lowdown on scattering

Discuss how polywell fusion works; share theoretical questions and answers.

Moderators: tonybarry, MSimon

Post Reply
ohiovr
Posts: 431
Joined: Mon Mar 02, 2009 6:36 pm
Contact:

lowdown on scattering

Post by ohiovr »

Is scattering the reason why you can't just take 2 beams of fusion fuel plasmas, collide them and net 1000x energy out of them? How many worthless collisions typically happen?

ladajo
Posts: 6258
Joined: Thu Sep 17, 2009 11:18 pm
Location: North East Coast

Re: lowdown on scattering

Post by ladajo »

There are other instabilities that kick in once collisions start.
The development of atomic power, though it could confer unimaginable blessings on mankind, is something that is dreaded by the owners of coal mines and oil wells. (Hazlitt)
What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)

prestonbarrows
Posts: 78
Joined: Sat Aug 03, 2013 4:41 pm

Re: lowdown on scattering

Post by prestonbarrows »

For the most part, two separate beams colliding head on is the same as a single beam with twice the energy into a stationary gas target.

In general, the coulomb scattering cross-section is on the order of 100's of times that of the fusion cross section. This means that on average there are ~100 collisions for every fusion reaction. When two particles collide, both of their energies tend move towards their average energy. Assuming the ions colliding have the same mass, each collision with a stationary ion reduces the fast ion's energy by about half. In most cases, this means it only takes ~5 collisions to slow the beam ions down to energies where fusion is basically not possible. Even after one collision, the fusion cross section will be greatly reduced. Most of your input energy just goes into random particle motion (heating up the target).

Even with two opposing beams, the average momentum of an ion flying to the left and an ion flying to the right is zero. So, each time particles from the two beams collide, they will tend to loose energy. Again, most particles just rattle to a stop before fusing.

In addition to this fundamental limitation, there are more subtle instabilities that pop up with plasma beams. The two stream instability for example.

You most certainly can do fusion with beam-on-target and get lots of fast neutrons, you will just never ever produce net energy this way. Even the high performance machines specifically built to do this only get on the order of 1,000,000 times less fusion energy out than what you put in to accelerate the ion beam; there is not really any way around it.

That is also the general idea behind magnetic confinement schemes. If you have a bucket of ions which are all in thermal equilibrium, then on average collisions don't slow any particles down and don't really matter. Since they are prevented from touching the cold wall, they just keep scattering off each other, changing direction while keeping about the same average energy, until they fuse eventually.
Last edited by prestonbarrows on Thu Apr 17, 2014 4:14 am, edited 1 time in total.

ohiovr
Posts: 431
Joined: Mon Mar 02, 2009 6:36 pm
Contact:

Re: lowdown on scattering

Post by ohiovr »

Thanks that was very helpful

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: lowdown on scattering

Post by D Tibbets »

Coulomb collisions generally far outnumber fusion collisions. The relative rates are highly dependent on temperature. As the temperature increases the coulomb collisions decrease at close to the square of the temperature. Another way of saying this is that the Mean Free Path goes up as the square of the temperature. Increasing temperature from 10 KeV to 20 KeV increases the MFP by a factor of 4 and the Coulomb collision rate is 1/4th.

The fusion rate is a different animal. Due to the Fusion cross section curve dependency on temperature, the collisions that result in fusion goes up with higher temperatures within limits. For D-T fusion reactions at the peak of the cross section curve (~50 KeV) the fusion collisions occur ~ one tenth as frequently as Coulomb collisions. For D-D at ~ 100KeV the fusion collisions occur at ~ 1,000th the rate of Coulomb collisions. At ~10 KeV the D-D fusion collision rate is less than 1 millionth of the Coulomb rate.

You can play with these numbers and derive other parameters without knowing the details. For instance Bussard has said that an ion has to make ~ 10,000 passes (assume ~10,000 to 30,000 meters) for a reasonable chance at fusion. Knowing the temperature and thus the speed you can derive a consistent required ion confinement time- which is about 20,000 meters / ~200 KM/s speed = ~100 ms. At higher temperatures (like 90 KeV )the speed would be three times faster, so ~ 30 ms or less depending on the baseline that was used for this relationship- where Bussard anticipated the operational temperature and thus the cross section and the anticipated machine diameter for his baseline statement.

You can also presume what the MFP is. For D-D if the Coulomb collisions are ~ 1000 times more frequent and the distance traveled till fusion is ~ 20,000 meters, then the MFP would be ~ 20 Meters. From this you can make calculations of the rough average density, etc. All of the numbers are interrelated. There are all sorts of variations possible, so the estimates could vary widely, but they should be consistent with each other.

Dan Tibbets
To error is human... and I'm very human.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Re: lowdown on scattering

Post by D Tibbets »

While particle confinement , if longer than the mean time to fusion, then the Coulomb collisions are perhaps unimportant. But it is not that simple. First the thermal spread of the ions means some ions are more likely to fuse than others. In a thermalized plasma like in the tokamak, it is the small portion of significantly upscattered (hotter) ions that participate in the most of the fusions. Much of the cooler plasma is just along for the ride and any energy input to heat them to the average or cooler temperature is wasted, though with some possible gotches in this still simple viewpoint.

Particle confinement and energy confinement are not the same thing though. Due mostly to Bremsstruhlung radiation, even a very good particle confined plasma will continually cool, and energy input is needed to keep it hot. this relationship is different for Maxwellian thermalized plasma and non thermalized plasma, and is a primary reason why thermalized plasmas probably cannot successfully burn advanced fuels like D-He3 or P-B11. Even this though is not an absolute. If you can recover enough of the radiated energy losses you might be able to make up the margin. This might apply to the DPF approach if E. Learner's highly efficient direct x-ray conversion scheme works. Note that suggested quantum effects may also suppress the Bremsstruhlung losses in the DPF with it's stupendously strong magnetic fields during the pinch.

In the Polywell, even with a non thermalized plasma the Bremsstruhlung losses may still be too great for P-B11. Several other properties of the plasma like cold electrons in the center where the ion density is the greatest, and dilution schemes may be needed. It should be noted though that the somewhat uncertain ability to burn these difficult fuels implies that the simpler and more forgiving fuels like D-D or D-T are a piece of cake. Other concerns (mostly concerning neutrons) apply but from a simple Q perspective, machines that are considered as candidates for advanced fuels are already presumed to be past the baseline D-T breakeven target. This is of course all theory and predictions. Actual experimental confirmation is yet to be seen.

Dan Tibbets
To error is human... and I'm very human.

Skipjack
Posts: 6805
Joined: Sun Sep 28, 2008 2:29 pm

Re: lowdown on scattering

Post by Skipjack »

But then we have Rostoker, Monkhorst and also John Slough and the MSNW team that believe that colliding beam fusion is possible (though their approach does a lot more than just two colliding beams).

Post Reply