Talk-Polywell.org

Greetings,
I keep seeing this graphic but I am not sure what all the factors are. Can someone help describe them?

http://upload.wikimedia.org/wikipedia/c ... ce.svg.png

For instance, what do they mean be the vertical axis "Quality of Confinement" and where would the WB-6 have fallen on that axis?

Is the DT Gain factor the same as "Q" for DT fuel? If so, is there a significance to there NOT being a 10^0 (a.k.a. one) line amongst the curves?

If it is Q, what was the Q for WB-6? Dr. N said the power in was ~10MW. The power out was about 1mW. Would that mean that for DD fuel, the Q was 10E-10? Since the X-section curve for D-T is about 100x higher than DD at the WB-6 drive voltage (~10kV), would that suggest that the Q for D-T in WB-6 would have been about 10E-8?

Lots o questions here. Any answers? HELP!

I'm inclined to read
- horizontal as ion temperature, which translates directly from ion energy, or in the case of a polywell well depth.
- vertical as computed for a Lawson product, nt in cm-3*s
- the curves as lines of constant gain. The lack of a 10^0 line along with the spacing suggests an error in the graph.

Any idea where the WB-6 would have fallen on the graph?

Somewhere toward the bottom right.

But no one really knows what confinement looks like in WB-6.

It's an odd graph. It seems intended to sell laser schemes.

If it is Q, what was the Q for WB-6? Dr. N said the power in was ~10MW.

I know it was 10MW for a reactor, I hadn't seen that # for WB-6. Let's see, if WB-6 was around 100KV, that would make it... 100A (100A x 100,000V = 10,000,000W)? I guess that's possible.

That's funny. Is the input really the same for WB-6/7 and a 100MW reactor? I guess that could work with B^4*R^3 power scaling and B^1/4 losses...

The WB6 needed to charge the grid, fill the grid with electrons, puff gas, compensate with more electrons, and wind up the magnets in a number of micro-seconds. That micro-seconds makes for MEGA watts very easily.

TallDave wrote: I know it was 10MW for a reactor, I hadn't seen that # for WB-6. Let's see, if WB-6 was around 100KV, that would make it... 100A (100A x 100,000V = 10,000,000W)? I guess that's possible.

http://www.emc2fusion.org/QuikHstryOfPolyPgm0407.pdf
WB-6 was driven at 12.5K V and2000A. So it was a very short run at ~25M W
at 2.5x10^9 D-D fusions per second, that gives a raw energy output of 0.00146 if I've done the math right (9-19+6 =-4, so it's the right range). That's a Q of 6x10-11, even assuming we can use all the energy. but the size was .15 m; scaling it up 10x in size and 6x in power might very well provide enough benefits.

TallDave wrote:Somewhere toward the bottom right.

But no one really knows what confinement looks like in WB-6.

It's an odd graph. It seems intended to sell laser schemes.

If it is Q, what was the Q for WB-6? Dr. N said the power in was ~10MW.

I know it was 10MW for a reactor, I hadn't seen that # for WB-6. Let's see, if WB-6 was around 100KV, that would make it... 100A (100A x 100,000V = 10,000,000W)? I guess that's possible.

That's funny. Is the input really the same for WB-6/7 and a 100MW reactor? I guess that could work with B^4*R^3 power scaling and B^1/4 losses...

My understanding of WB6 input power during the brief time it was at ~ Beta=1 was 12,000 volts at 40 amps (480,000 watts) electron power. The magnet current was several thousand amps, but low voltage, so add ~ 20,000 watts, for a total of ~ 500,000 watts.
If ~ 1 milliwatt of fusion power was produced, then the Q = ~ 0.000000002 for WB6.
I'm not sure what assumptions Nebel made in the 10 MW input power for a breakeven reactor. If it was 1.5 meters radius with 10 Tesla magnetic fields, the input scaling at r^2 would be 50 MW (assuming superconductors). Perhaps he factored in some electron input efficiency improvements realized with WB7, or perhaps he was anticipating that a radius of ~ 0.7 meters would suffice (that would give ~ 10 MW of input power at r^2 scaling). This is similar to the computer model presented last October. Lets see, power out at r^3 B^4 scaling would be 0.7M/0.15M = ~4.8M and that to the 3rd power= ~119 radius scaling. That multiplied with the magnetic scaling of 10 Tesla / 0.1 Tesla (100^4) = 110 * 10^8 = ~ 10^7 or 10,000,000 watts. This represents a faster scaling of the magnetic field with radius than Bussard used, but I don't know what the limits with superconductors/ neutron heat loads/ etc. would be. If it works the numbers add up.

Dan Tibbets

The graph looks to be set up for thermalized plasmas and D-T fuel (see where the isophotes bottom out at ~ 30 KeV ( the least "quality of confinement " value needed to reach a Q at a given KeV. The "quality of confinement" (without digging into the actual values) seems to be a number derived from the fusion crossection X density / confinement time. As has been highlighted by arguements with ChrisMB, this is a relative term. In Tokamacs, confinement times need to be very long to compensate for thermalized conditions and density at a given average energy. In a Polywell the confinement time can be much shorter. So the "quality of confinement" would be similar despite large variations in the factors that provide this number. In laser inertial confinement the the "quality of confinement" is comparable because while the confinement time is very short, the density is huge.

I don't know where the data point for 'inertial confinement systems' comes from. Hirsch's D-T tests yielded ~ 10^12 fusions per second. The Q for those tests were probably around 10^7 million so it would be off the bottom of the graph at ~ the 30,000 EV position. I'm guessing the "quality of confinement" would have been ~ 10^8. Extrapolating what Bussard said about WB 6 compared to Hirsch's efforts with D-D fuel being ~ 100,000 times better in terms of fusion yield. "Quality of containment" would place the WB6 results ~ 3-4 orders of magnitude better- a "quality of containment" of ~ 10^11. WB6 had better yield, but at ~ 20-40 X the input power of Hirsch's machine) This would place the point somewhere on the bottom right of the graph. Since these machine easily reach these (~30,000 eV) drive conditions, the improvement would be almost exclusively from improvements in "quality of confinement" driven by the 5th power net gain scaling. The slope would be almost vertical till it leveled off at a Q of perhaps 100-1000 for D-T fusion.

Dan Tibbets

It's not really appropriate to compare a beam-type process with this graph, which is showing the density x confinement time for a thermal plasma. In a beam process, theoretically the density doesn't matter, instead it is about how efficient you can get fast ions into collisions.

It's chalk-and-cheese, I am afraid, and misleads.

To explain this graph a bit more - the Lawson criterion defines the minimum rho x tau for a given reaction. For DT it is around 1E14s/cc, I thought. So above 1E14 you can expect net gain, on this graph and for DT. I guess they are showing an upper limit line there which covers Q=10 (not sure why they don't include the break-even line, or maybe my memory fails and I've got that number wrong), so the closer you are placed to that upper line, the closer to q=10 you'd be. rho x tau isn't relevant for beam fusion methods, unless you get a handle on the minimum energy input rate and the confinement time, which defines the minimum fusion power it can generate, thus will define how many collisions per sec you will need, thus 'density', to a certain extent.

The reality is that WB6 would have been operating at 1 micron or so, with a confinement time of a ms at best (as this was the pulse time), so it'd appear at best at around (25keV,10E10), but it's comparing apples with oranges so you can't really read much into that, either way.

D Tibbets wrote: I don't know where the data point for 'inertial confinement systems' comes from. Hirsch's D-T tests yielded ~ 10^12 fusions per second.

I think you will find that that has nothing to do with Inertial ELECTRO-STATIC confinement, but more like an early laser and electron beam implosion "Inertial Confinement" condition.

D Tibbets wrote: My understanding of WB6 input power during the brief time it was at ~ Beta=1 was 12,000 volts at 40 amps (480,000 watts) electron power. The magnet current was several thousand amps, but low voltage, so add ~ 20,000 watts, for a total of ~ 500,000 watts.
If ~ 1 milliwatt of fusion power was produced, then the Q = ~ 0.000000002 for WB6.

To make the 1,200G field with 200 turns and a 0.15m radius, the current had to be ~150A. I think he said 12V batteries at one time, so ~1.8kW for magnet current.

In a post in the topic "What were the energy and power inputs into the WB-6 reactor?"

Dr. Nebel wrote:Mr. Simon has it right. Batteries for the coils (high current, low voltage), capacitors for the coil cases (high voltage, low current). WB-6 power input ~ 10 MW.

In the document that WizWom linked to above, it said 12.5kV and an Ie <2000A. That leaves a lot of wiggle room to be at 10MW.

KitemanSA wrote:

D Tibbets wrote: My understanding of WB6 input power during the brief time it was at ~ Beta=1 was 12,000 volts at 40 amps (480,000 watts) electron power. The magnet current was several thousand amps, but low voltage, so add ~ 20,000 watts, for a total of ~ 500,000 watts.
If ~ 1 milliwatt of fusion power was produced, then the Q = ~ 0.000000002 for WB6.

To make the 1,200G field with 200 turns and a 0.15m radius, the current had to be ~150A. I think he said 12V batteries at one time, so ~1.8kW for magnet current.

In a post in the topic "What were the energy and power inputs into the WB-6 reactor?"

Dr. Nebel wrote:Mr. Simon has it right. Batteries for the coils (high current, low voltage), capacitors for the coil cases (high voltage, low current). WB-6 power input ~ 10 MW.

In the document that WizWom linked to above, it said 12.5kV and an Ie <2000A. That leaves a lot of wiggle room to be at 10MW.

Again, I don't know how Dr Nebel got 10MW for WB6 input power. I've assumed he meant for a breakeven machine like WB100 or WBD. In the WB6 results, the electron gun current was ~ 40 amps during the ~ 1/4th ms when Beta was near 1. As the puffed neutral gas escaped and the external magrid pressure climbed above ~ 5-10 microns Pashin discharge started and quickly built up until the electron guns were essentially shorted out to the walls. That is when the current climbed into the thousands of amps, but this was irrelevant to the actual physics testing (except for it's effect on limiting the test time). Dr Nebel may have achieved much longer testing times ( over 10 ms, or perhaps even as much as a 100 ms?) with WB7.1, if it was equipped with ion guns. The data would give more reassuring (or disappointing) answers, especially if the instrumentation was also improved.

Dan Tibbets

D Tibbets wrote:The graph looks to be set up for thermalized plasmas and D-T fuel (see where the isophotes bottom out at ~ 30 KeV ( the least "quality of confinement " value needed to reach a Q at a given KeV. The "quality of confinement" (without digging into the actual values) seems to be a number derived from the fusion crossection X density / confinement time. As has been highlighted by arguements with ChrisMB, this is a relative term. In Tokamacs, confinement times need to be very long to compensate for thermalized conditions and density at a given average energy. In a Polywell the confinement time can be much shorter. So the "quality of confinement" would be similar despite large variations in the factors that provide this number. In laser inertial confinement the the "quality of confinement" is comparable because while the confinement time is very short, the density is huge.

I don't know where the data point for 'inertial confinement systems' comes from. Hirsch's D-T tests yielded ~ 10^12 fusions per second. The Q for those tests were probably around 10^7 million so it would be off the bottom of the graph at ~ the 30,000 EV position. I'm guessing the "quality of confinement" would have been ~ 10^8. Extrapolating what Bussard said about WB 6 compared to Hirsch's efforts with D-D fuel being ~ 100,000 times better in terms of fusion yield. "Quality of containment" would place the WB6 results ~ 3-4 orders of magnitude better- a "quality of containment" of ~ 10^11. WB6 had better yield, but at ~ 20-40 X the input power of Hirsch's machine) This would place the point somewhere on the bottom right of the graph. Since these machine easily reach these (~30,000 eV) drive conditions, the improvement would be almost exclusively from improvements in "quality of confinement" driven by the 5th power net gain scaling. The slope would be almost vertical till it leveled off at a Q of perhaps 100-1000 for D-T fusion.

Dan Tibbets

Let me try again. The performance of Hirsch's machine was closer to a Q of ~ 10^-4 or 10^-5 (~ 1 watt fusion power out / ~ 10,000 watts in). WB 6 Q (converting to D-T fuel) was ~ 10^-6 or 10^-7. While at first glance the WB6 looks inferior, remember it was operating far outside it's ideal and most importantly it's claimed achievable conditions. As ChrisMB said, otherwhise the graph is difficult to cross reference.

Dan Tibbets

chrismb wrote:It's not really appropriate to compare a beam-type process with this graph, which is showing the density x confinement time for a thermal plasma. In a beam process, theoretically the density doesn't matter, instead it is about how efficient you can get fast ions into collisions.
...


...The reality is that WB6 would have been operating at 1 micron or so, with a confinement time of a ms at best (as this was the pulse time), so it'd appear at best at around (25keV,10E10), but it's comparing apples with oranges so you can't really read much into that, either way.

True. Actual target beam - target values are generally obtained by shooting one ion into a stationary target like a thin foil. Beam- beam values come from shooting two ion beams at each other.
Gas/ plasma conditions for both interacting particles complicates things if they are thermalized, but I believe the average collision vectors would average out to being ~ equivalent to beam target fusion, while a centrally converging ion population in a spherical geometry would be ~ equivalent to beam- beam fusion (if you can prevent thermalization and there are not too many neutrals in the way).

As for pressure, it would probably be ~ 0.1 to 1 microns outside the magrid, but if the Wiffleball trapping factor is real the pressure inside the magrid will be ~ 1000-3,000 (or more in larger machines?) times higher. I'm not sure where you get ion lifetimes of a millisecond in Polywells. The number I have settled on for electron confinement in WB6 is ~ 0.3 ms without recirculation, and ~ 3 ms with recirculation. This is based somewhat on what I have read (can't recall the reference) and figuring the electron speed, and claimed transit passes. If speed is ~ 10^7 M/s, and it transits 10^5 times across a 30 cm wide Magrid, then lifetime = 0.3M *10^5 / 10^7 M/s = 3 ms. At similar energies the deuterium ions would be traveling well below 10^6 M/s. I've never seen a a difinative claim of the number of passes an ion makes in the machine befor upscattering and escaping, but the general openion seems to be that it exceeds the electron transits, possibly by as much as 1-2 orders of magnitude. So with my poorly justified assumption that the ion transit number is equal or greater than the electron transit number, the ion lifetime may be ~ 0.3 M * 10^5 / ~5 x 10^5 M/S = ~ 6 ms. If the transit numbers are higher then the confinement time would increase accordingly. Also, larger machines would increase the ion lifetimes if the transit numbers are maintained. And (I think) increasing B fields will increase electron confinement time. I'm not sure what it will do to the ion confinement time sense that is primarily electrostatic, but if the ion losses do not cost much energy, saving on the electron costs will improve your energy balance.

Also, along the same line of reasoning, recall that Bussard said ion losses were a small energy loss concern compared to the electrons. So, if the ion confinement time is short enough that most escape before fusion, they can be replaced at low cost, which is almost as good as longer confinement times (especially if longer confinement times allows more thermalization).

Dan Tibbets

D Tibbets wrote:

Dr. Nebel wrote:Mr. Simon has it right. Batteries for the coils (high current, low voltage), capacitors for the coil cases (high voltage, low current). WB-6 power input ~ 10 MW.

Again, I don't know how Dr Nebel got 10MW for WB6 input power. I've assumed he meant for a breakeven machine like WB100 or WBD. In the WB6 results, the electron gun current was ~ 40 amps during the ~ 1/4th ms when Beta was near 1.

Do you have a reference for that 40A?