# Need some help understanding fusion.

1. Jun 11, 2012

### Andrew042

So I have recently been reading up on fusion with Hydrogen atoms.

I understand most of it except one essential part, thus bringing me to my question:

Can one smash two Hydrogen atoms at extremely high speeds in say room temperature and still get a Deuterium atom?

2. Jun 11, 2012

### Drakkith

Staff Emeritus
You have a misunderstanding as to what temperature means. Temperature is the measure of the average velocity of a group of particles. The more massive the particles the slower they go for a given temperature.

When we smash atoms together in fusion, we can use the velocity of each particle as a measure of the temperature a material would have if there was a lot of these atoms moving around at the same velocity. So smashing hydrogen together at high velocity CANNOT occur at room temperature, as the hydrogen wouldn't be moving very quickly. And we cannot just shoot high velocity ions through air either, as the average distance before collision with a gas molecule is a fraction of a millimeter.

3. Jun 11, 2012

### the_emi_guy

Yes you can, and pretty easily. The coulomb barrier for deuterium-tritium is only 100KeV, easily reached in a particle accelerator. This approach, by itself, is too inefficient for energy production. Heating a plasma and counting on the thermal motion of the nucleons to cause fusion is more practical (thermonuclear fusion).

Look up beam target fusion.

4. Jun 11, 2012

### Drakkith

Staff Emeritus
True, but the OP was asking specifically about room temperature fusion.

5. Jun 12, 2012

### sophiecentaur

Temperature is the mean energy of all the particles in a system. If you briefly accelerate a beam of ions to high speed - enough to cause fusion- then you could say that the temperature of that beam is very high but the tube they are in could still be stone cold. So you could call it room temperature fusion but it would be only 'words'. The motion of the ions would not be thermal (random) so I would say the temperature is not high.

6. Jun 12, 2012

### Andrew042

Okay so just to make sure I understand this:

If I shoot Hydrogen Atoms at a certain velocity, the temperature wouldnt be room temperature because temperature is affected by the velocity of the particles. So if I increase the velocity of particles, I increase the temperature?

So this leads me to one more question:

What is the equation to find the temperature at a certain velocity?

7. Jun 13, 2012

### sophiecentaur

It is not meaningful to ascribe a temperature to non-random motion. You wouldn't do it when describing a fast car so why do it for a beam of ions? This is just about definitions again. There are more fruitful things to discuss.

8. Jun 13, 2012

### Drakkith

Staff Emeritus
As Sophie said, you wouldn't use temperature for beam-beam fusion. You would use the velocity or energy of the ions instead, usually expressed in kiloelectronvolts, keV. In a plasma contained by magnetic fields it is generally expressed as a temperature, as the particles are moving about randomly in the plasma. To convert electronvolts to kelvin see here: http://en.wikipedia.org/wiki/Electronvolt#Temperature

9. Jun 13, 2012

### Darwin123

There is no well defined temperature for two isolated particles. So the "say room temperature" is irrelevant.
There is no way that a collision between two protons, isolated from the rest of the universe, would generate a deuterium nucleus and only a deuterium nucleus. Such a collision would violate many conservation laws. However, a high energy collision between two protons could generate a deuterium nucleus and a lot of other particles. Hence, in order to fuse two protons have to have a very high kinetic energy in the center of mass frame in order to go over the potential barrier and to create the extra particles.
The reaction can be "catalyzed" if a third particle were at the center of mass of the two protons. The third particle could compensate and allow the conservation laws to be generated with fewer particles generated. Note this type of nuclear catalysis is hypothesized to occur at the center of the sun. However, it doesn't occur on earth even in an accelerator.
Here are some conditions for two protons to fuse into a deuterium nucleus.
1) The relative speed has to be high enough to go over the potential barrier caused by the electric charges.
The two particles will repel each other at large distances because like charges repel. The electric charge works over a large distance. The two particles will attract each other at short distances because of the nuclear strong force. So the initial kinetic energy in the center of mass frame has to be high enough to bring the two protons close enough to each other to attract.
2) A third particle has to be involved to balance the electric charge.
-There are two positive charges in two protons and one positive charge in a deuterium nucleus. Therefore, some other charge has to balance.
-A specific case would be if a positron were emitted in the collision.
3) A fourth particle would have to be created to balance the lepton number.
-A specific case would be if a neutrino were generated to balance the positron.
4) If the extra particles would have to have sufficient energy to satisfy conservation of energy and conservation of linear momentum.
-If the collision was spot on, and the protons spinning in opposite directions, the positron and the neutrino generated may be enough to satisfy all conservation laws.
5) If the protons are slightly off center, yet another particle may be necessary to satisfy linear momentum, conservation of energy and conservation of angular momentum.
-Photons and pions may be generated to conserve all the conservation laws in an off center collision.

10. Jun 13, 2012

### Drakkith

Staff Emeritus
How so? The fusion of two protons in the Sun's core leads to the creation of deuterium. A neutrino and a positron are released to conserve charge and such.

Got a reference to this? It's not something I've heard before.

Some of your conditions seem to be simple products of the reaction, such as the production of a neutrino and positron, not a condition for it to happen. As for conservation of momentum, that is taken care of by simply having two protons. Remember, we can view the collision as both protons having equal kinetic energy with respect to each other.

11. Jun 13, 2012

### Staff: Mentor

The neutrino and positron violate the "and only deuterium" requirement. However, I don't see why this should be interesting in any way.

Regarding the "catalysator", which is not a catalysator: The pep reaction fuses two protons plus an electron (which does not have to be at rest) to deuterium and a neutrino. As it requires 3 particles at the same time, it is quite rare.

12. Jun 13, 2012

### Darwin123

I got this link from one of the other posters on this thread. However, it is well worth looking at. Note that the electric charge is balanced not by emitting a positron (as both you and I had conjectured) but by electron capture. Thus, the initial conditions have three particles not two. The PEP reaction is not merely a two proton collision, as indicated in your question.
The PEP reaction is actually a three body collision. It could only take place under very high pressure.
It occurs to me that the PEP reaction could take place even at a low temperature if the pressure is high enough. After all, there is a mass defect between deuterium and protonium. Energy would be given off once the two protons are joined together as deuterium. According to quantum mechanics, the protons can tunnel over the potential energy given enough pressure. Tunneling doesn't require kinetic energy, just density. Even if the protons were not moving at all, a force slowly pushing them together could cause fusion.
I don't know if this is actually the case in the center of the sun. I defer to those who know nuclear physics a bit more. It may be that the average kinetic energy of the protons in the center of the sun is sufficient to cause fusion. However, the PEP reaction would definitely be speeded up by the high density of electrons and protons. So I don't know whether most of the fusion in the sun is caused by pressure, temperature, or whether it requires both at the same time.
Thermodynamics applies to any system close to equilibrium. It applies even to nuclear reactions. In order to apply thermodynamics, one has to know something about both the pressure and the temperature. I am sure that pressure and temperature are fairly well defined quantities in the center of the sun. To see what reactions are likely to take place in the sun, one has to discuss both the pressure and the temperature.
In the PEP reaction, a neutrino has to be given off to preserve lepton number. Therefore, there has to be some extra energy necessary to supply a neutrino. There is also a spin condition necessary to preserve angular momentum. All these conditions raise the threshold of energy for this reaction to take place.
Also note that I used the word catalysis wrong. The electron is absolutely necessary for the reaction to take place. It doesn't merely speed up a reaction that would occur anyway at a slower rate.
http://en.wikipedia.org/wiki/Proton–proton_chain_reaction#The_pep_reaction
“The pep reaction
Proton–proton and electron-capture chain reactions in a star.
Deuterium can also be produced by the rare pep (proton–electron–proton) reaction (electron capture)”

I am not sure that there isn't a nuclear catalyst in the sun that speeds up the fusion of deuterium. I thought the carbon nucleus with six neutrons speeds up some of these reactions. There are other isotopes in the sun that speed up or slow down some nuclear reactions.
Regardless, the PEP reaction does not start with only two protons. It requires an electron to be present, too. Obviously, the PEP reaction can't occur unless the density of electrons is very big. I don't think TOKAMACK creates the conditions of a PEP reaction, even nearly.
I should of realized that the reaction in the sun involved electron capture, not positron emission. I think that I read about positron emission in one of Gamow's books. In any case, I should have checked.
Le' Chateliers principle applies to nuclear reactions as well as chemical reactions. Since the plasma in the center of the sun is under high pressure. The favored reactions are those that relieve this high pressure. Emitting a positron would only increase the pressure. Absorbing an electron would decrease the pressure. Therefore, electron capture is the more likely process. So PEP would be the more likely process under conditions of high electron pressure.

I did say that the two protons have to have enough energy to produce all particles necessary to satisfy all conservation laws. So the conservation laws do require some initial conditions to be satisfied.
Your argument is correct with regards to linear momentum. However, there is one caveat when you include angular momentum.
You are right, if you are talking about any state of the deuterium nucleus. However, the ground state of the deuterium nucleus has zero angular momentum. The deuterium nucleus in its center of mass frame has zero angular momentum. An off center collision of the two protons has an initial system with a nonzero angular momentum. Therefore, the result of a two proton collision that is off center has be an excited deuterium nucleus.
There is a limit to how much angular momentum one can put into a deuterium nucleus. At some threshold of angular momentum, the deuterium nucleus can't even form. So for very high relative velocities in an extremely off center collision, the deuterium can't form unless there is another particle around to carry off the angular momentum.

I have to thank both you and the posters who answered you. I didn't know about the PEP reaction before.

13. Jun 14, 2012

### Drakkith

Staff Emeritus
Sure, in the PEP reaction this happens, but given that it's ratio to normal PP reactions is 400:1 PP-PEP, I assumed we were talking about normal PP fusion.

Of course, quantum tunneling can indeed allow fusion well under the normal energy threshold. However it is very very rare once you fall significantly under the threshold, with the number of events falling to absolutely miniscule levels once you get to low temperatures. Miniscule as in one should happen every million to billion years. (Rough guess)

I believe the temperature in the core of the Sun is too low for the CNO cycle to have anywhere near the number of events has the PP chain does. In stars more massive than the Sun the CNO cycle is the primary source of fusion events.
Yes, I misunderstood what you meant. You did say "generate a deuterium nucleus and only a deuterium nucleus.". You are correct, a positron and a neutrino are indeed created along with the dueterium.

14. Jul 22, 2012

### Fast77

Wow, I didn't really read the entire post, only a few, but there's a mistake from the beginning. If you fuse 2 H atoms you get helium 2, not deterium which is hydrogen 2.

15. Jul 22, 2012

### Drakkith

Staff Emeritus
Not with normal hydrogen with only a proton in the nucleus. The proton-proton chain in stars fuses two hydrogen together, but one MUST change into a neutron. It does so by beta decay, emitting a positron and a neutrino. Otherwise the diproton immediately decays into two protons and no energy is released.

16. Jul 22, 2012

### Fast77

Ah, I knew I was missing something. I couldn't be the only one noticing a mistake.
Thanks for the clarification

17. Jul 22, 2012

### Darwin123

If there is such an isotope as helium 2, then it must be highly unstable. Protons are always positive. Therefore, there is a very big electrostatic repulsion between any two protons.
Neutrons are needed to make the helium nucleus stable. The strong force isn't strong enough to keep the two protons together unless there are a neutron to contribute.
The most common isotope of helium has two neutrons. The next most common isotope of has one neutron. You are hypothesizing a helium nucleus with no neutrons. I conjecture that this nucleus is impossible to form even in the sun.
Two protons and an electron can be fused together to form deuterium with the emission of a neutrino. The negative electron cancels out the positive charge of one of the protons.
This process of forming deuterium could hypothetically happen in the center of the sun where there is a high density of both protons and electrons. Of course, there is also a low density of neutrinos. So the emission of neutrinos is also quite likely.
If I am wrong, there is an isotope of helium with no neutrons that has been manufactured somewhere. This would be bigger news than the Higgs boson!

18. Jul 22, 2012

### Drakkith

Staff Emeritus
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