Where's the beef?

TallDave · Post by **TallDave** » Sat Jul 12, 2008 8:06 pm

(1) that nobody really understands them, and (2) that they give roughly accurate results anyway.

Heh.

I only ask you to remember that the experimental as well as the theoretical basis of the concept is extremely speculative.

Always important to keep in mind.

In my view, having a good, experienced experimentalist is absolutely essential.

Amen to that.

Art Carlson · Post by **Art Carlson** » Sat Jul 12, 2008 9:02 pm

rnebel wrote:I would also like to comment on the question of simulations vs. experiments. ... Simulations and experiments have to go hand-in-hand. ...

Amen. I didn't really mean to put simulations and theory ahead of experiment in any absolute sense. Just keep the balance.

Finally, a few words about FRCs. ... As I’m sure Art knows, they also have issues like ....

Yup. That's a good laundry list. I once tried to get the Max Planck Institute to give up tokamaks and build FRCs. Those were the technical arguments they brought against it, especially MHD stability to the tilt mode. (There were political arguments, too.) In the end I think they made the right choice. (Their decision to build a large, superconducting stellarator may be a different matter, considering the funding level available.) The theoretical and experimental basis for FRCs is much stronger than it is for the polywell, but it's still a long shot. I guess I have my fantasies, too.

Torulf2 · Post by **Torulf2** » Sat Jul 12, 2008 9:31 pm

There is a FRC concept called “The pulsed high density experiment” how is said to com near break even and makes possible to build small reactors and have direct energy convention. May this is is suitable for alternative financing?

TallDave · Post by **TallDave** » Sat Jul 12, 2008 11:18 pm

Torulf2,

Do you have a link?

Torulf2 · Post by **Torulf2** » Sun Jul 13, 2008 3:56 pm

Here is some links.
http://www.springerlink.com/content/h4385177275n0j62/
http://fire.pppl.gov/fpa06_woodruff.pdf

Tom Ligon · Post by **Tom Ligon** » Mon Jul 14, 2008 1:03 am

Art,

Since you know Langmuir probes, what causes this effect? Attempting to run the probes with a swept bias, you are supposed to get a pair of breakpoints, on either side of zero volts. Someone posted a link to one of Miley's experiments, and it shows the two breaks. Ours showed a break at one polarity, but a straight line on the other end that seemed to go on forever.

I'm definitely not a Langmuir probe expert, and have forgotten 90% of the little I ever knew about them.

Art Carlson · Post by **Art Carlson** » Mon Jul 14, 2008 8:56 am

Tom Ligon wrote:Since you know Langmuir probes, what causes this effect? Attempting to run the probes with a swept bias, you are supposed to get a pair of breakpoints, on either side of zero volts. Someone posted a link to one of Miley's experiments, and it shows the two breaks. Ours showed a break at one polarity, but a straight line on the other end that seemed to go on forever.

The part of the I-V characteristic that causes the least indigestion is the "ion branch", when the probe is negatively biased. Although even this part gets confusing if you look too closely, everyone agrees that the ion saturation current in a magnetized plasma is n_e*c_s*A_proj, where n_e is the electron density, c_s is the sound speed (which can also get a bit tricky if the ions are not cold), and A_proj is the area of the probe projected along the magnetic field (times 2 if the probe is not in front of a wall). Within 50% or so. That is bound to be the "break" that you saw.

When the probe is not quite so negative, then you start to collect electrons. The exponential rise of the current, at least up to floating potential or so, should be a reasonable reflection of the electron temperature. With the ion saturation current plus the exponential rise, you can calculate density and temperature and go about your business.

The bear is the electron branch. The naive theory expects the I-V to saturate with sufficient positive bias at a current that is about a factor of the square root of the ion-electron mass ratio greater than the ion saturation current. Nobody ever sees this. In deuterium plasmas, where sqrt(m_i/m_e) = 60, a typical measured ratio is 6-8, but anything from 3 to 12 is common. The strangest thing I have ever seen is a few cases where we measured an electron saturation current that was actually lower than the ion saturation current. This all is not too bad. It is easy to draw pictures that would lead you to expect a smaller electron saturation current. (In fact, you have to work a bit to explain why the ratio in a magnetized plasma is greater than 1 at all.) Where it gets harder is when you don't see electron saturation at all. With the probes on ASDEX Upgrade, we were able to plausibly and quantitatively explain why we saw a slope in the ion "saturation" curve, so we could work on a break plus a slope in the electron branch. Unfortunately, we (and others) sometimes saw what you saw, an electron branch that seems to increase linearly. There have been some attempts to explain this, but they have not gotten very far.

The upshot is, if you use probes in a magnetic field, limit your measurement (or at least your analysis) to voltages around the floating potential and below. The density and temperature you get out will probably be usable. Avoid the electron branch like the plague.

drmike · Post by **drmike** » Mon Jul 14, 2008 8:40 pm

Now I really want to build some hardware and get back into this stuff! The plasma sheath has always been a hard problem even without magnetic fields to make the math impossible.

Unfortuantly I first have to fix my winxp partition because I blew it away having a touch too much fun with linux.... That's what backups are for, and I actually have them!

OneWayTraffic · Post by **OneWayTraffic** » Tue Jul 15, 2008 3:25 pm

Art Carlson wrote:
Just remember that a smallish tokamak running on deuterium has a power density comparable to the sun. If it came down to having a tokamak or a star in your back yard, which one would you think is the better concept?

Luminosity of the sun: 4*10^26W
Mass: 2*10^30kg
Volume: 10^27 cubic metres

Power density <1W per kg or per cubic meter.

Hmm. That sounds about right for tokamaks.

Edit: I see that I've been beaten to it. Oh well.

Art Carlson · Post by **Art Carlson** » Fri Jul 18, 2008 7:21 am

In another thread I commented

I haven't even seen a calculation telling me that 2 neutrons per pulse from a polywell is a lot. Maybe we should be expecting thousands, but the experiments are a dismal failure.

Does anyone have an answer to that? If we take everything at face value (a risky proposition, but we have to start somewhere), what do these two neutrons per shot tell us about the confinement time? We have to assume we have a decent potential well and a corresponding ion temperature. (You can explain away any poor result by hypothesizing that the temperature was too low for a decent fusion cross section. Before you are allowed to get excited about fusion neutrons, you have to either measure the temperature or assume it was reasonably high.) The fusion rate then gives us a handle on the density. Is this number consistent with the assumption that beta = 1 was reached? That's a side question (but an important consistency check, where few are available). What we want is a confinement time. For that we either need a decay rate of the density or a feed (ionization) rate. Do we have either of these? Or limits on them? If not, then why are the fusion neutrons seen as so encouraging? They could be the result of simply driving a lousy machine hard enough. (Of course, if we ever get that far, I will want to convert the confinement time to an effective loss area, which I will then compare to various combinations of the system radius and the electron gyroradius. But I know how to do that part myself.)

drmike · Post by **drmike** » Fri Jul 18, 2008 1:15 pm

Temperature doesn't matter, CM energy matters. I don't remember what the voltages were, but the CM energy will be twice that if you assume perfectly radial currents. (Detected neutrons) * 4pi/(detector angular section) gives total neutron count and implies fission rate. My recollection is that this was in the 1000's.

93143 · Post by **93143** » Fri Jul 18, 2008 2:33 pm

13000 neutrons per count, for a quarter millisecond pulse (roughly). The first test and the destruct test both showed one count. The second and third tests, at increasing drive and B, showed 2 counts each. The best test result was 3 neutrons, at 12.5 kV drive, corresponding to about 3e8 D-D fusion events per second, or about five orders of magnitude better than a fusor at the same voltage.

Gas feed rate was way too high - arcing ended all the tests.

Art Carlson · Post by **Art Carlson** » Fri Jul 18, 2008 3:38 pm

A number I have handy (Wikipedia) is a power density of 0.5 W/m3/kPa^2 for D-D at the optimum temperature (15 keV). Does somebody have the field and volume? Let's guess B = 0.1 T so the magnetic pressure is B^2/(2mu_0) = 1e-2/(2*4pi*1e-7) ~ 4e3 Pa = 4 kPa, which equals the plasma pressure if beta = 1. Take a sphere with radius 5 cm (I'm hoping somebody who's better informed will redo this calculation.), so the volume is (4pi/3)(5e-2m)^3 ~ 5e-4 m^3. Gives me a power of (0.5)(5e-4)(4)^2 ~ 4e-3 W. How many neutrons per second is that? (4e-3W)/(12.5 MeV/fusion)/(1.6e-19 J/eV) ~ 2e9 neutrons per second. (The first time I did this calculation, I got 8 orders of magnitude less. I'm glad I spotted the mistake before I pressed "Submit".) This is (serendipitously) nearly exactly equal to Bussards's claim of 1e9 neutrons per second, so there's at least that much consistency in the claims.

Now, the real question was how to deduce a confinement time.

93143 · Post by **93143** » Fri Jul 18, 2008 4:13 pm

Earlier in this thread Tom Ligon mentioned 14 amps of drive current for WB-6. Considering the crude fueling system and short pulse, this may not be enough to deduce anything much.

The magnetic field for the destruct test was 1000 gauss. All the other tests were somewhat lower; the document that showed the exact numbers seems to be gone... I'm pretty sure the 3-neutron 12.5-kV drive shot was done with at least 800 gauss.

EDIT: It appears I misremembered. The destruct test was 1000 A. The 3-neutron shot was 800 A, or 1000 gauss. Thanks, Aero.

Art Carlson · Post by **Art Carlson** » Fri Jul 18, 2008 10:01 pm

93143 wrote:Earlier in this thread Tom Ligon mentioned 14 amps of drive current for WB-6. Considering the crude fueling system and short pulse, this may not be enough to deduce anything much.

I am assuming (one of many big ifs) that convection is the predominant energy loss mechanism. If the 14 amps of drive current is the particle feed rate, then that is (14Cb/s)/(1.6e-19Cb/particle) ~ 1e20 particles/s. The particle inventory is around V*P/kT ~ (5e-4 m^3)*(4e3 Pa)/(1.6e-19 J/eV * 1e4 eV) ~ 1e15 particles, so the confinement time is (could conceivably be) on the order of 10 microseconds. The electron transit time is R/v = R/sqrt(2kT/m) = (5e-2 m)/sqrt(2*(1.6e-19 J/eV)*(1e4 eV)/(9.1e-31 kg)) ~ (5e-2 m)/(60 m/microsecond) ~ 1 ns, so the confinement factor is (1e-5 s)/(1e-9 s) = 1e4. We will have to consider within how many orders of magnitude we trust this result and whether it is a relevant calculation at all. For now I simply note that it is (I believe) on the order of (R/rho)^2, consistent with confinement like point cusps, but not necessarily inconsistent with confinement like line cusps, (R/rho)^1. In both cases without any credit for recirculation.