I have come across some interesting research by Kiyoshi Yoshikawaa,of the Institute of Advanced Energy, Kyoto University, and others proving the formation of the Polywell.
For those of you who have not been following along here is how my understanding has been evolving.
Polywell As I Currently Understand It
Polywell - Adding Details
A schematic of the evolution of the Polywell design can be found in slides 8 and 11 in this Power Point slide show (link at bottom of page).
In the Hirsh/Farnsworth machine in slide 8 the reacting positive ions (like charged Deuterium particles for one kind of operation) are attracted to the center to collide and produce fusions.
In the Elmore/Tuck/Watson machine in slide 11 electrons are accelerated to the center of the machine where they form a grid sort of like what happens in a beam power tube. In the beam power tube the virtual grid is called a space charge. These negative electrons attract the positive fuel ions and fusion reactions take place. The advantage is that there is no grid near the reaction space so losses are reduced.
That is the theory any way. However, in any person's mind who has a little understanding of the physics involved the question is: is that really happening? Are we fooling ourselves? Which brings us back to the Yoshikawa paper. What is the evidence?
Yoshikawaa correctly states the central issue:
...it is essential to clarify the mechanism of potential well formation (see Fig. 5) predicted to develop in the central plasma core within the cathode, since potential well formation due to space charge associated with spherically converging ion beams plays a key and essential role in the beam-beam colliding fusion, i.e., the major mechanism of the IECF devices. Actually, this has been the central key issue for IECF researchers for the past 30 years, until the first successful direct measurement of the double-well potential profile in the IECF device through the laser- induced fluorescence (LIF) method at Kyoto University  in 1999 with an approximately 200 V dip at the center in the helium plasma core as will be described below.So they have proved the formation of the Polywell. Outstanding!
Many theoretical results so far predicted strongly localized potential well formation, and actually for the past 30 years, many experiments were dedicated to clarify this mechanism using, such as, electron beam reflection method , spatially collimated neutron  or proton [8,9] profile measurements, or an emissive probe , as is seen in Table 2, but, neither seems to be perfectly conclusive in convincing that well does form.He again hits the nail on the head. Lots of results that could have more than one interpretation. He then gives a list of past attempts at verification of the Polywell. Now let us get to how what he claims was the definitive experiment was done.
...we have adopted optical diagnostics by using the Stark effects, sensitive to the local electric fields, to the IECF device with a hollow cathode. Also to enhance S/N (signal to noise) ratio as well as to specify radial potential profile, we introduced the LIF method. Consequently, we could have finally measured the double-well potential profile (see Fig. 11) with an approximately 200 V dip at the center for the first time in the helium plasma core (Fig. 7) in the IECF device.He goes on in even more technical detail. The end result? The dual (cathode and anode) potential well forms.
In any future experimental regimes such a measuring system should be used to verify machine operation and to provide machine diagnostics.