000000001%), mostly confined to the atmosphere and superficial deposits, particularly of peat and other organic materials.[37] This isotope decays by 0.158 MeV β emission. Because of its relatively short half-life of 5730 years, 14C is virtually absent in ancient rocks, but is created in the upper atmosphere (lower stratosphere and upper troposphere) by interaction of nitrogen with cosmic rays.[38] The abundance of 14C in the atmosphere and in living organisms is almost constant, but decreases predictably in their bodies after death. This principle is used in radiocarbon dating, invented in 1949, which has been used extensively to determine the age of carbonaceous materials with ages up to about 40,000 years.[39][40]

There are 15 known isotopes of carbon and the shortest-lived of these is 8C which decays through proton emission and alpha decay and has a half-life of 1.98739×10−21 s.[41] The exotic 19C exhibits a nuclear halo, which means its radius is appreciably larger than would be expected if the nucleus were a sphere of constant density.[42]

Formation in stars

Main articles: Triple-alpha process and CNO cycle

Formation of the carbon atomic nucleus requires a nearly simultaneous triple collision of alpha particles (helium nuclei) within the core of a giant or supergiant star. This happens in conditions of > 100 megakelvin temperature and helium concentration that the rapid expansion and cooling of the early universe prohibited, and therefore no significant carbon was created during the Big Bang. Instead, the interiors of stars in the horizontal branch transform three helium nuclei into carbon by means of this triple-alpha process. In order to be available for formation of life as we know it, this carbon must then later be scattered into space as dust, in supernova explosions, as part of the material which later forms second, third-generation star systems which have planets accreted from such dust. The Solar System is one such third-generation star system.

One of the fusion mechanisms powering stars is the carbon-nitrogen cycle.

Rotational transitions of various isotopic forms of carbon monoxide (e.g. 12CO, 13CO, and C18O) are detectable in the submillimeter regime, and are used in the study of newly forming stars in molecular clouds.



Category:Nucleosynthesis – Wikipedia, the free encyclopedia

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My Note –

just before this very last entry – I had the last hour of work and the durn Firefox crashed before I hit update – so here are the links and I will complete the series tomorrow night – these links are backwards to the order they would have appeared.

– cricketdiane


Carbon – Wikipedia, the free encyclopedia

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