Nuclear fusion using a plasma jet

[timbot]

As per a previous thread, if you fire two plasma jets of deuterium at each other at high enough relative velocity, the deuterons would collide and fuse into helium.

Does anyone know what is the relative velocity in kilometers per hour necessary for deuterons hitting each other head on to fuse into helium?

How is this calculated?

 

[hamster143]

As calculated in the previous thread, you're looking at velocities of ~500 km/s, whether for hydrogen or deuterium (square root of two or 40% lower for deuterium, which does not help all that much) and we don't know how to accelerate macroscopic objects to this kind of speed ... Note that there's no minimum fusion "threshold", but probability of fusion between two nuclei goes up quickly as you add more energy.

There's an easy way to accelerate individual ions, you basically strip the deuterium atom of electrons and stick it into strong electric field, tens of kilovolts ... if you create a vacuum chamber with two concentric electrodes, apply 10 kV between electrodes, and put a small quantity of deuterium gas into the chamber, you _will_ see fusion events, but, to the best of our knowledge, this process can't be optimized to result in net production of energy.

 

[timbot]

Hi Hamster143,

The reason i keep hammering this point is that I have thought of a method to accelerate plasma jets to a very high speeds, using an accelerating magnetic field.

The figure you mentioned is in the realm of feasibilty.

Half of 500 km/s for each plasma jet is 250 km/s (directed against each other). Times 60% for deuterium is 150 km/s. That is 540,000 km per hour.

Now if you want only 1% of the plasma jet to fuse, a statistician friend told me you can reduce the averge velocity to 25% of 540,000 km/hour, or 135,000 km/hour, assuming a normal distribution of particle velocities.

A plasma accelerator which can accelerate plasma to an average speed of 135,000 km/hour is well within the realms of feasibility.

I think continuous commercial plasma fusion is quite feasible if you direct two high speed plasma jets of deuterium againast each other.

 

[Bob_for_short]

Thirty years ago, when I was a young researcher, I was told that one of our colleagues (Leopold Skripnik) had already proposed (theoretically) a “solid-state/beam thermonuclear reactor”. Indeed, he took a solid target and a fast beam of deuterons or so, I do not remember now. He calculated the efficiency of such a system. In a solid body the charged projectile loses its energy but can provoke an energy release due to fusion. He found that starting from some energy the losses are smaller than the gain but nobody believed it. In fact, it is a question of efficiency. Theoretically it is possible in a solid target. I do not know how about two colliding jets, where there is a region of their velocities to make the fusion energy release superior to projectile energy losses.

 

[Bob S]

The reason i keep hammering this point is that I have thought of a method to accelerate plasma jets to a very high speeds, using an accelerating magnetic field...I think continuous commercial plasma fusion is quite feasible if you direct two high speed plasma jets of deuterium againast each other.

I have never seen or read of magnetic acceleration of any charged particles except electrons. Are you talking about a "betatron" accelerator for deuterons? See
http://en.wikipedia.org/wiki/Betatron
I have seen and used 14.1 MeV neutrons from (I think) 300 KeV deuterons hitting a tritiated tantalum (or tungsten) target yielding D-T fusion, but it was extremely inefficient, like maybe 1 neutron per million deuterons or worse.

 

[Bob_for_short]

I have seen and used 14.1 MeV neutrons from (I think) 300 KeV deuterons hitting a tritiated tantalum (or tungsten) target yielding D-T fusion, but it was extremely inefficient, like maybe 1 neutron per million deuterons or worse.

300 KeV is too small energy for the projectile to get a reasonable efficiency. It should be increased by a factor of 100 or even more.

 

[Bob S]

300 KeV is too small energy for the projectile to get a reasonable efficiency. It should be increased by a factor of 100 or even more.

So you're saying 30 MeV. Is this per beam in the center of mass, or deuterons on a fixed (stationary) target? What is the fusion cross section there? Considering that the energy release including neutrons in D-T fusion is only about 17 MeV, it is hard to visualize break-even power output with 30 MeV beams.

 

[Astronuc]

300 KeV is too small energy for the projectile to get a reasonable efficiency. It should be increased by a factor of 100 or even more.

Not for fusion. Look at the kinetic energies of the reactants for the Q values of the reaction and those are in the low MeV range, so it is impractical to accelerate deuterons much beyond 1 MeV in order to induce fusion. The optimal temperature for d+d fusion is around 500 keV - 1 MeV, and with diminishing returns one would probably want a temperature on the order of 300-400 keV.

d + d -> T (1 MeV) + p (3 MeV), or 3He (0.82 MeV) + n (2.45 MeV)

Colliding beams have been considered. With losses due to scattering, I believe the concept was found to be impractical.

Another consideration is the neutrality of plasma. Usually injected deuterons are neutralized, otherwise the local positive charge can induce plasma instability as well as dispersion of the deutron beam. So either one collides neutral deutron beams or one has to add similar current so electron beams to the reation volume.

 

[Bob_for_short]

So you're saying 30 MeV. Is this per beam in the center of mass, or deuterons on a fixed (stationary) target? What is the fusion cross section there? Considering that the energy release including neutrons in D-T fusion is only about 17 MeV, it is hard to visualize break-even power output with 30 MeV beams.

I really do not know all the numbers - I never did it myself. But what is necessary to reach is to obtain the thermo-nuclear reaction for sure and recuperate as much of lost energy as possible. I do not know details of his calculations. Anyway, all energy release is then used in a heat machine with a known efficiency so there may be some positive output.

 

[hamster143]

300 KeV is too small energy for the projectile to get a reasonable efficiency. It should be increased by a factor of 100 or even more.

DT fusion cross section peaks at ~60 KeV CM:

http://media.photobucket.com/image/...on6808/FusionCrossSections-grid-81pct-l-1.jpg

 

[Bob_for_short]

DT fusion cross section peaks at ~60 KeV CM

Yes but one has to diminish the losses too. The loss cross section may decrease faster with E than the reaction cross section. Besides, I do not know what target and what projectile Leopold used in his calculations.

 

[Bob S]

DT fusion cross section peaks at ~60 KeV CM:

http://media.photobucket.com/image/...on6808/FusionCrossSections-grid-81pct-l-1.jpg

Hi Hamster
Yes, but the integrated cross section. from incident deuteron beam energy of ~300 KeV to zero energy in a tritiated target, has the greatest probability of producing a D-T fusion reaction.
Bob S

 

[timbot]

For more information about the plasma acceleration device I have designed, go to my blog
http://collidingplasmafusion.blogspot.com

 

[dswill]

Would the d-d cross section graph be the same for magnetic confinement as for inertial confinement? What about cold fusion? In fact I'm struggling a bit with the concept of cross-section. It doesn't seem to mean just the physical measurement of the area of a 'cross-section'. Correct?

It seems from some things I've been reading that the cross-section is dependent on the process, or derived from the experimental reaction rate rather than the physical dimensions of the deuteron. (E.g. http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/nucrea.html#c3; http://www.iupac.org/goldbook/R05169.pdf; http://fds.oup.com/www.oup.co.uk/pdf/0-19-856264-0.pdf at p.3)

DT fusion cross section peaks at ~60 KeV CM:

http://media.photobucket.com/image/...on6808/FusionCrossSections-grid-81pct-l-1.jpg

 

[Bob_for_short]

...In fact I'm struggling a bit with the concept of cross-section.

We speak of scattering cross sections or of reaction cross sections. It is not an atomic size squared. It is a process-dependent thing and is determined as a ratio of the reaction output within a certain solid angle to the incident particle (projectile) flux.

 

[Bob S]

Lawrence Berkeley Lab, in conjunction with Lawrence Livermore Lab, at one time built a rotating target neutron source (RTNS) that produced a 5 milliamp beam of deuterons at 400 KeV hitting a tritiated target.
RTNS rotating target 5 ma 399 KeV euerium
http://www.nuc.berkeley.edu/research/fusion/belgr1.pdf
see also
http://accelconf.web.cern.ch/accelconf/p79/PDF/PAC1979_3058.PDF

Bob S

 

[dswill]

So the cross-section of d-d would be different for a tokamak than for the NIF or cold fusion? I'd like to try to compare these. Does anyone know of good sources online or a primer of sorts? Or a source that explains why cross-section is not atomic radius squared? Thank you greatly.

We speak of scattering cross sections or of reaction cross sections. It is not an atomic size squared. It is a process-dependent thing and is determined as a ratio of the reaction output within a certain solid angle to the incident particle (projectile) flux.

 

[Bob S]

So the cross-section of d-d would be different for a tokamak than for the NIF or cold fusion? I'd like to try to compare these. Does anyone know of good sources online or a primer of sorts? Or a source that explains why cross-section is not atomic radius squared? Thank you greatly.

See Fig 1.4 on pdf page 6/9 in for cross section plots of D-D and D-T reactions.
http://www.tdr.cesca.es/TESIS_UPC/AVAILABLE/TDX-0114104-103202//05CAPITOL1.pdf
10^-28 m² is 10^-24 cm² = 1 barn is more than geometric for a proton (~ 60 millibarns).

(It is very difficult to find appropriate physics papers that are not pay per view)

Bob S

 

[Astronuc]

So the cross-section of d-d would be different for a tokamak than for the NIF or cold fusion? I'd like to try to compare these. Does anyone know of good sources online or a primer of sorts? Or a source that explains why cross-section is not atomic radius squared? Thank you greatly.

One would have to compute the temperatures of the d-d plasma under NIF or cold fusion conditions.

One thought on cold fusion was that the palladium atoms, or rather the electron field around the palladium nucleus, somehow allowed the deutrons to approach each other so that the fusion reaction could occur at lower temperature.

 

[mheslep]

http://books.google.com/books?id=7k...age&q=deuterium coulomb cross section&f=true"

The fusion scheme described by the OP is typically called beam-beam or accelerator based fusion. These approaches can produce fusion, but they are hopelessly inefficient. The problem is that the coulomb (or Rutherford) scattering cross section is 1000x, maybe 10000x greater than the fusion cross section for a given beam/plasma energy, as indicated in Figure 11.3 of the reference. This means for every collision that succeeds in producing fusion, another 1000 will 'bounce' away. These bounced ions have begun to 'thermalize', or trend towards the average energy (temperature) of all the particles in the system, at which point we no longer have a beam with which to smash into something.

Say the beam energy per ion is 50 keV, well up towards the sweet spot for D+T fusion cross sections. Then every successful D+T fusion releases 17 meV, but on average it required ~1000 x 50keV, or 50meV to be wasted.

 

[dswill]

That's what I suspected. What I'm looking for is a book or article to help me study those calculations for cross sections specifically for cold fusion or beam-target studies (perhaps focusing on Oppenheimer-Phillips or electron screening). But I don't have access to college libraries or online pay journals, only the NY public library. I guess I should first ask what physics journals are available online and then search those myself?

One would have to compute the temperatures of the d-d plasma under NIF or cold fusion conditions.

One thought on cold fusion was that the palladium atoms, or rather the electron field around the palladium nucleus, somehow allowed the deutrons to approach each other so that the fusion reaction could occur at lower temperature.

http://books.google.com/books?id=7k...age&q=deuterium coulomb cross section&f=true" * * *

 

[mheslep]

That's what I suspected. What I'm looking for is a book or article to help me study those calculations for cross sections specifically for cold fusion or beam-target studies (perhaps focusing on Oppenheimer-Phillips or electron screening). But I don't have access to college libraries or online pay journals, only the NY public library. I guess I should first ask what physics journals are available online and then search those myself?

Tom Dolan's University of Illinois 421 class:
http://npre421.ne.uiuc.edu/

MIT also has their undergrad physics curriculum online.

 

[timbot]

http://books.google.com/books?id=7k...age&q=deuterium coulomb cross section&f=true"

The fusion scheme described by the OP is typically called beam-beam or accelerator based fusion. These approaches can produce fusion, but they are hopelessly inefficient. The problem is that the coulomb (or Rutherford) scattering cross section is 1000x, maybe 10000x greater than the fusion cross section for a given beam/plasma energy, as indicated in Figure 11.3 of the reference. This means for every collision that succeeds in producing fusion, another 1000 will 'bounce' away. These bounced ions have begun to 'thermalize', or trend towards the average energy (temperature) of all the particles in the system, at which point we no longer have a beam with which to smash into something.

Say the beam energy per ion is 50 keV, well up towards the sweet spot for D+T fusion cross sections. Then every successful D+T fusion releases 17 meV, but on average it required ~1000 x 50keV, or 50meV to be wasted.

I have noted the comments of 'mhslep' above. Mhslep says that beam-beam based fusion is hopelessly inefficient because every collision that succeeds in producing fusion, another 1000 will 'bounce' away.

It appears that the basis of this misunderstanding is the use of the term 'beam-beam'. Obviously in the past physicists have been used to only beam collision experiments and this has constrained their thinking.

What I am talking about is the collision of dense plasmas. If this happens, even if only one in 1000 collisions succeed in producing fusion, you will still succeed in producing usable fusion.

Now the core of the hslep's argument is in his second pargraph. Yes, D+T fusion appears to be hopelessly inefficient according to these calculations. Deuterium needs to be accelerated to very high velocities to achieve fusion.

However Hydrogen has a coulomb barrier of of one thirtieth of Deuterium, I believe. So the beam energy per ion required is one thirtieth of 50 kev, or 1.6 kev. Massively smaller. The energy output tips in favour of hydrogen collisions.

Yes, the hydrogen fusion reaction is a p + p reaction, and this requires several steps to complete the fusion process. [reference to personal theory deleted]

So a step by step fusion reaction dies out under low plasma densities because of the improbability of collision of the various required particles. However you can increase the probababilty of a sustained hydrogen fusion reaction if you increase the density of the plasma. INCREASING THE DENSITY OF THE PLASMA IS THE KEY TO THE FUSION OF HYDROGEN.

And this is why those experiments fixated on low density particle beams got nowhere. (Indeed Tockamacs cannot sustain very high densites for a useful period of time).

However high density head-on hydrogen plasma beams will fuse! High density plasma beams supplying the plasma density which exists at the centre of the sun are certainly feasible. And this can produce continuous energy output.

[reference to personal theory deleted]

 

[mheslep]

...

However Hydrogen has a coulomb barrier of of one thirtieth of Deuterium, I believe. So the beam energy per ion required is one thirtieth of 50 kev, or 1.6 kev. Massively smaller. The energy output tips in favour of hydrogen collisions.

No, see the definition of the coulomb barrier here
http://en.wikipedia.org/wiki/Coulomb_barrier
The energy barrier depends on charge and distance, not mass, so protons and deuterium have the same coulomb barrier at a given distance. The fusion cross section, i.e., the likelihood of fusion given an encounter, depends on other factors besides besides this barrier, and it turns out proton-proton fusion is dramatically less likely to occur at a given energy level than is d-d or d-t fusion.

However you can increase the probababilty of a sustained hydrogen fusion reaction if you increase the density of the plasma. [...]

Yes, that's true. But the the 1000:1 ratio given above does not depend on density. As the fusion rate goes up with density, so does the scattering loss.

 

[Vanadium 50]

I have removed the references to personal theories here. Please, let's try and keep this within PF guidelines.

Timbot, your argument that Tokamak scientists got it all wrong would be bolstered if you would devote more effort into studying what they have actually done. Or at least studied it enough to spell Tokamak correctly.

 

[Astronuc]

However Hydrogen has a coulomb barrier of of one thirtieth of Deuterium, I believe. So the beam energy per ion required is one thirtieth of 50 kev, or 1.6 kev. Massively smaller. The energy output tips in favour of hydrogen collisions.

Incorrect. A deutron and proton have the same charge. The Coloumb barrier is essentially the same - particularly at the atomic scale.

Yes, the hydrogen fusion reaction is a p + p reaction, and this requires several steps to complete the fusion process. [reference to personal theory deleted]

Yes - one can see this in the pp-cycle of stars.

So a step by step fusion reaction dies out under low plasma densities because of the improbability of collision of the various required particles. However you can increase the probababilty of a sustained hydrogen fusion reaction if you increase the density of the plasma. INCREASING THE DENSITY OF THE PLASMA IS THE KEY TO THE FUSION OF HYDROGEN.

Step by step processes occur in stars, e.g., the Sun where the core pressures are about 200-340 billion atmospheres. The best we can possibly do on Earth is about 70 atm in a confined magetic field. In the Suns core, the plasma density is about 150 grams per cubic centimeter, nearly 15 times the density of lead, and even with that, the probability of pp fusion is quite low.
Ref: http://www.nasa.gov/worldbook/sun_worldbook.html
http://hyperphysics.phy-astr.gsu.edu/hbase/astro/procyc.html

And this is why those experiments fixated on low density particle beams got nowhere. (Indeed Tockamacs cannot sustain very high densites for a useful period of time).

However high density head-on hydrogen plasma beams will fuse! High density plasma beams supplying the plasma density which exists at the centre of the sun are certainly feasible. And this can produce continuous energy output.

Quite incorrect, and technically unfeasible!

 

[timbot]

OK. However given what is now the immediate necessity of finding a way to create usable hydrogen fusion, I would have thought it is worth a try. Tokamacs (see I have spelt it right!) have not worked, and without wanting to sound nasty, have over the past 50 years provided little more than a pension to the participants. And building bigger ones will fare no better.

With all due respect to these obviously knowledgeable physicists, proving something 'mathematically' that it will not work is falling into the same trap as Lord Kelvin, who proved mathematically that the sun will expire in one million years and mechanical flight was impossible. What is needed now is experiment to see if there is something in this idea, as all alternatives have proved a dead end. On the density issue, I am pretty sure that if you accelerate the plasma at a high enough rate, you will momentarily achieve half the density required for fusion. (Remember you are talking about a head-on collision).

 

[Astronuc]

OK. However given what is now the immediate necessity of finding a way to create usable hydrogen fusion, I would have thought it is worth a try. Tokamacs (see I have spelt it right!) have not worked, and without wanting to sound nasty, have over the past 50 years provided little more than a pension to the participants. And building bigger ones will fare no better.

With all due respect to these obviously knowledgeable physicists, proving something 'mathematically' that it will not work is falling into the same trap as Lord Kelvin, who proved mathematically that the sun will expire in one million years and mechanical flight was impossible. What is needed now is experiment to see if there is something in this idea, as all alternatives have proved a dead end. On the density issue, I am pretty sure that if you accelerate the plasma at a high enough rate, you will momentarily achieve half the density required for fusion. (Remember you are talking about a head-on collision).

One cannot direct individual particles in a beam with dead-on accuracy for a head-on collision. One is inherently constrained by the physics of particle collision and the technical constraints of the materials with which one has at hand.

The physics
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/impar.html#c1

The technical contraints relate to the maximum pressure one can achieve with the maximum magnetic field or the material strength of the magnet/supporting structure, whichever is limiting.

Even under the most ideal conditions in the sun - which we cannot reproduce by any man made object (while we can accelerate protons to necessary energy (100 keV), but we cannot reproduce the particle densities of the sun) - protons cannot exist for something like millions of years and not fuse by p-p, which is the rate limiting step in the pp-chain.

 

[mheslep]

With all due respect to these obviously knowledgeable physicists,

To be clear I am not a physicist, I'm an electrical engineer by training.

 

[timbot]

I apologize to everyone for my outburst.

However I feel that if an experiment is conducted to collide dense plasmas (not beams), I am sure that fusion will be detected at even quite low velocities i.e. gamma rays etc. The question is, as you increase the speed of collision will the rate of fusion increase faster than the speed? If so, all this stuff about "cross-sections" will have neglected some very important points.

Given the importance of the subject, and yes, the complete failure of the Tokamacs for all practical purposes, (except maybe some experimental results), I strongly suggest that experiments should be conducted along the lines proposed.

A final warning. This site is US of A centric. But I am not from the USA. Other readers, such as the Chinese, are on to this site also. Somebody (some country) is going to get in first. Now I personally would have no objection. The result would benefit the world. But this result would be egg on the face of the Lawrence Livermore labs, Los Alamos, Chicago, etc. Wouldn't it?