Well Formation

[MSimon]

Does anyone know of any theory or experiments that covers well formation? I'm specifically interested in well depth (voltage) vs size, electron injection, and anything else that matters.

[hanelyp]

My impression is that well depth, and probably profile, is a function of electron energy profile.

[D Tibbets]

I suspect you may have most , if not all of these references.
A paper by well respected physicist Dr Krall may be a good starting point:

http://www.askmar.com/Fusion_files/Form ... aining.pdf

Other papers from the Askmar site may also be useful. Some Physics Considerations of the Polywell may bear revisiting.

Some other sources, if you can find them, may be useful directly or via their bibliographies.


Convergence, electrostatic potential, and density measurements
in a spherically convergent ion focus
T. A. Thorson,a) R. D. Durst, R. J. Fonck, and L. P. Wainwright
University of Wisconsin—Madison, 1500 Engineering Drive, Madison, Wisconsin 53706
~Received 18 June 1996; accepted 11 October 1996!

"Unique measurements of the basic plasma-flow characteristics in a low pressure ~<53 mPa H2!
spherically convergent ion focus are obtained using high-voltage ~<5 kV! emissive and double
probes. The radial plasma potential distribution agrees with a collisionless, recirculating,
space-charge-limited current model. Flow convergence increases with voltage and neutral pressure
and decreases with cathode grid wire spacing and current. Core radii within 4–5 times the ideal
geometric limit are measured, and the observed core sizes are consistent with predictions from a
multipass orbit model which includes asymmetries in the accelerating potential well. A virtual
anode is observed in the converged core region, and no evidence for multiple potential well
structures in the core is found. Measurements of the core ion density ~nic;1015 m23! are consistent
with simple flow convergence models."
© 1997 American Institute of Physics.
@S1070-664X~97!02701-8#




Review Article: Magnetic Electrostatic
Plasma Confinement
By Thomas James Dolan, Idaho National Engineering Laboratory, EG&G Idaho,
PO Box 1625, Idaho Falls, ID 83415-3880, USA




Potential Well Structure
Associated with the
Periodically Oscillating
Plasma Sphere (POPS)
Michael David Sekora



Some of the Japanese papers or presentations at the Joint US- Japanese Workshops may be useful. I am thinking that the 2011 workshop my have several presentations on potential well shapes and developement in IEC devices.


Measurements of strongly localized potential well proles
in an inertial electrostatic fusion neutron source
K. Yoshikawaa, K. Takiyamab, T. Koyamaa, K. Taruyaa,
K. Masudaa, Y. Yamamotoa, T. Tokua, T. Kiia, H. Hashimotoa,
N. Inouea, M. Ohnishic, H. Horiiked
a Institute of Advanced Energy, Kyoto University, Uji, Kyoto
b Hiroshima University, Higashi, Hiroshima
c Kansai University, Suita, Osaka
d Osaka University, Suita, Osaka
Japan
Abstract." Direct measurements of localized electric elds have been made by the laser induced
fluorescence (LIF) method using the Stark e
ect in the central cathode core region of an inertial
electrostatic connement fusion (IECF) neutron (proton) source. These are expected to have various
applications, such as luggage security inspection, non-destructive testing, land mine detection and
positron emitter production for cancer detection, currently producing continuously about 107 n/s D{
D neutrons. Since 1967, when the rst fusion reaction was successfully proved to have taken place
in a very compact IECF device, potential well formation due to the space charge associated with
spherically converging ion beams has been a central key issue remaining to be claried in beam{
beam collision fusion, which is the major mechanism of the IECF neutron source. Many experiments,
although indirect, have been done so far to clarify the nature of the potential well, but none of them
has produced denitive evidence. The results found by the present LIF method show a double well
potential prole with a slight dip for ion beams with relatively larger angular momenta, whereas for ions with smaller angular momenta, a much steeper potential peak develops."




Dan Tibbets

[MSimon]

I suspect you may have most , if not all of these references.

Dan Tibbets

Thanks for refreshing my memory. Let me add:

http://www.askmar.com/Fusion_files/Poly ... oncept.pdf

Convergence, electrostatic potential, and density measurements
in a spherically convergent ion focus
http://www.minds.wisconsin.edu/bitstrea ... file_1.pdf

Magnetic Electrostatic Plasma Confinement By Thomas James Dolan
http://www.askmar.com/Fusion_files/Magn ... nement.pdf

[mvanwink5]

CSI has done some testing of potential well depth, but they had trouble getting good well depth with their first device (continuous operation, steady state)

http://www.convsci.com/sites/default/fi ... ummary.pdf

[D Tibbets]

And, don't forget Joel Rogers work. [Edit- name corrected]

https://www.google.com/search?q=joel+ro ... 8&oe=utf-8

The later work is promising (first two links).

In another paper he described the potential well depth vs B field strength. I cannot find that one right now.

Dan Tibbets

[D Tibbets]

Perhaps this is the paper I was thinking of. Rogers is not an author but it was at the same University.

Abstract:

http://scitation.aip.org/content/aip/jo ... /1.4894475


Dan Tibbets

[MSimon]

And, don't forget Jorl Rogers work.

https://www.google.com/search?q=joel+ro ... 8&oe=utf-8

The later work is promising (first two links).

In another paper he described the potential well depth vs B field strength. I cannot find that one right now.

Dan Tibbets

And google leads to:

viewtopic.php?t=4007

[MSimon]

The depressing thing about well vs magnetic field from Rogers:

Well depth decreases with increasing magnetic field.

[D Tibbets]

The depressing thing about well vs magnetic field from Rogers:

Well depth decreases with increasing magnetic field.

Myhand waving take on this is that it reflects the increasing difficulty of injecting electrons as B increases.

My rough calculation for electron injection efficiency in WB 6 was ~ 2-3%. I am assuming that injection efficiency reflects the cusp confinement at low Beta. In WB6 this was ~ 60 passes (from patent application). A rough assumption that the inward cusp rejection of electrons is similar to the outward rejection at low Beta, then injection efficiency should be ~ the reciprocal of the low Beta cusp confinement (as measured by number of passes befor escape). Thois further assumes the flight paths of the electron gun electrons is roughly matching the outward electron streams that eventually escape from the interior- similar dispersion/ cone of the cloud of electrons. Some corrections may need to be made as the geometry is not identical, but.. The high Beta effectively decreases the escape area of the cusps for internal electrons, but I think the extrenal entry cone is not changed much as the external B field is not compressed. What happens as the electrons entering the machine reach very close to the midplane radius of the magrid is more uncertain were conversion from spiraling motion to linier motions of the electrons. Recirculation of electrons in WB6 would seem to imply that if the electron paths are very close to parallel to the cusp axis and inline with the cusp then penetration (injection efficiency) may up to ~ 90%.

This suggests that very good alignment of external electron guns along with good maintenance of the collimation of a tight electron beam will penetrate well. Achieving this with high electron current (density) in the beams is the challenge. Preventing electron spread (loss of tight collimation) of the inward directed electron beam is the key (I think). And this needs to be done without extra charged structures near the magrid. Magnetic focusing and positive charge on the magrid is what I currently envision as the possible solution.

Note that the low Beta confinement in Mini-B was only ~7 passes. I suspect this is much worse than WB6 claims for two reasons. The seperation between the magnets was much greater, especially relative to magnet major radius. I hope this implies that the WB8 showed better low Beta cusp confinement so that increased relative ExB losses in the cusp needs to be addressed(to keep it from becoming dominate).
Secondly the cables with supports were sticking into the machine and were probably poorly magnetically shielded (especially as Beta was increased) This may be compared to the poorly insulated nubs on WB6, except these loops in Mini-B had much more surface area exposed to the plasma.. While this is not strictly cusp losses, still it is presumably a huge loss pathway for electrons and even energetic ions.
Note also, that the magnet separation to allow a desired number of electron jumps (ExB jumps) is a constant selected for the system. This is independent of overall machine size. In WB6 the magnet separations were ~ 1/2 cm. In Mini-B the separation was over 1 cm (I think I measured almost 1.4 cm seperation. This translates into a net difference in cusp width of ~ 4 fold relative to machine size. WB6 was ~ 2 times wider. The low beta surface area and the high Beta surface area of the internal confinement quasi sphere is dependant on the machine radius at constant B and magnet separation. With the size ~ 1/2 and the magnet seperation ~ 2 times greater, there was a double whammy. The net difference in cusp confinement could more than 4 fold at constant B. Mini- B ran at ~2,700 Gauss so some of the difference was made up but I suspect not all*. The magnetic field measuring cables stuck inside could easily have been a dominate loss pathway in addition to cusp considerations.
The design did it's job, but it was far from an idealized confinement configuration.

Another point is that the E gun faced a ring centered point cusp. The minor radius vs the major radius considerations as it applies to overal machine radius and B field strengths in the wall of this cusp suggests to me that the opening for electron injection was narrower relative to the WB6 corner cusps. So, even with better electron beam focusing (was it better?) the injection efficiency was no better than in WB 6 with it's coner place and almost omnidirectional electron guns. A unknown modifier in the comparison is the focus that may have been done by the positively charged magrid in WB6. I speculate that a distant, tightly focused and aimed E-gun at moderate voltage combined with a moderate positive charge on the magrid might significantly improve injection efficiency. This has other consequences that need to be considered, but it may be the best compromise.

* What is the B field drop off from the magnet can surface to the center of the cusp? Is it linear with distance (I don't think so). Is it 1/d^2, or even 1/d^3 ? With a single magnet, the inverse square law should apply, but with two closely separated and opposing magnets, I am sure it is more complicated.

Dan Tibbets

[hanelyp]

Magnetic field on axis as a function of distance from a current loop, http://hyperphysics.phy-astr.gsu.edu/hb ... oo.html#c3
Bz = (u0/4pi)*(2pi*R^2*I)/(z^2+R^2)^(3/2)
Varies as 1/d^3 where d is distance from toroid minor axis. Field from electric and magnetic dipoles generally follows inverse cube.

This is (roughly) the field gradient an electron fighting to get through a low beta cusp would encounter. Off axis is a much messier calculation.