FYI . My perceptions about corner sizes, shielded surfaces (or partially shielded surfaces like the Coaxial cables in 'Mini B') corner potential well voltage droop, Low Beta loss size- number of passes- mentioned 10-60 passes here, etc. is mostly derived by the information given in this patent application from 2008. Thee is a claimed sweet spot (distance beyond cusp) for positive magrid electron gun location to get good extraction, but acceptable cusp potential well voltage droop. Was this found to not be the case?http://www.freepatentsonline.com/y2008/0187086.html
Excerpts from the patent application:
A larger version of the closed box device (PXL-1) was built as WB-5 (2004-2005), to test improvements in magnetic insulation by use of external surface and cusp coils at high fields. Its test results showed 1000-fold improvement (in ability to reach deep fractional well depth at given starting pressures; early work was limited to 3E-9 torr, while WB-5 ran at 3E-6 torr) from early work on a larger closed-box machine but its inability to be driven beyond this increase illuminated the critical and dominating effect of unshielded surface losses of electrons, on overall system performance.
In order to reduce electron loses, it is preferable to have less than 1/10,000 of all surfaces. unshielded. Most desirably, no B fields should intersect any metal surfaces in the system. To this end, all coil containers should be substantially conformal in shape to the B fields they produce.
Coil corner spacing must be at least 3 electron gyro radii and up to 10 or so, but not markedly greater;
3. The results of all of the experimental studies to date have shown physics limitations that suggest engineering configurations and designs to use of fully electron-recirculating machines, within external vacuum shells or Faraday cages, with only the internal machine at high electric potential. In this arrangement, the electron emitters/sources and the external shell are all at ground potential.
Another key feature of embodiments of the present invention is the placement of the electron sources outside and around the machine (i.e., outside the magnetic field coils). These emitter/repeller plates 102 can be simple active emitters in the form of filamentary electron emitters, heated by ohmic currents, and emitting electrons according to a modified Child-Langmuir law. These are placed on-axis of the main faces of the polyhedral field geometry, and biased negatively with respect to the device itself. By this means, the device coils become the accelerating potential drivers for extraction of electrons from the emitters. The machine coils may be at high positive potential and the emitters at ground potential, for example, in which case the external shell or cage surrounding the entire system within a vacuum pumping system will also be at ground potential. The only object at high electric potential, then, are the coils. Electrons from the emitters (emitter/repeller plates 102) will be emitted effectively only if they are located sufficiently close to the attracting surfaces of the machine. However, they must not be too close, else their potential difference will cause suppression of the well depth at the edges along the cusp axes. This “droop” would make ion confinement less attractive, and less feasible. The appropriate distance to place the emitters has been found to be at about that of the radius of the cusp face and more generally at about 1-1.5 times the radius of the cusp face on whose axis the emitters are placed. The droop then expected is less that 15% of the well depth. At further distance the extraction will be poor, and closer in, the droop will become excessive.
The term emitters/repeller plates 102 has been used herein to designate either active emitters (as shown in FIG. 12) or repeller plates. Repeller plates are not active emitters but rather generate electrons from secondary electron emission due to ion bombardment from ions escaping along cusp lines (because of the droop just discussed). It has been found by experiment that, given sufficient magnetic field trapping of interior particles, it is possible to run such a system entirely on secondary electrons from non-active repeller plates on cusp axes, if the B fields are above 500-800 G. These repeller plates must be positioned within a few cm of the cusp axes, as must the emitters, and at about the same distance from the machine (i.e., coils) as the emitters, just discussed. They must be held at ground potential (for the example given) by an external power supply, just as must the emitters themselves. Of course, the potential of the system could be inverted, with the machine and all surrounding structures held at ground potential, while the emitters and repellers are held at high negative potential, but the preferred embodiment is that of the first-above description.
4. An alternate potential arrangement could be used, in which the only elements at high negative potential are the emitters. This can work if it employs driven, negatively biased repellers at every cusp axis position, to prevent excessive electron loss by streaming out along each axis. Such repellers could also act as secondary electron emitters (from ion bombardment) to the degree that the primary driven emitters may be turned off, as shown in tests on WB-5.
5. In these systems electron loss phenomena are primarily to (metal) surfaces of the machine system. Cross-field losses are well understood and can be controlled. However, losses to poorly shielded (by fields) or unshielded surfaces can constitute major loss channels. From WB-5 and WB-6 it has been shown that that the fractional area of unshielded surfaces must be kept below 1E-4 to 1E-5 of the total surface area, if electron losses are to be kept sufficiently small so that net power can be achieved. And, further, that no B fields should be allowed to intersect any such internal surfaces of the machine.
6. This requirement has two main consequences: (a) All coil containers/casings should be of a shape conformal to the B fields produced by their internal current conductors, and; (b) The finite size of real coils forces design so that no coils/containers should be allowed to touch each other, but all corners should be spaced at some distance from the adjacent coils, to avoid B field intercept.
7. This is the principal criterion for design and construction of any real, finite material coil and system, no matter the plan-form shape of the coils, which is of no major significance (i.e. round, square, polygonal or triangular, etc). The spacing between coils should be such that the central plane B field is approximately the same as that of the B field on main face axes. Typically, this may be at minimum the order of a few (5-10) electron gyro radii at the inter-corner field strength, but not greatly larger than this (to avoid excessive degradation of the internal WiffleBall—WB—electron trapping factor in the machine main field. This Wiffle Ball trapping factor (Gwb) is not a measure of losses in any recirculating machine, thus its value need not be as large as those potentially possible with high B fields (1E3 vs 1E6), thus greatly relaxing the need to strive for super-high Gwb factor values.
8. This Wiffle Ball trapping factor (Gwb) is NOT a measure of losses in any recirculating machine, thus its value need not be as large as those potentially possible with high B fields (1E3 vs 1E6), thus greatly relaxing the need to strive for super-high Gwb factor values.
9. Wiffle Ball behavior is of value to establish the density ratio from the machine interior to its exterior, and this is important to assure suppression of Paschen arc breakdown outside, which destroys the electron injection drive and well potential.
10. These considerations have been driven by the long array of experiments described above, first on WB-2, then some on WB-3, then the last series of WB-4, with parallel tests of unique-feature other devices, MPG-1,2 and PXL-1, PZLx-1. Finally experiments were run in tests subsequent to these on WB-5, and lastly on WB-6, the final machine, with greatly reduced losses, and record-breaking DD fusion output.
Initially, when the electron density is small, internal B field trapping is by simple “mirror reflection” and interior electron lifetimes are increased by a factor Gmr, proportional linearly to the maximum value of the cusp axial B field. This trapping factor is generally found to be in the range of 10-60 for most practical configurations. 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=8πmE/B2.
The highest value that can be reached by electron density is when this ratio equals unity; further density increases simply “blow out” the escape hole in each cusp. And, low values of this parameter prevent the attainment of cusp confinement, leaving only Gmr, mirror trapping. When beta=unity is achieved, it is possible to greatly increase trapped electron density by modest increase in B field strength, for given current drive. At this condition, the electrons inside the quasi-sphere “see” small exit holes on the B cusp axes, whose size is 1.5-2 times their gyro radius at that energy and field strength. Thus they will bounce back and forth within the sphere, until such a “hole” is encountered on some bounce. Analyses show that this factor can readily reach values of many tens of thousands, thus provides the best means achieving high electron densities inside the machine relative to those outside the magnetic coils, with minimal injection current drive.
Also, on page 9 in this paper it is mentioned that keeping B constant while increasing plasma current to inflate the Wiffleball- approach Beta= 1 is one way, ie: Mini-B.
Alternately, current can be constant while B is low and then increased to gradually develop high Beta. Cusp confinement scales as B squared, so Beta should gradually increase as B is increasedhttp://www.askmar.com/ConferenceNotes/2 ... 0Paper.pdf
. A combination of both may give a more controllable solution. Mini- B was the first approach, and I do not know what was used in WB7 or 8.
This paper may be related. On a side note I think it puts the Wiffleball radius (for most conditions of intrest) at 83% of the radius to the magnets. This question had been asked in another thread.http://www.askmar.com/Fusion_files/EMC2 ... lywell.pdf