Evidently EVERYONE knows the math for this and are mocking me personally for not figuring it out myself or NOBODY understands the math for this and are just making things up as they feel like it.
Generated power scales as
P_g = B^4 * R^3
That is, magnetic field strength to the fourth power times radius to the third power. This power scaling is widely accepted because it is the same for a Polywell and for other machines using like technology.
Power input replaces power lost during operation of the Polywell. There is no agreement on this forum as to how the input power scales. Dr. Bussard wrote that input power scales (power lossses) as
P_in = R^2
That is, radius squared, like the surface area of the Polywell.
Again, there is no agreement here, and Dr. Nebel and the Navy are still running experiments to evaluate the input power needs.
(And maybe to reduce them.)
Is there a reference design to refer to in order to get figures from this equation? It is incomplete as is.
P_g = some Testlas * some radius. What is a Telsta radius? What is it worth? Magnetic field strength is a force. Not a power. Could that be a multiplier we could use on a base coefficient? Wouldn't different fuels make for different coefficients in a properly operating ideal polywell?
We need an ideal polywell law, like the ideal gas law or carnot cycle. Something I can poke in a calculator and get some figures to mess with.
I can understand kinetic energy. Kinetic energy in joules = .5 * mass in kilograms * velocity in meters per second^2
Perfectly elegant, acknowledged everywhere until relativistic velocities.
Or how about e=mc^2
energy in joules = kilograms * 299,792,458^2
Or ohms law: Power in watts = volts * amps
units, examples please. Thanks in advance
I'm just trying to verify for myself what has been theorized and proposed.
Yes, that was a little sloppy of me. Power scales as --- it is not equal to. There is a gain factor which accounts for the units. We recently went through this on another thread. See 93143's calculations here: viewtopic.php?t=1182&postdays=0&postorder=asc&start=45
That should give you insight to manipulate the math.
Hmm not a good clear picture of things in that link. We are far far from a consensus. Quit calling this whatever this is a scaling Law. It isn't even a scaling principle. No one can agree on Bussards claim. This is a dimensionless void meaningless and estranged from all reality.
ohiovr wrote:Hmm not a good clear picture of things in that link. We are far far from a consensus. Quit calling this whatever this is a scaling Law. It isn't even a scaling principle. No one can agree on Bussards claim. This is a dimensionless void meaningless and estranged from all reality.
B^4*r^3 is a very standard power scaling law for magnetic confinement schemes. r^5 is Bussard's claim of how gain scales. Others have different opinions.
Wouldn't different fuels make for different coefficients in a properly operating ideal polywell?
They would have different cross-sections, of course, and different bremsstrahlung problems, as well as different electric conversion ratios. But it's all pretty rough at this point anyway.
We need an ideal polywell law, like the ideal gas law or carnot cycle. Something I can poke in a calculator and get some figures to mess with
That would be nice, but it's very difficult to predict how losses (and therefore gain) will scale. Tokamaks ran into a lot of issues on that point. You can accept Bussard's estimate, or someone else's, or come up with what you think it will be.
Last edited by TallDave on Wed Apr 01, 2009 5:35 pm, edited 1 time in total.
Hey, I just realized -- duh, I can calculate power inputs with this:
e.g. 100 -500 Amps at 15-30 kV for DD and
Okay a watt is an amp at a volt. 100A * 15,000V (can I convert an eV to a V here? sure hope so) = 1,500,000W = 1.5MW, or 7.5MW for the high end on amps, or 15MW for 500A @ 30kV.
Hooray! We have a Bussard estimate of losses for 100MW! I think.
Now, if I can just find that comment from Rick on the input power he was estimating...
Last edited by TallDave on Wed Apr 01, 2009 2:16 pm, edited 1 time in total.
ohiovr wrote:Wouldn't different fuels make for different coefficients in a properly operating ideal polywell?
Wikipedia has a table including the maximum value of (fusion power density)/(plasma pressure)^2 in units of (W/m^3/kPa^2) for various fuels. In this forum we are running on the assumption that the plasma pressure is equal to the magnetic field pressure, B^2/(2*mu_0) (MKSA units). The only other thing you need to calculate a total fusion power output is a volume.
As several others have already observed, this much is agreed on by all sides. The maximum practical magnetic field for a given device radius is the subject of gentlemanly discussions. When it gets to the question of an equation to calculate the loss rate, which determines the minimum possible (or impossible) machine size, the fur flies.
Magnetic field strength is evidently a lot more important than the radius. I'm not an expert on electromagnets but this is what I've gleaned from wiki:
Ferromagnetic core electromagnets can be thousands of times more powerful than electromagnets with just air cores. An iron core magnet therefore requires less than a thousandth the current required for operation as an air core magnet for the same strength. I don't know what kind of electromagnet wb-6 used but I would like to know. Anyway the strongest ferromagnetic electromagnet can be 1.6 Teslas or 16 times greater than wb-6.
the 4th power of 16 is 65536
Now with superconducting magnets things get interesting. We can get 10-20 teslas with no ohmic heating. If they fail it can be catastrophic (explosion) so engineering has to be extra tight. They require extreme cooling and that seems to be a bit rediculous near a source of extreme heating (I want GIGAWATTS). 10 teslas is 100 times more powerful than wb-8
the 4th power of 100 is 100,000,000
Size seems to be the least complicated part compared to the thermodynamics of keeping something 20 K next to a surface that is several million k. It is evidently possible the ITER people are trying to do it.
In my spreadsheet I get 5.86E-4 joules per second out of wb-6 a really really tiny number especially next to that 500A*15,000V=7,500,000W input.
But if we could get 1.5 teslas at 100th the cost in amps using an iron core polywell it comes out to a 75,000 watt input.
Lets make this thing BIG. Make it 30 meters in radius, 200 times larger than wb-6
200^3 = 8,000,000
And use the cheap iron electromagnet with 1.5 teslas
Neat, except that with an iron core, the field goes THRU the core which means there is MUCHO unprotected metal and so the losses exceed the gains no matter what.
DrB has estimated that there can be no more than about 10E-5 of the total area that is unprotected metal or the electron losses will prevent break-even from ever being reached.
Last edited by KitemanSA on Fri Apr 03, 2009 12:02 am, edited 1 time in total.
ohiovr wrote:Now with superconducting magnets things get interesting. We can get 10-20 teslas with no ohmic heating.
One of the things we have all been glossing over is the exact meaning of the field spec. You might be able to get up to 10 or 20 Tesla in a SC before it quenches, but you will want to de-rate that considerably to allow higher current densities, more manageable temperatures, and a margin of safety. Perhaps more important is that the field at the surface of the plasma will be several times less than that at the surface of the coils. In ITER, the maximum field on the (toroidal field) coils is 11.8 T, but the field on axis (useable to confine plasma) is only 5.3 T. It's a straightforward engineering design question, but I have never seen a number for a polywell. I would take a factor of 2 reduction from your favorite SC field limit as a working value.
AFAIK, the field has always been quoted at the center of the plan-form of the coil for Polywell usage. The field at the surface of the winding may be related in some simple manner unlnown to me. I are a mechanical engineer. To me, electrons are peas flowing thru pipes.
If they fail it can be catastrophic (explosion) so engineering has to be extra tight.
I recently read Bussard arguing somewhere Polywells were inherently safer in this regard. I forget exactly why.
Size seems to be the least complicated part compared to the thermodynamics of keeping something 20 K next to a surface that is several million k.
M Simon has some calculations on the heat transfer requirements bouncing around in Design somewhere. His design used trinary cooling with insulating vacuum chambers in between layers.
