regarding recirculation

[happyjack27]

from what i can tell from my sims:

1. w/an uncharged grid, electron losses to the chamber are primarily through point cusps.
2. w/an uncharged grid, once an electron gets outside the inscribed sphere, it's pretty much lost.

presumably w/a charged grid:
1. well the grid of course pulls electrons back into the sphere, so an electron outside the inscribed sphere is not neccessarily lost.
2. as electrons get near the outside of the inscribed sphere, they see the unevenness of the charge distribution on the magrid (that it is not really spherically uniform), and are thus attracted to the close approach of the coils. _this_ is what appears as "funny cusp" losses, and where they need room before the chamber for the grid to pull them back into the sphere. and _this_ is why you need coil separation.

[D Tibbets]

I don't know if your simulation includes mirroring or bouncing along the magnetic field lines. A charged particle that is trapped on a field line tends to travel a distance, then reverse. This behavior is determined by the local B field strength, and charged particle properties. As you approach a corner or edge cusp the B field is compressed more so reversal of the particle is more likely. I'm not sure if the mirror confinement gives a containment of 5 or ~ 50 transits. I think the mirror confinement is worth ~ 5-10 transits, while cusp confinement (the modified long line cusps have compressed (stronger)magnetic fields so the charged particles (electrons) tend to reverse before they get completely through the line cusps, and this results in containment of ~ 50 or more transits. If you are visualizing, monitoring the electron behavior in two dimensions at any given time, then the point cusps would leak more because they have weaker magnetic fields. But if the sim is truly a continuous 3-D model the line cusps should be losing more electrons. Either that or the reasoning about the Polywell is way off, or the claims that the line cusps are effectively converted to higher magnetic field strength point like cusps is indeed true. I cannot find the reference to defend my claim, but I believe Busard said somewhere that the corner cusps leaked ~ 3-5 times as much as the true point cusps. I assume this included the entire corner cusp extending between all 4 nubs that defined it (in WB6). The situation without nubs may be different. Recircultation accounts for any additional input energy gains.
Two things that might apply. How are you injecting your electrons, high voltage guns, or positive accelerating magrid? If you are magically creating your electrons in the center or using a high voltage gun, remember to ground, or apply a positive charge to the magrid. Otherwise it will float and have a negative potential from the electrons that reach it through the magnetic field (that is if your sim includes cross field transport). Otherwise the grid may obtain a pos potential due to induction with the excess electrons (again assuming charge induction is included in your sim.).
The other thing to consider is the relative energy of the electrons. If the electrons outside the magrid are at low voltage, they do not represent much of an energy loss. It would be a concern though, from a maintainable vacuum/ arcing standpoint.

Dan Tibbets

[happyjack27]

not modeling charge induction. charge of grid is just zero right now. always. electrons and ions introduced randomly throughout the inscribed sphere. so in a sense simulating ionization, (though the excess electrons would of course be physically impossible if you started w/neutral particles.)

anyways on the topic of loss energies. i looked at the momentum space view of the electrons and if i zoom way out i see they're contained w/in a sphere. i presume since i'm looking at _classical_ momentum and i'm modelling particle acceleration and lorentz force relativistically, that sphere represents the speed of light times the mass of an electron. so good, i've deduced that, and it's how it should be. so what's my point?

well the fact that i can clearly see the outline of the sphere tells me that i have a substantial number of electrons traveling at relativistic velocities. (mind you, the non-relativistic core is a lot denser, as it should be.)

these particles don't dissappear visually, which they would if they'd be near enough the edge of the chamber to hit it and thus be "lost". also they wouldn't stick around long enough to acquire such high energies if they were near the chamber edge. i presume they're probably very near the magnetic coils. and from the position space view that's where the fast electrons look to be. and it just makes sense.

so this tells me if i was modelling grid losses, the more upscattered of these would hit the grid and be lost. presumably before they acquired so much energy. and so while it's an energetic loss channel, you're essentially cutting off that energy gain so that the particles don't become infinitely more energetic by the time they're lost.

does that all sound right?

[D Tibbets]

I'm unsure of your interpratation significance. Except, it sounds something like what a. Carlson (a plasma physisist) claimed for upscattered charged particles, I think he was referring to ions. He claimed that the potential well needed to be several million volts to contain upscattered ions ( presumably from an initial ion energy of perhaps a hundred thousand eV. But, this ignored the claimed annealing. For electrons, containment is purely magnetic, except for recirculation which will apparently recapture non upscattered electrons. Up scattered electrons that leave a cusp are lost (with the recovery of the accelerating potential on the magrid) eg: a 25,000 eV electron leaves past the + 20,000 V magrid. Terminal velocity would be 5000eV. One claim for the Polywell (I think) is that the loss rate through the cusps is fast enough that the progressively upscattered electrons cannot accumulate to much energy before they escape. So most of their energy is recovered by the magrid. This limits energy loss from lost electrons, and also, prevents the buildup of contained upscattered electrons that would increase Bremsstrulung losses. Or, in short , escaped electrons should not have to much energy. They will fly to the vacuum vessel wall within a fraction of a microsecond. In your simulation do the electrons hang around? If so a portion of them may be upscattered to very high energies from coulomb collisions occuring in this external space.

Dan Tibbets

[happyjack27]

I'm unsure of your interpratation significance. Except, it sounds something like what a. Carlson (a plasma physisist) claimed for upscattered charged particles, I think he was referring to ions. He claimed that the potential well needed to be several million volts to contain upscattered ions ( presumably from an initial ion energy of perhaps a hundred thousand eV. But, this ignored the claimed annealing. For electrons, containment is purely magnetic, except for recirculation which will apparently recapture non upscattered electrons. Up scattered electrons that leave a cusp are lost (with the recovery of the accelerating potential on the magrid) eg: a 25,000 eV electron leaves past the + 20,000 V magrid. Terminal velocity would be 5000eV. One claim for the Polywell (I think) is that the loss rate through the cusps is fast enough that the progressively upscattered electrons cannot accumulate to much energy before they escape. So most of their energy is recovered by the magrid. This limits energy loss from lost electrons, and also, prevents the buildup of contained upscattered electrons that would increase Bremsstrulung losses. Or, in short , escaped electrons should not have to much energy. They will fly to the vacuum vessel wall within a fraction of a microsecond. In your simulation do the electrons hang around? If so a portion of them may be upscattered to very high energies from coulomb collisions occuring in this external space.

Dan Tibbets

depends on the excess charge compared to the mag field strength. to much and they'll blow right out the faces of the magnets. but ofcourse i like to avoid too much, so they hang around for quite some time. plenty of time to upscatter. the ones in the center stay cold, though. teh ones that leak out from the cold core through the cusps, or simply don't start out there, seem to get progressively faster and more distributed over time. i'm thinking of the doedec magrid right now. that one after a time becomes a big fuzzy sphere surrounded by a light fog of seemingly randomly moving electrons that nonetheless stay within the sphere inscribed by the coils for the most part. in fact, if i recall correctly, the few that leak out and hit the chamber don't really look to be all that energetic, comparatively.

[erblo]

from what i can tell from my sims:

1. w/an uncharged grid...

I don't exactly remember what you said was the problem with the charge on the wires but I took a look at your static e-field code. The equation you're using seems right but I don't know if you implemented it correctly due to the lateish hour (combined with my very basic C/C++ coding skills).

However, a quick search resulted in equation 25 from Field + potental from finite line charge which seems about as simple as it'll get (bold=vector or position):

E(r)=k*lambda*2*L/((r1+r2)^2-L^2)*(r1/r1+r2/r2)

(The e-field at r due to a line charge from p1 to p2)

k = 1/(4*pi*epsilon_0) is the constant in Coulomb's Law
lamda is the (constant) linear charge distribution
r1 = r - p1: the vector from the start of the wire to position r
r2 = r - p2: the vector from the end of the wire to position r
(r1 and r2 are their lengths)
L = r12 is the length of the vector r12 = p2 - p1 (aka the length of the wire)

Should be easy to code if you want to use it.

Merry Christmas everyone!

[happyjack27]

from what i can tell from my sims:

1. w/an uncharged grid...

I don't exactly remember what you said was the problem with the charge on the wires but I took a look at your static e-field code. The equation you're using seems right but I don't know if you implemented it correctly due to the lateish hour (combined with my very basic C/C++ coding skills).

However, a quick search resulted in equation 25 from Field + potental from finite line charge which seems about as simple as it'll get (bold=vector or position):

E(r)=k*lambda*2*L/((r1+r2)^2-L^2)*(r1/r1+r2/r2)

(The e-field at r due to a line charge from p1 to p2)

k = 1/(4*pi*epsilon_0) is the constant in Coulomb's Law
lamda is the (constant) linear charge distribution
r1 = r - p1: the vector from the start of the wire to position r
r2 = r - p2: the vector from the end of the wire to position r
(r1 and r2 are their lengths)
L = r12 is the length of the vector r12 = p2 - p1 (aka the length of the wire)

Should be easy to code if you want to use it.

Merry Christmas everyone!

perfect. thanks. i'll comment out my current code and put this in and test it. merry christmas.

[happyjack27]

i implemented it and tested it.
it looks right.


this is my implementation:

b.w is relative voltage density of the wire segment.
ll is length of the wire squared.
v1 and v2 are r1 and r2 respectively. vh1 and vh2 are their lengths squared.

Code: Select all

...

   T4 lvector = translate(b,a);
   T ll = dot(lvector,lvector);
   lvector.w = rsqrt(ll);

   T4 v1 = translate(p,a);
   T vh1 = dot(v1,v1);
   v1.w = rsqrt(vh1);

   T4 v2 = translate(p,b);
   T vh2 = dot(v2,v2);
   v2.w = rsqrt(vh2);

...

T denom1 = sqrt(vh1)+sqrt(vh2);
denom1 = denom1*denom1-ll;
T eforce_multiplier = 1.0f*2.0f*sqrt(ll)*b.w * voltage_density_scale/denom1;

...

	T4 efield;
	efield.x = eforce_multiplier*(v1.x*v1.w + v2.x*v2.w);
	efield.y = eforce_multiplier*(v1.y*v1.w + v2.y*v2.w);
	efield.z = eforce_multiplier*(v1.z*v1.w + v2.z*v2.w);

it's not the right constant scaling factor yet, but that's trivial enough.

here's the first test. just a charged wire: http://www.youtube.com/watch?v=2777bJllMqo

second test is two wires skew to each other of opposite charge and current. i vary the current and charge in the video so i can see the effects of both. i'm uploading that now, got about half an hour left.

EDIT: http://www.youtube.com/watch?v=cCd9aedKmIk

so now we can have a charged magrid! thank you erblo!

[happyjack27]

happy holidays magrid: http://www.youtube.com/watch?v=-RERk022P18

coil charge is obviously too high. the electrons greatly prefer the intersections. this would be more the case with a nonzero radius grid, 'cause the segs wouldn't be cylinders, they'd be cyllinders w/hemispherical caps, thus there'd be an additional sphere of charge at the intersections. likewise the current would be doubled at the intersections.

[happyjack27]

here's a real run w/the charge on:

http://www.youtube.com/watch?v=v7EMqnaWwxU

[ladajo]

You tube blocked it as too large.

[happyjack27]

You tube blocked it as too large.

yeah, i see that. :/ by 2 minutes. i just cut it in two and i'm uploading the first half now. should take about a few hours. for both halves.

[happyjack27]

here we go, first half. i should warn that the program i used to split it somehow added a soundtrack. so you may want to turn the sound down. then again it's oddly consanant and melodic. also oddly it doesnt have a name.

this is volume elements from center on the x-axis, radial momentum on the y axis.

http://www.youtube.com/user/happyjack27 ... rXAfC06kaQ

[happyjack27]

part 2: http://www.youtube.com/user/happyjack27 ... 0B3gNFeu58

here i put axial momentum on the z-axis.

partly through i notice something's wrong - some electrons get stuck the the grid. so i turn down the charge on the grid to get them off.

later on i put potential energy on the y-axis.

and at the end i show fusion cross section on the z-axis.

[happyjack27]

after running a while, some phase space views.

this starts off with volume elements from center on x, radial momentum on y, and axial momunetum on z. then i show some fusiont cross section on the z around 4:15. around 6:20 i should electric potential energy. don't recall if this includes the grid charge. might just be the prarticles. i don't remember exactly but it looks like the ions have already been through their first pass through the center and are on their second:

http://www.youtube.com/watch?v=mv7iNGOs4ZU

and the position space view. this is a separate run i think so the params might be different:

http://www.youtube.com/watch?v=kieEw6e3vkM