minimum energy for fusion

[observer1]

If we have a volume of hydrogen gas, when not heated, only collisions without much change in heat (say it is in room temp.)
If the volume is heated a bit, the collisions increase and the temperature of hydrogens in it also increase.
If even MORE heat is supplied, the electrons in the hydrogen leave the atom and get excited.
If WAY MORE energy is supplied, we might get nuclear fusion, (like what happens inside the sun), 
the volume is constant and the pressure increases with temperature.
The question is:- What is the minimum energy required for an atom (say carbon (or) hydrogen) to undergo fusion and below the energy, it undergoes excitation and collision
heating is basically giving the system energy

[swansont]

30 minutes ago, observer1 said:

The question is:- What is the minimum energy required for an atom (say carbon (or) hydrogen) to undergo fusion and below the energy, it undergoes excitation and collision

Which one, hydrogen or carbon? It’s different.

Nuclei have to overcome the Coulomb barrier (electrostatic repulsion) to get close enough to fuse. Two protons don’t fuse easily (you’d form He-2) but deuterium and tritium do; they require about 0.1 MeV.

It’s not an exact number, because the particles can tunnel through the barrier

[MigL]

While you would think you can fire protons at a target ion, say a Tritium nucleus, with enough K energy to get the two to fuse into a Helium nucleus, that process really doesn't happen because center of momentum frame considerations lead to a zero momentum Helium nucleus that is in an excited state, and the strong nuclear force breaks it down again.
So it isn't just the minimum energy that determines whether the two will fuse, but also the type of reaction.

Expanding on the above example, if you fire a Deuterium nucleus at a Tritium nucleus, then, in the center of momentum frame , you have two products, a neutron and a non-excited Helium nucleus, plus a release of energy.
And you have a viable fusion reaction.

[observer1]

15 hours ago, swansont said:

Which one, hydrogen or carbon? It’s different.

For carbon
 

 

15 hours ago, MigL said:

While you would think you can fire protons at a target ion, say a Tritium nucleus, with enough K energy to get the two to fuse into a Helium nucleus, that process really doesn't happen because center of momentum frame considerations lead to a zero momentum Helium nucleus that is in an excited state, and the strong nuclear force breaks it down again.
So it isn't just the minimum energy that determines whether the two will fuse, but also the type of reaction.

Expanding on the above example, if you fire a Deuterium nucleus at a Tritium nucleus, then, in the center of momentum frame , you have two products, a neutron and a non-excited Helium nucleus, plus a release of energy.
And you have a viable fusion reaction.

So i am guessing the reaction will occur only if the product is non-excited and that also depends on the TYPE of reaction. and it is also not an exact number but a range which depends on some initial conditions.

[observer1]

so what is the minimum kinetic energy i have to send a proton towards carbon atoms to form nitrogen?

[swansont]

The Coulomb barrier is given by U= kQq/r^2

Having 6x the charge means the barrier is 6x higher (It’s also wider, which would affect tunneling) so the naive solution would be that you need 6x the KE, but there are also momentum considerations since the masses are quite different.

But it will be of order a few MeV

[Leojames26]

That’s a really interesting question! Fusion, like what happens in the sun, requires an incredible amount of energy because you're essentially forcing atomic nuclei to come together, which naturally repel each other due to their positive charges.

To get to the point where fusion can happen, you need to overcome the Coulomb barrier, which is the energy barrier due to the electrostatic force between the positively charged nuclei. For hydrogen atoms, specifically, this happens at extremely high temperatures—like millions of degrees Kelvin.

In the core of the sun, where fusion happens naturally, temperatures are around 15 million degrees Kelvin. The minimum temperature needed to start fusion in hydrogen (like in a hydrogen bomb or in stars) is roughly in the range of 10-15 million degrees Kelvin.

To put it in terms of energy, you’re looking at needing around several keV (kilo electron volts) of energy per particle. For fusion in laboratory conditions, like in a tokamak or other fusion reactors, the conditions are even more extreme due to the lower density compared to the sun.

So, below these extreme temperatures (and corresponding energies), the hydrogen atoms won’t fuse—they’ll just get excited or ionized, which means electrons will leave the atoms and you’ll have a plasma, but not fusion. The energy levels required for ionization are much lower than those needed for fusion.

In short, the energy required for fusion is incredibly high, much higher than just causing excitation or ionization. It’s why we can have plasma at much lower energies, but actually achieving fusion is a whole other challenge.

[studiot]

On 7/4/2024 at 1:50 PM, observer1 said:

If we have a volume of hydrogen gas, when not heated, only collisions without much change in heat (say it is in room temp.)

How much hydrogen ?

5 molecules or 5 x 10²³ molecules ?

 

The problem is one of energy density, not of energy per se.

 

If you have enough gas (eg a big enough star)

The probability of a local collision achieving the necessary energy density is sufficient to iginite the process.

As the volume gets smaller the probability drops so you have to wait longer, maybe longer than the age of the universe.

So you supply some energy (not necessarily heat) to increase that probability to an acceptable level.

 

But you then run into the second and bigger problem.

Containment.

Gravity does this in a star.

But if you use a solid container the temperatures are so high that the walls would vapourise.

One alternative is to use the electromagnetic force instead of gravity.

Up to recently most efforts have been directed this way.

 

Another alternative is to use the fusing material itself and use kinetic or laser energy to create a collision somewhere within the body of the target material.

This is now being tried more often.

But the problem with this then becomes keeping the reaction going until it can become self sustaining.

 

So the amount of energy required depends upon exactly what you are trying to do.

[swansont]

3 hours ago, Leojames26 said:

To put it in terms of energy, you’re looking at needing around several keV (kilo electron volts) of energy per particle

That’s average energy per particle. Since you have a Maxwell-Boltzmann distribution, this will mean some fraction of the particles will have much higher energy, and can undergo fusion.

If you simply had two beams of protons with a few keV undergoing collisions, you wouldn’t get fusion.

[Mordred]

For fusion there is a useful relation that determines the ignition temperature called Lawson criterion.

https://en.m.wikipedia.org/wiki/Lawson_criterion

This is the point where fusion is self sustaining ie net energy exceeds supplied energy.

Edited August 24 by Mordred

[Leojames26]

On 8/24/2024 at 7:17 PM, swansont said:

That’s average energy per particle. Since you have a Maxwell-Boltzmann distribution, this will mean some fraction of the particles will have much higher energy, and can undergo fusion.

If you simply had two beams of protons with a few keV undergoing collisions, you wouldn’t get fusion.

You're right, the average energy per particle is just part of the story. In any gas, some particles will have much higher energy than others because of the Maxwell-Boltzmann distribution. It's those higher-energy particles that might actually manage to fuse, while the rest won't contribute much to fusion at all. That's why in practical scenarios like fusion reactors, we aim to push the overall energy so high — to increase the chances of these successful high-energy collisions. It’s quite a challenge to get enough particles up to those needed energy levels.