Looking at ion-ion scattering, it seems a worst case interaction leaves one ion at rest in the center of the electrostatic well, and a second ion flying out with twice nominal energy. If well depth is matched to nominal ion energy (plus a small margin) the second ion escapes with the energy. However it occurs to me that if the well depth was twice the nominal ion energy the up scattered ion is contained, and annealing in the low ion energy regions can re-normalize it. Which leaves a problem of introducing ions at a depth inside the well. I'm thinking a properly engineered jet of gas ionized at the proper depth inside the well should do it.
On the other hand, I don't know how severe up-scattering will be and whether such means will be needed or worth the trouble.
worst case scattering and deeper wells
Typical coloumb logarithms for reactor plasmas are about 20, this mean that for every 20 90 degree collisions that result from an accumulation of small collissions, 1 will be the result of a single large collission, what fraction of these simply result in both ions changing their direction without significantly changing their speed and what fraction will qualify for your worst case scenario, I do not know.
Worth mentioning increasing the well depth is not for free, the deeper you make the well the harder the electrons will push against the field, so at a given field strength, if you double the well depth you may have to half the electron density, which inturn requires you to halve the ion density, with in turn reduces fusion power by a factor of 4.
Also worth mentioning, annealing in the low energy region will not be as efficient for ions that overshoot significantly. How annealing works is that when the ions slow down, their cross-section for collision balloons, annealing works when all the ions slow down in the same region. This region represents a paperthing film where all the ions are moving very slowly with very high crossections for collission. If an ion is significantly upscattered it will shoot through this region like a bullet through paper and will have a much smaller cross-section than the other ions, infact, since the annealing region is at a significantly lower density than the core region, for ions that have been suddenly and significantly upscattered, collisions in the core are likely to dominate collisions in the edge so these ions may infact experience no annealing effect at all.
One method I considered would be to inject atoms in through a gas nozzle and have a laser continuously firing in the electrostatic sheath region, the laser would be finetuned to excited the gaseous atoms into a high n state (n=40 say) since the electric field is a fuction of position in the polywell by adjusting the wavelength of the laser you could determine exactly which wavelength the electric field was strong enough to ionize the atoms, this might offer great control over their birth energy.
Worth mentioning increasing the well depth is not for free, the deeper you make the well the harder the electrons will push against the field, so at a given field strength, if you double the well depth you may have to half the electron density, which inturn requires you to halve the ion density, with in turn reduces fusion power by a factor of 4.
Also worth mentioning, annealing in the low energy region will not be as efficient for ions that overshoot significantly. How annealing works is that when the ions slow down, their cross-section for collision balloons, annealing works when all the ions slow down in the same region. This region represents a paperthing film where all the ions are moving very slowly with very high crossections for collission. If an ion is significantly upscattered it will shoot through this region like a bullet through paper and will have a much smaller cross-section than the other ions, infact, since the annealing region is at a significantly lower density than the core region, for ions that have been suddenly and significantly upscattered, collisions in the core are likely to dominate collisions in the edge so these ions may infact experience no annealing effect at all.
One method I considered would be to inject atoms in through a gas nozzle and have a laser continuously firing in the electrostatic sheath region, the laser would be finetuned to excited the gaseous atoms into a high n state (n=40 say) since the electric field is a fuction of position in the polywell by adjusting the wavelength of the laser you could determine exactly which wavelength the electric field was strong enough to ionize the atoms, this might offer great control over their birth energy.
Even in the vast majority of those cases, it won't have the right trajectory. I would imagine most will end up on long spirals that bleed their momentum to the high-density, low-energy ions at the edge of the well such that they cannot escape.If well depth is matched to nominal ion energy (plus a small margin) the second ion escapes with the energy.
From the Valencia paper:
Ions spend less than 1/1000 of their lifetime in the dense, high energy but low cross-section core region, and the ratio of Coulomb energy exchange cross-section to fusion crosssection is much less than this, thus thermalization (Maxwellianization) can not occur during a single pass of ions through the core. While some up- and down- scattering does occur in such a single pass, this is so small that edge region collisionality (where the ions are dense and “cold“) anneals this out at each pass through the system, thus avoiding buildup of energy spreading in the ion population (Ref. 14). Both populations operate in non-LTE modes throughout their lifetime in the system. This is an inherent feature of these centrally-convergent, ion-focussing, driven, dynamic systems, and one not found (or even possible) in conventional magnetic confinement fusion devices.
You can get it here.TallDave wrote:BTW does anyone have a copy or a link to the referred doc?
[14]. Bussard R.W. and King K.E., “Bremmstrahlung and Synchrotron Radiation Losses in Polywell™ Systems“, EMC2 Technical Report 1291-02, December 1991.
This is interesting too:
http://stinet.dtic.mil/cgi-bin/GetTRDoc ... tTRDoc.pdf
http://stinet.dtic.mil/cgi-bin/GetTRDoc ... tTRDoc.pdf
Lots of fun equations therein. Bussard seems to claim transverse momentum will generally get knocked into radial momentum.FUSION LIFETIME LIMITS ON ION UPSCATTERING
All of the effective fusion reactions will take place where the ion density and energy are both large. This is well within the radial position r = 0.83R over which the ion density scales as the inverse square af the radius, thus the fusion rate Qf can be evaluated without significant error by use of n(r) = n¢(r/r)2 for r > r and n(r) = nC for 0 < r < re.
...
However, other mechanisms ARE available to provide a limit on the maximum value of f. These are the isotropizing collisional effects which will occur in scatterings that take place in both the outer edge region 4 of the system and in the central ion core5 . The outer edge isoscattering will act to transform transverse momentum into radial momentum within a limiting value of f set by a balance between core Maxwellianization upscattering time and edge energy exchange collision time. The core isoscattering will transform transverse into radial momentum at the same rate as core collisional upscattering, if the energy distribution function of the core ions rises with increasing transverse energy. This is the case for the SCIF ECRH-driven ion source, but is not the case for the source distribution used in the EKXL code; this is a square function for which no net momentum transformation can occur in core scatterings.
I had a long talk with Luis Chacon about the ion scattering a few weeks back. We concluded that for the Polywell, these issues were a red herring. The reason is that the densities are so high in the Polywell that you really don't need the ion focussing to be all that good. If you are running a gridded system where particles are lost every 20 passes or so, then it is an issue. For the Polywell, the electron recirculation fraction appears to be ~ 1e5 so the effective energy loss from the electrons is small. Consequently, you don't need huge focussing to get the density high.
Tall Dave:
There's really nothing to tell at this point. We don't yet have enough power yet to get into the regimes of interest. There are some circuit issues that we are dealing with. We don't want to get too gung-ho too soon and start breaking things. We're on such a tight schedule that we can't afford to make any mistakes. If we do, we won't have time to recover. This is not the way one would like to run a program, but you have to play the cards you're dealt.
There's really nothing to tell at this point. We don't yet have enough power yet to get into the regimes of interest. There are some circuit issues that we are dealing with. We don't want to get too gung-ho too soon and start breaking things. We're on such a tight schedule that we can't afford to make any mistakes. If we do, we won't have time to recover. This is not the way one would like to run a program, but you have to play the cards you're dealt.
Dr. Mike - concur.
If you are really in a hurry take your time.
My rule of thumb is 5 days planning 2 days work.
The projects I have worked on always went better if I checked every thing out before I turned on the main switch. I spent a lot less time debugging.
The Navy teaches that as well. Always evaluate the situation before you take action. Boyd also taught that in the Air Force in what he called the OODA loop. Observe. Orient. Decide. Act. I first saw that in a Navy manual in the late 70s.
If you are really in a hurry take your time.
My rule of thumb is 5 days planning 2 days work.
The projects I have worked on always went better if I checked every thing out before I turned on the main switch. I spent a lot less time debugging.
The Navy teaches that as well. Always evaluate the situation before you take action. Boyd also taught that in the Air Force in what he called the OODA loop. Observe. Orient. Decide. Act. I first saw that in a Navy manual in the late 70s.
Engineering is the art of making what you want from what you can get at a profit.