Talk-Polywell.org

How would you answer the following Polywell FAQ?

About how many times do the ions collide before a fusion event can occur?

It is simply the ratio of the cross-section for non-fusing collisions to the cross-section for fusion.

A sample calculation is as;

viewtopic.php?p=13240#13240

You can use the same method to establish total non-fusing collisions by sticking in the cross-section for non-fusing collisions.

So, e.g.;

Consider the proton-boron fusion collision at 550keV = 1.2barns = 1.2E-28m^2

Consider the proton-boron non-fusion collision at 550keV = 1E-20m2 = 1E8barns.

So for each individual particle moving through the medium at a given density, rho, so there will be a non-fusing collision every 1/(rho)(1E-20) meters of its track, and a fusing one every 1/(rho)(1.2E-28 ). The second distance gets longer and longer very quickly as the particle looses its energy.

So you see that a median proton has to undergo 1E8 collisions before getting to a fusion event, and that's presuming it keeps its 550keV energy - and it is clearly not going to keep that energy during 1E8 collisions.

This was why I put that point in my first post. It was roundly ignored, so I am now hiding out in the thickets with an occasional visit to amuse myself. This question seemed to bring me neatly full-circle to my very first post, so that is that!

The solution to "beam-target" [non-thermonuclear, high energy] fusion, like Polywell is attempting, is to keep that energy in the particle because the sum losses for the particle in 1E8 collisions is less than the fusion energy gained - i.e. net energy is still possible - but fusible protons will go 'cold' before it gets anywhere near a 'bulk fusion' outcome if there is no energy input back into each individual particle after each individual collision.

What we see in a fusor is the 10-sigma tail-end of particles that 'got lucky' on their first few collisions at high energy. And they are pretty lucky; the probability of a fusion is around the same as winning the lottery squared - that's like winning twice, on two consecutive weeks!

I also have avoided discussing the question of charge-exchange that is even worse than just loosing energy in one collision - the fast ion energy turns into a fast neutral and it's gone - you've lost it! I've posted with calculations on that topic also.

I would just post a link to the cross-sections. It's a question whose answer depends on a few different parameters that aren't given in the question. Maybe you could give a couple answers at different conditions/assumptions.

FWIW, Bussard says in Polywells, all neutrals in the reaction space are ionized in a very very short time (usecs iirc). I haven't seen anyone directly dispute that, that I can recall.

The problem of ions losing energy before fusion (downscattering) is solved by the fact there's a well; low-energy ions can't sit at the bottom without gaining energy from ions falling in the edge. The upscattered ions are supposed to anneal at the edge, so the energy doesn't leave the system. (Chacon and Nebel reportedly agree upscattering is a red herring in this kind of machine. There's some question whether you can maintain anything like a monoenergetic distribution, but Chacon's paper found large Q values to be possible in partially relaxed distributions.)

Chrismb's interpretation seems misleading (or at least confusing for me), though the numbers may be accurate.

To give a perspective on the rates/ lifetimes involved, lock at this link.
A straight forward method to calculate the fusion rate and a comparison of ion lifetimes before fusion in three systems:

http://fusedweb.llnl.gov/CPEP/Chart_pag ... Works.html

"Plasma Fusion Reaction Rate = R * n1 * n2

n1,n2 = Densities of reacting species (particles/m3); R = Rate Coefficient (m3/s).
Multiply by Ef to get fusion power density.
Discussion:

To calculate the rate of reactions per unit volume, multiply the rate coefficient, R, by the particle densities of the two reacting species (divide by two if there is only one species, in order to avoid double-counting the reaction possibilities). The p + p => D reaction rate coefficient in the sun is much lower than that achievable with a deuterium-tritium fuel mix, because the p + p reaction proceeds by the weak nuclear interaction. Despite the sun's high density, the low rate coefficient means a proton in the sun will exist for an average of billions of years before it fuses. By comparison, a deuteron in a magnetic fusion power plant would only exist for about 100 seconds, and a deuteron in an imploding, fully-burned inertial confinement pellet only for 1.0E-9 seconds".

These are all Maxwellian systems and do not incorporate the narrow energy spread and confluence benifits claimed for the Polywell

To see some real world numbers perhaps Chrismb can crunch some numbers from Jet. It produced ~ 15MW of fusion, Assume this would represent ~ 10 ^16 D-T fusions per second. Assume that Jet had a density of ~ 10^20 ions per cubic meter (generous number?), a volume of ~ 100 cubic meters (?) and a temperature of 5,000 eV ( actually I believe only a small tail of the Maxwellian distribution would have had an energy approaching this in Jet). Using 20 MW of input power to maintain this reaction should allow the effective containment time for the system to be calculated.
Compare the resultant numbers with the above.

Then throw in the added benefits in energy density that the Polywell can achieve (Dr Nebel mentioned ~ 60,000 fold advantage-due, I guess, to the increased particle density thanks to the Wiffleball trapping factor and some degree of ion focusing). For simplicity, assume the narrow energy distribution (non Maxwellian) claimed for the Polywell is counterbalanced by the advantages of burning D-T fuel in the Tokamac with a thermalized Maxwellian plasma.

Crunching these numbers should show the relations between real performance and things like derived perameters like MFP and fusion crossections. If they don't add up there is something wrong or missing.


As for neutral recombinations, I speculate that with the claimed narrow energy spreads at energies well above 10's of KeV, recombinations would be uncommon and short lived enough so that their effects would be tolerable. If most collisions occur the core or the border regions as claimed, and not in the mantle (in between regions) the effects on radial and angular spread would be further reduced. In the core collisions (weather between ions, or ions and neutrals) could not introduce much angular momentum. In the border the claimed annealing effects would also help the upscatering and down scattering effects (I'm uncertain if the claimed annealing effect has much effect on angular momentum spread(?).
Another way of stating it, is that in a large enough machine the distance a recombined neutral would travel before being re ionized would be so short in comparison to the diameter of a large machine, the effects would not be much different than the backgrounf ion- ion collisions. This is why Bussard claimed that the diassadvantages of the neutral gas puffers in WB 6 would dissappear once the machine grew to dimensions necessary for net power production.

I might (will) add that the distance traveled by a neutral before re ionization is so short compared to the machine diameter that a neutral created deep inside the machine would re ionize before escaping the machine. Only those neutrals that are born from recombined ions in the border (edge) regions could survive long enough to escape and the ions that birthed the neutral are at their lowest energies there so this would not be a path for significant energy loss.

Dan Tibbets

D Tibbets wrote: I might (will) add that the distance traveled by a neutral before re ionization is so short compared to the machine diameter that a neutral created deep inside the machine would re ionize before escaping the machine.

Outright guesswork! Why do you make this claim?

Try objective numbers;

viewtopic.php?p=21955#21955

chrismb wrote:

D Tibbets wrote: I might (will) add that the distance traveled by a neutral before re ionization is so short compared to the machine diameter that a neutral created deep inside the machine would re ionize before escaping the machine.

Outright guesswork! Why do you make this claim?

Try objective numbers;

viewtopic.php?p=21955#21955

From Bussards paper:
RESULTS AND FINAL CONCLUSIONS

"5. This requires that the ionization (of neutral gas) density within the machine be very
large relative to that outside; and this can be attained only by neutral gas injection directly
into the machine, followed by subsequent very rapid ionization of this gas, before it can
escape into the exterior region. In small machines this is difficult, as time scales for
neutral transport to the exterior are measured in fractions of a millisecond, and
dimensions within the machines are not sufficient to allow rapid ionization at the limited
electron currents and densities attainable. In large machines, such as power reactors
(typically 2-3 m in diameter) with high power electron drives (e.g. 100-500 Amps at 15-
30 kV for DD and 180-220 kV for pB11), it is easy to show that almost total ionization of
inflowing neutral gas can be achieved in a few cm of electron path length at the system
edge, but small devices can not reach this condition."

Ionization of cold neutrals would occur in a short distance. Hot neutrals created from hot ions deeper in the potential well may be another matter.

I don't know what the recombination rate would be under these conditions.
Are you sure you are not thinking of charge exchange reactions? If, so, remember that background neutrals will be in a small minority by a factor of ~ 1000- based on what Bussard claimed for the wiffleball traping factor which can maintain this ratio within the magrid- but only for charged particles, neutrals float freely throughout the system and need to be pumped out to maintain this ratio. This deficit of neutrals would severely limit recombinations [EDIT- sorry, I should have said charge exchange reactions] and their subsequent relative effects on ion flows.

[EDIT] Chrismb. In your reference to an earlier post you mention charge exchange - which means an ion and neutral changes places by transferring an electron. I assume a capture of a high speed electron to recombine with and neutralize an ion is an entirely different story and is what applies here. In an environment in which neutrals are rapidly ionized, to claim the reverse is a dominate process is counter intuitive.

Dan Tibbets

TallDave wrote:I would just post a link to the cross-sections. It's a question whose answer depends on a few different parameters that aren't given in the question. Maybe you could give a couple answers at different conditions/assumptions.

Can you provide the links and give some "answers at different conditions/assumptions"? This is totally out of my ken.

I might (will) add that the distance traveled by a neutral before re ionization is so short compared to the machine diameter that a neutral created deep inside the machine would re ionize before escaping the machine.

Yep, it seems pretty unlikely neutrals are going to carry off any significant amount of energy given how fast they ionize. It's not a fusor; the cathode is virtual and doesn't sit in a cloud of neutrals drifting around waiting to be ionized. Ionization energies are eV, fusion energies are keV. Even if you somehow got some (short-lived) neutrals at the edge, the ions out there are at their lowest energy.


Kite,

The basic concept is covered here: http://en.wikipedia.org/wiki/Nuclear_fu ... quirements

It would be interesting to calculate mean distance travelled per fusion in WB-7, 8 and 9 conditions (the last wold be very speculative of course). It would be a little bit of work. I think (?) you just need to get temp (voltage), density (function of B), fuel mix. But I need to sleep.

I recall Dr. B (or was it Rick?) said that there are 60 collisions per fusion in a pB11 machine (or was it D-D?).

Chris - I'm reluctant to give any credence to the numbers you present because I have seen you exaggerate by several orders of magnitude (in the bad direction) on other questions. i.e. pumping is technically "impossible".

[quote="MSimon"]I recall Dr. B (or was it Rick?) said that there are 60 collisions per fusion in a pB11 machine (or was it D-D?)....

Mmmm... I have heard that 1000 orbits/ passes are required for a fusion to occur. If 1 in 60 collisions are fusions, then one thousand passes would give 1 fusion collision and 60 coulomb collisions. In a 3 meter machine the ions would have ~ 50 meter MFP. Is that reasonable? Would that include the jumbling of the ions at the top of the well where the low energy thermalization is susposed to occur and where there is a higher claimed likelihood of collisions ( annealing process). Any focusing of ions towards the center, and different ion energies complicates trying to calculate the equivalent average density in the system.

Dan Tibbets

MSimon wrote:I recall Dr. B (or was it Rick?) said that there are 60 collisions per fusion in a pB11 machine (or was it D-D?).

Chris - I'm reluctant to give any credence to the numbers you present because I have seen you exaggerate by several orders of magnitude (in the bad direction) on other questions. i.e. pumping is technically "impossible".

I am dumbfounded [squared] that after so long on the forum I didn't realise how lacking is your understanding of the very basics of this whole bongdoogle; nuclear collisions.

It is an absolute fact that the ratio of the rate of fusing to non-fusing collisions is the ratio of the cross-sections for fusing to non-fusing collisions.

This is why you bother to measure collision reaction rates as 'cross-section' so that you can compare like-for-like - this is the very purpose of that measure!!!!

It is also the case that such numbers for cross-sections are easily and readily available, in the references I have so often repeated yet [it appears] have so often been ignored by people that seem to think physics is 'democratic' so that if enough people wish for a good bit of data then it must exist and so they don't have to bother to go look for it!

chrismb wrote:

MSimon wrote:I recall Dr. B (or was it Rick?) said that there are 60 collisions per fusion in a pB11 machine (or was it D-D?).

Chris - I'm reluctant to give any credence to the numbers you present because I have seen you exaggerate by several orders of magnitude (in the bad direction) on other questions. i.e. pumping is technically "impossible".

I am dumbfounded [squared] that after so long on the forum I didn't realise how lacking is your understanding of the very basics of this whole bongdoogle; nuclear collisions.

It is an absolute fact that the ratio of the rate of fusing to non-fusing collisions is the ratio of the cross-sections for fusing to non-fusing collisions.

This is why you bother to measure collision reaction rates as 'cross-section' so that you can compare like-for-like - this is the very purpose of that measure!!!!

It is also the case that such numbers for cross-sections are easily and readily available, in the references I have so often repeated yet [it appears] have so often been ignored by people that seem to think physics is 'democratic' so that if enough people wish for a good bit of data then it must exist and so they don't have to bother to go look for it!

Some preaching, but no wrestling with numbers to support your position this time.

Lets see, using the high vacuum numbers from

http://en.wikipedia.org/wiki/Mean_free_path

My estimate of 50 meters MFP is probably in the ballpark. Since the ions are supposedly not in a Maxwellian distribution and there is supposed to be confluence towards the center, I'm not sure how close the calculation presented in Wikipedia will get you.

Using these guestimate numbers:
MFP=~100 m
Speed =1,000,000 m/s
fusion to coulomb collision ratio of 1/60 (this seems very generous to me but I cannot argue it).

Then the 'average ion' would have a coulumb collision 10,000 times per second , and would survive for ~ 150 milliseconds before it fused (10,000 coulomb collisions/s divided by 60 coulomb collisions/ fusion collision).
This seems to be a good range to fit in the numbers I referenced in another thread- where the lifetime to fusion of a typical ion was ~ 800 seconds in a Tokamac and ~ 1 nanosecond in an implosion devise (bomb). If the Polywell has a energy density ~ 60,000 times that of Tokamacs (or is that Tokamaks?) as claimed by Nebel, again the numbers seem to make sense(or are at lest consistent).

Dan Tibbets

chrismb wrote: the very basics of this whole bongdoogle; nuclear collisions.

It is an absolute fact that the ratio of the rate of fusing to non-fusing collisions is the ratio of the cross-sections for fusing to non-fusing collisions.

Can you direct me to a reasonable complete source for both the fusion cross sections and the collision cross sections? Being totally outside my field, I really haven't the foggiest where to start; and for once, Wikipedia hasn't helped.

Thanks

D Tibbets wrote: Some preaching, but no wrestling with numbers to support your position this time.

Where do you people come from?

I gave you numbers above, and everyone else has thrown their own guesses at it. What do you *mean* I haven't given numbers!!!!!!!!!!!!!!!!!!

I am the only one that *HAS* given numbers!!!

Your "mfp"s, &c., are just guesses. The reaction cross-section IS the reaction rate. That's what the ferkin' thing MEANS!!!! Don't you understand the very very most basic of basic elementary simple as simple-can-be concepts of particle physics??!

A typical cross-section for coulomb collisions is around 1E-20/m2 yet for *high yield* fusion event it is around 1E-28/m2. Geez, the best fusion rate there is is DT that peaks at 5E-28/m2 yet the electric size of a deuteron is 7 orders of magnitude bigger.

No matter how much wishful thinking and handwaving you wish to put into this, this is the reality of nuclear fusion - it is a very very unlikely event compared with other nuclear interactions.

KitemanSA wrote:

chrismb wrote: the very basics of this whole bongdoogle; nuclear collisions.

It is an absolute fact that the ratio of the rate of fusing to non-fusing collisions is the ratio of the cross-sections for fusing to non-fusing collisions.

Can you direct me to a reasonable complete source for both the fusion cross sections and the collision cross sections? Being totally outside my field, I really haven't the foggiest where to start; and for once, Wikipedia hasn't helped.

Thanks

The plots for fusion have been printed up here many many times, but sufficed to say that all the 'good' ones are of the order of units of Barns (a Barn is 1E-28/m2).

In regards non-fusing collisions, there are many varieties with ionisation being dominant at low energies, Coulomb collisions gaining ground at fusion energies, and various other lossy reactions that can go on.

As I have referenced before, you need to read up 'Massey: Atomic Collisions' - this is the bible. For data go to http://www.nndc.bnl.gov/ and fish around for the particular thing you are after (if my 1:1E8 generalisation isn't to your taste). I'm sure you'll figure it out.