Important point, the thermal motion is not totally chaotic. There are two considerations. Coulomb scattering collisions can result in two processes- up scattering and down scattering collisions, and transverse or angular momentum changing collisions. One aspect of the Polywell is that there is some confluence or central focus of the ions. How much is debatable, but there will always be some. As such , any Coulomb collisions that occur near the center cannot induce as much angular momentum randomization, compared to collisions away from the center. With confluence in the spherical geometry, the density in the center is greater and thus the collision frequency is greater. This distorts the angular momentum randomization rate and thus the angular momentum thermalization times (it takes longer relative to the total number of collisions occuring in the system. Again, whether this non random/ non chaotic bias is minor or major depends on your assumptions about the confluence of the average ion over it's lifetime.Joseph Chikva wrote:Motion of ions can be considered as combination of two:93143 wrote:I'm explaining how it's supposed to work.
· harmonic oscillation around the center
· chaotic (thermal) motion
Because they are going to increase B-field strength from 0.8 to 10 T, so in12 times, and expect that number density will increase in 144 times (also dubious expectation), chaotic motion intensity will become comparable with harmonic (so called thermalization) faster.
Due to permanent neutralization of electron cloud the depth of potential well will decrease by entering of new portion of ions.
So, amplitude of harmonic oscillation of ions entered machine later will be slower than initially.
etc. etc. etc.
For up/ down scattering , non chaotic effects are several fold. First the issue of edge annealing can be very important. The density in various regions of the machine and associated MFP considerations vs machine diameter are important. There is some density limit where the MFP is much (or mildly?) less than the machine diameter, so that edge annealing becomes meaningless- full thermalization occurs in one pass of the ion through the core and mantle regions. Raising the KE of the particles retards this, while increased density favors this.The balance is the issue. I believe that the density and ~10 KeV potential well in WB6 allowed for average MFP's great enough for annealing to work. How this would extend into larger, more plasma dense and energetic systems is more challenging. Nebel commented on this and admitted that in larger machines this threshold might be exceeded. It doesn't mean that edge annealing stops, but that it cannot keep up with global thermalization. With D-D this does not preclude success, though it does increase Bremmstruhlung issues for P-B11 fusion.
Another process that impeads full thermalization is that the high energy tail ions will leave through the cusps faster than the average ion. Once the potential well energy is exceeded by the up scattered ions the confinement becomes magnetic, and losses through cusp exit (or ExB diffusion) is more rapid both from a number of passes perspective and from a time perspective. . The up scattered ions have a lower collisionality (scales as the 1/KE squared) and ythus less opportunity to share their energy with the average ion. The effect may be trivial or significant, but it is present. In a Tokamak the confinement time is huge (hundreds of seconds) versus the 10's of millisecond lifetimes in the Polywell (even much less for highly up scattered ions). There is no provision for preferential extraction of the up scattered ions so the full high thermalization tail has sufficient time to form. This is not the case in the Polywell. Again, the significance of this difference is debatable, but real. I think the confinement time for ions in WB6 was ~ 10-20 milliseconds. This was due to the electrostatic confinement, and at ~ 10 KeV energies this correlated to ~ 160,000 M/s. With 10,000 passes confinement, the distance traveled would be ~ 3,000 meters, so this distance would be traveled in ~ 18 ms. which is consistent with statements*.
An up scattered ion in isolation whith twice the velocity (4 times the KE) would have a confinement time shorter by this amount except that the electrostatic confinement is lost, so that the number of passes would be closer to the Wiffleball trapping factor which is closer to 1000. So the net confinement time for this up scattered ion might be ~ 1 ms. This depletes the high energy tail of the thermalization distribution to a degree. Compare this to a Tokamak with eg: 800 to 1000 second confinement time. The difference is ~ 1 million. The density in the Polywell might be 100 times greater with a resultant conditionality 10,000 times greater. This still leaves a 100 fold difference in dwell time in which the up scattered ion can continue to contribute to the thermalization process. The difference in average temperature also plays a role. A Tokamak might struggle to reach an average temperature of 10 KeV, while the Polywell might be operating at 100KeV. This results in an average thermalization time- collision frequency of 10^2 or 100 times less in the Polywell. The net result is that the Polywell density- energy conditions results in thermalization profiles that is up to ~ 10,000 less less relative to the ion lifetimes, compared to a Tokamak. Even with a 1000X difference in density, the Polywell still trails by a factor of ~ 100.
Thus claims that the Polywell ions do not thermalize over the lifetime of the ions does not seem to be an outrageous claim, at least on the surface. I again point out the the often used term- monoenergetic energy is misleading. Of course there is some spread. The important point is that it is not full thermalization. Even with annealing overwhelmed, the high energy thermalized tail is truncated to an uncertain amount.
* A clearification for me and others(?). The ion confinement time may be represented as time to escape, of number of passes till escape. Electron confinement time is often stated as ~ 100,000 with recirculation, or ~ 10,000 passes without. Ions are considered confined better with the electrostatic potential well, and I have sometimes considered confinement of perhaps 1,000,000 passes as representative. But this is wrong. The deuterium ions travel ~ 60 times slower than the electrons, so it takes 60 times longer to complete one pass. Bussard mentioned ~ 10,000 passes being required to achieve adequate fusion rates. Multiplied by 60 results in ion confinement times of ~ 6 times that of the electron confinement times (with recirculation). 12-18 ms for the ions vs 2-3 ms for the electrons. Again the numbers are consistent.
This also gives a representation of the energy costs of electron vs ion losses. Ion losses account for ~ 20% compared to the electrons (accounting for ion acceleration as they pass beyond the magrid). It is safe to say the electron losses dominate the picture.
Dan Tibbets