some questions

[chrismb]

The WB effect is the key because confinement is the major challenge in IEC (temp being relatively easy) and we get better density since we operate at high beta. Rick said at one point without WB "we can kiss our behinds goodbye." Whether we like it or not, this poorly understood (by us, anyway) phenomenon is the heart of the concept.

Thanks for that link. Now it becomes a little clearer.

Basically, the hope really is, simply, for 'spherical' confinement, thermalised plasma or otherwise.

Which raises the very simple question in my mind; if cusps can be closed by dia-magnetic effects, why don't the cusps 'close up' in a mirror machine, which only has two cusps? Why does adding extra cusps, over and above that in a mirror machine, improve the chance of the wiffleball effect working?

[Roger]

however sphericity for focusing the ions adequately for fusion is another matter.

I assume we dont need a "focal point", but convergence within a broader area where fusion takes place? But no so broad of an area as to lower fusion events ?

[icarus]

chrismb:

Which raises the very simple question in my mind; if cusps can be closed by dia-magnetic effects, why don't the cusps 'close up' in a mirror machine, which only has two cusps? Why does adding extra cusps, over and above that in a mirror machine, improve the chance of the wiffleball effect working?

Very good point.

I would argue that you could close the cusps in a simple, two-coil mirror machine, IFF a sufficiently strong orthogonal electric was applied to the plasma-magfield interface, in the same manner as it is on the Polywell.

Roger:

I assume we dont need a "focal point", but convergence within a broader area where fusion takes place? But no so broad of an area as to lower fusion events ?

Can't say I'm very knowledgeable (yet;)) on this topic but I noticed Chrismb wrote some good stuff on fast-fast versus fast-slow fusion ratios in fusors, he might have some better thoughts on electron plasma sphericity needed for "good enough" fusion rates ...

[chrismb]

Can't say I'm very knowledgeable (yet;)) on this topic but I noticed Chrismb wrote some good stuff on fast-fast versus fast-slow fusion ratios in fusors, he might have some better thoughts on electron plasma sphericity needed for "good enough" fusion rates ...

err... not sure I do. If we're talking a fusor-like mechanism, dominantly fast-slow fusions, then the only concern is the total number of fast ions participating. They can be going any-old-way. Evenness, regularity, focussing, etc. are unimportant. If we move to fast-fast fusions at a central focus, then I can only speculate; I'd say it would get pretty important else I think you could easily conceive of a very chaotic, tumbling system forming very rapidly.

[TallDave]

why don't the cusps 'close up' in a mirror machine, which only has two cusps? Why does adding extra cusps, over and above that in a mirror machine, improve the chance of the wiffleball effect working?

Probably has to do with the geometry of how fields deform in a polyhedron. Mirror machines had an axis rather than polyhedral symmetry.

However, if the magnetic field can be “inflated“ by increasing the electron
density (by further injection current), then the thus-inflated
magnetic “bubble“ will trap electrons by “cusp confinement“
in which the cusp axis flow area is set by the electron gyro
radius in the maximum central axis B field. Thus, cusp
confinement scales as B2. The degree of inflation is
measured by the electron “beta“ which is the ratio of the
electron kinetic energy density to the local magnetic energy
density, thus beta = 8(pi)nE/B2.

[TallDave]

I assume we dont need a "focal point", but convergence within a broader area where fusion takes place? But no so broad of an area as to lower fusion events ?

Rick pointed out a ways back we should get 62500 times the power density of ITER with the same magnets, even without any ion convergence at all.

It would certainly help, though. It could have a huge impact on the size of a machine that can be a useful power producer. It might be the difference between merely being better than ITER and being world-changing.

[icarus]

Dave:

Probably has to do with the geometry of how fields deform in a polyhedron. Mirror machines had an axis rather than polyhedral symmetry.

I think you are probably right on this one. But by the same reasoning you'd have to argue that the perfect spherical field deformation, that you are claiming for the truncube Polywell, is not going to happen except in the limit of a polyhedral with infinitely many faces, i.e. cusps.

If the n=2 inflated-cusp deformed field is a very poor approximation to a sphere, n=4 (i.e. truncube Polywell) is somewhat better ... but NOT perfectly spherical .... not gonna happen, gonna be a lumpy ball.

[rcain]

hi chaps,

i'm still catching up with all the good content above. i have been burried in my own calculations and find myself evolving a notation for WB. i thought id share it.

i hope these are legible to people. (they are simple canonical ascii diagrams/connected graphs).

i am presupposing we can use the previous pic icarus posted up, to set origin and orientation of the poly-cube.

i'm supposing a 1.5d a cross section through the device looks like this::

w---mg---o---mg---w

where:
w=wall of chamber
mg=magrid
0=geometric centre
--- = vacuum

then establish mag & leky fields:

-----------kV(+).I-----------0---------kV(+).I-------
|--------------|-|------------------------|-|-----------|
V[w]---[QXB][mg]--------|-------[QXB][mg]---V[w]
|--------------|-|-|----------|----------|-|-|----------|
w-------------mg----------o-----------mg----------w


and a particle distribution looking something like:

w--------mg----------o-----------mg--------w
|---------|------|-----|-----|-------|---------|
v[w]----v[d]-v[e]--v[o]--v[e]--v[d]----v[w]



perhaps injext some ions and electrons: (in some 4d sequence = s) of scalars d/t and e/t::
-------s
---d\--|--/e
w----mg---....

and establish a (state solution) distribution, with some velocities::

w---mg---e(2-)-d(4+)-e(2-)--d(2+)--e(1-)-d(1+)----------------o------------(1-)-d(1+)-e(1-)---d(2-)--e(2-)-d(4+)-e(2-)---mg---w
|-----|||------|------|---------|-----|------|----|----------------------|0|
v[w],v[mg],v[e1],v[d2],v[e2],v[d3],v[e3],v[d4]----------v[+/-0]


where
e=electon
d=deuteron (for the purpose of this simple thought expriment at least)
o=neutral H (also, always in flux between +1, -1, o), (seeded as virtual electrode e(-) as initial condition)
(signed-integer+) or (signed-integer-) = mass.charge of prefix token
v[index]=velocity vectors for particle species (mass/charge) -
- eg: v[e1]=0 == first electron band in where elecrons have 0 radial velocity
- relative speed/positions may also be specified eg: v[e1]v[d2]v[e1] means the electron velocity across v[d2]=0 trapped ions, etc.
{population mass/charge distributed as m (arctan x):: ={4-,2-,1-,0-,0+/-,0+,1+,2+,4+,..} - scaled so here only to obviate order of magnitude variations between population centres.}


by contrast, a similar schematic of a traditional iec fusor looks something like this i believe::

w---d(1+)-------cg------o-----cg-------d(1+)-----w
|-----|------------|-------|------|----------|---------|
0---v(+0)-----v(1)--vr(o)--v(-1)-----v(-0)--------0

where cg=cathod-grid.
v=velocity
v(x)=velocity according to (eliptic?) trajectory, where, 0<x<pi (or 0<x<n.pi for multipasses)

i have some old lab data for this, in order to test.

meanwile, back in the bat-cave, i have been preparring some QB field slices. i hope that these will help me verify the velocity-mass-charge distributions (convolving the temperature surfaces).

we are interested in what happens at (various) cusps, and in 'spikier' and 'flatter' bits, and most particularly around the Beta=1 manifold as well as the 'inner' core'.

wonderful pix again, thanks icarus

i construct, a small number of representative sample cylinders, crossing (..though not necessarily) the origin (geometric centre/ core) of the machine. these cyclinders can be characterised, in spherical polar coordinates, as:

(r1,pi/4,pi/4 ) :: the line (/ cylinder/cone) across corner cusps,
(r2,pi/8,pi/8 ) :: the line across the inner contained sphere, where our concave Beta=1 surface bulges in most.
(r3,0,0 ):; the line across central face cusps, (projecting through) through the centre of the coils
(r4,pi/2,0 ):: the line across the mid-way cusps, those that project through the closest meeting of (circular) colis, arranged around our cube faces

please tell me if you spot any ambiguous/wrong conventions. i'll do my best to improve it.

i'll put up any reasonable output from my endeavours, as soon as i get any. this is just a straw-man here. i'm having a go at a grand-notation in the other thread (intersecting spheres)

anyone got any better notations?

cheers (back to catching up)

ps. some very interesting points raised on your previous narratives gentlemen. i'll get back to you as soon as i can.

[TallDave]

icarus,

I agree, I don't think the truncube's field ends up perfectly spherical. I don't think the dodec gets there, either. I do think the dodec field is probably spherical enough that the ion distribution might look something like the spherical model the Chacon paper utilizes.

One of the questions I've pondered: is the wiffle-ball effect partly the result of long, very narrow pipe-like cusps that fill with electrons, blocking other electrons from leaving?

[rcain]

icarus,

I agree, I don't think the truncube's field ends up perfectly spherical. I don't think the dodec gets there, either. I do think the dodec field is probably spherical enough that the ion distribution might look something like the spherical model the Chacon paper utilizes.

One of the questions I've pondered: is the wiffle-ball effect partly the result of long, very narrow pipe-like cusps that fill with electrons, blocking other electrons from leaving?

hi talldave

..i am thinking of it as a (4d) tuned volume. (we would also like it to rectify i think).

i would be particularly interested in seeing instrumentation / spectometry data against pulse and chirp on all the inputs. i recall msimon posted some nice ultra-wide-band a/d kit recently.

i think the focusing arguments are spot on. similarly, the model i'm starting to understand, would favour very precise injection of (fuel) particles.

the whole 'anealing' thang i have another take on now also - when i get a tick. ( triple-points.).

btw: there are some very good java appletss up by someone on this forum, demonstrate very well what happens when you wack the mag-field right up. sweet spots. my understanding is, that the phenomena are an largely fundamental artifact of geometric scaling about the device configuration (magic numbers). there is a certain 'squiginess' to it, short-range repellers (hevy ions), but also a damped righting moment. maybe i was imagining it.

[icarus]

Dave:

One of the questions I've pondered: is the wiffle-ball effect partly the result of long, very narrow pipe-like cusps that fill with electrons, blocking other electrons from leaving?

Me too. I guess you have to define long in terms of electron travel times or some such first. I think we are talking about the same thing but finding a way to describe it self-consistently and unambiguously is difficult. They way I'm thinking about it is this,

i) the electrons in the Carlson sheath that make it onto mag field lines will on average have only a small beta_1 surface tangential velocity component, compared to the surface normal component, due to the influence of the strong electric potential field in that region that is purely surface-normal directed. (In magnetic mirror parlance this is called the "pitch angle" http://en.wikipedia.org/wiki/Magnetic_mirror)

ii) then only those electrons that spiral along field lines and into the cusps that had velocity pitch angles lying inside the loss cone (http://farside.ph.utexas.edu/teaching/p ... ode21.html or here http://pluto.space.swri.edu/image/glossary/pitch.html) are going to escape .... some of the others will just gyrate in the same place and become effective blockers in the cusp (these are the ones you are talking of I think), others will mirror and head back towards the core.

iii) my contention is that with a strong enough beta_1 surface-normal electric field not many of the electrons will actually have velocity pitch angles lying inside the loss cone ... how many is too many is the loss question I suppose?

[rcain]

Dave:

One of the questions I've pondered: is the wiffle-ball effect partly the result of long, very narrow pipe-like cusps that fill with electrons, blocking other electrons from leaving?

...

iii) my contention is that with a strong enough beta_1 surface-normal electric field not many of the electrons will actually have velocity pitch angles lying inside the loss cone ... how many is too many is the loss question I suppose?

that is the way i am seeing it also.

loss-cones into well edges are more 'orderly'. the insides of (virtual) wells themselves, suffer greater discontinuity/inflexion (hence focusing, esp. in the case of the Carlson sheeth and WB cone scaling). their basic geometry ensures this. at least thats the way i'm visualising it right now.

[icarus]

rcain:

loss-cones into well edges are more 'orderly'. the insides of (virtual) wells themselves, suffer greater discontinuity/inflexion (hence focusing, esp. in the case of the Carlson sheeth and WB cone scaling)

Maybe you could elaborate further, start with first principles and take it from there.

The so-called "annealing", I'm thinking, is nothing else than the beta_1-surface-normal electric field "polarising" the electron velocities back towards the radial, i.e. reducing tangential components. At the same time, the electric field in this region will re-monoenergise the speeds of scattered electrons returning from the core to this periphery; this is simply due to the fact that any electrons crossing the Carlson sheath from the plasma core side to the field side must have the energy given by the field potential after making the traversal.

So it works to stop loss-cone scattering as well as stop thermalising of the electrons' speeds. I.e., both magnitude and direction of the electrons' velocity vectors will be influenced by the electric field being perpendicular to the Carlson sheath. The velocity vector direction re-alignment will reduce electron losses from the wiffle-lump and the speed adjustment keeps the plasma mono-energetic.

Polywell nirvana reattained thanks to the Carlson sheath. where's Art?

[rcain]

rcain:

loss-cones into well edges are more 'orderly'. the insides of (virtual) wells themselves, suffer greater discontinuity/inflexion (hence focusing, esp. in the case of the Carlson sheeth and WB cone scaling)

Maybe you could elaborate further, start with first principles and take it from there.

erm....i'll try. but i may have to go to bed and return to it.

briefly, i see::

all particles are in orbits about manifiold surfaces, shells. they are not exactly spherical. i think of them as lozenge shaped (eliptical, but in fact i think they are really rather like your 1st pic - the one of the ( -wanabe-) perfect sphere, highlighting the contours of lower energy troughs/channels/conduits. that is more like the shape of them.

all is arranged according to balanced moments about manifiold surfaces.

the geometry is so constructed that lines of recirculating/reconnecting charge are formed (eg: corner cusps to/from face pole - in this case (your pic 1) we cheat the plasma by presenting a dimpled-punctured sphere, which it successfully treats as one of its own)

manifolds will fequently colide/intersect, at various angles. most often, they graze each other tangentially, concentrically. plasmoids go most wriggly. sometimes there is good space between them. plasmoids are silky.

the exact couplings between manifolds, are themselves, manifolds. as per my post above. there are many electrode regimes to try out (I love Dolan's paper - why isnt he doing anything any more?).

many diametrically varied modes of succesfull operation are possible. from what i have read

the manifolds can also be thought of as refractive medium.

i feel safer assuming that all particles carry some thermal velocity as well as both kenetic and potential angular momentum, or are coupled to such.

particles can flow and bounce around within the inside swept volume of their shells edge, or they can cut through the middle co-concentric/co-tangent shells, they can bounce between two sourounding shells with various harmonics. occassionally they might get caught up in an axial stream or cusp and get whisked around the outside of the system for a quick brisk stroll. to recycling.

mostly we want to accumulate them within some regular, periodic, space(s), 'total internal reflection' (coherence) on the inside surface of a high velocity cavity, with a tight focus, on the spherical surface of our real fuel burning core.

we arrange zones (cones) of intercept where we can be most certain of net productive collisions only.

we accept that in order to achieve required particle densities and reflectivity (reflexivity), we will have to suffer some non-productive over-shoot/undershoot collisions, oblique and glancing transactions/intercepts. especially (non-radial) thermalisation and other processes that get negatively out of scale with the local equilibria.

we posit, that with some ineficiency (work function), our device is able to pump any recirculataing stuff back uphill a bit and, an then let it syphon its way back into the system towards a relative ground state/reconnection point (whatever that appears to be at some instance).

when a slowing ion entres the space of denser, slower bretherin, all of a sudden, he is in for a surprise.

firstly, how did he get there? he probably just wandered too close to the exit cone off his usual fast regular orbits (assume for simlplicity there is only 1 net loss-cone). if the system is perfectly tuned and loaded, only imperfect collisions innermost will get him there - ie, he deserves to be there, he is degenerate and must be pumped back around the system and reconditioned.

as he entres, however fast, there is resistence and people move away (unless they are electrons), but they are kool (ish)

they spiral out of the way, very elestrically, along contiguous curved edges of least resistance, along a great cirlce. spin.

we would would rather they conserve energy. so would the dipole-charges. but the heat, will have none of it and just mixes. were it counter-polarised it would not, and sum and difference residues might be recovered.

as soon as any thermlisation begins, these babies (ions) are exploring their local connected manifolds, unless pushed of jostled up, they prefer downhill. they will be graded in their distributions according to mass/charge, temperature, (local) moments, and most importantly, precisely how they enterd, and what they encontered.

we would rather avoid all that in future), but intrincically we are required to pump up and squeze out +/ve and -ve) ions, and that disturbs the pools and makes them 'slosh over', or worse, burst completely.

thats a part of anealing as i understand it. there may be others, for example hard target vapourisation. i suppose the 'inverted' metal ion (was it?), might be another extreme example.

my favourite thing to try on the Polywell WB might be thermoacoustic/Alfven-wave/Microwave - pops/pulse-jet i suppose.

unless we can contain, compress, accumulate and pump (rectify) through the well structure, then it may as well thermalise off to the wall, it would be no good to us. its also no good to us if it doesnt present us (or itself) with some hard target sufaces to aim at. then its down to the lenses and the take-off.

i propose intentionally puncturing all of the corner cusps:

(a-b)recycle loop
(a+b)resupply loop
+x input port
-y output port = b-a/x^2 , somesuch...

and insert ports and 3-way valves. some gubins looped around outside the magrid, a snail-shell/filter cavity.

it would also present the machine with a natural 'handed-ness' or driving stator.

particles transitioning between radial and tangential orbits (for whatever reason), up or down, experience/exhibit work moments. (unless they struck lucky and caught a big, very fast one)

luckily, the electrons keep everything in check with a hard 'ringing' wall off the mag field (Carlson sheeth/WB/electro-magnetic inflexion). this couples as a reflective (stiff-elastic) impedance, along with other higher-frequency highier energy coulomb couplings, linearised back through the system. things are kept tight and ringing back and forward. i think you can see it hints of it on Bussards Valencia machine graphs. diamagnetism has also been proposed/observed and i recall there is an appropriate inflexion in the mag field map.

anyway, it sings.

or i hope it will some day.

i digress, i was going to bed.

l8's

rob

(btw. theres an excellent compound conical pedulum java app on wolfram alpha, if you know it. or the famous water-clock in berlin perhaps).

[MSimon]

The WB effect is the key because confinement is the major challenge in IEC (temp being relatively easy) and we get better density since we operate at high beta. Rick said at one point without WB "we can kiss our behinds goodbye." Whether we like it or not, this poorly understood (by us, anyway) phenomenon is the heart of the concept.

Thanks for that link. Now it becomes a little clearer.

Basically, the hope really is, simply, for 'spherical' confinement, thermalised plasma or otherwise.

Which raises the very simple question in my mind; if cusps can be closed by dia-magnetic effects, why don't the cusps 'close up' in a mirror machine, which only has two cusps? Why does adding extra cusps, over and above that in a mirror machine, improve the chance of the wiffleball effect working?

Pure speculation here:

It may have to do with giving scope for plasma rotation. Such rotation may make the leakage "tube" longer and narrower thus lowering losses.