Help fill in my understanding of the Polywell fusion reactor Polywell is a proposed new type of fusion reactor, which is designed to use magnetic fields to overcome the problems with the Elmore-Tuck-Watson fusor.  I'm trying to understand exactly how it works.

An Elmore-Tuck-Watson fusor ... consists of a vacuum chamber containing a negatively charged outer grid (which may be the chamber) and a positively charged inner grid. Electrons are injected into the system and accelerated toward the inner grid. Most of the time, the electrons pass through the grid, through the core, and through the inner grid again, which then decelerates them and reaccelerates them inward wherein they return through the core. As they pass repeatedly through the core, they generate a negatively charged zone, a potential well, which is called a virtual cathode.

Question 1: So this device uses a constant high voltage applied to the electrodes to produce a region of negative electric charge in the center.  How is this possible?  Electrons repel each other, so creating a region in empty space in which electrons are more dense than their surroundings would seem to require a constant energy input.  Without any energy input, they'll just fly apart to a minimum energy equilibrium where the charge density is equal everywhere.  Applying a voltage to electrodes with no current flowing between them does not use up any energy, however.  So where is the energy to hold the clump of electrons together coming from?

Like the Elmore-Tuck-Watson (ETW) fusor, the polywell confines positive ions through their attraction to the negative potential well which is created by the electrons that are held inside a positively charged grid. However, to avoid the losses related to the electrons striking the grid, the Polywell uses magnetic fields to shield the grid. The magnetic fields are configured in a way that adds to the confinement of the electrons so that there are many more electrons inside the core than outside.

Question 2: So the magnetic fields generated by the grid would supposedly prevent the electrons from hitting the grid.  The positively charged inner grid is attractive to electrons, but it's also magnetized, and somehow the magnetic fields repel electrons away from the grid?  But how can unchanging/steady-state magnets confine (or repel) electrons?  A bar magnet doesn't create any kind of movement or displacement of charge.
 A: A charged particle moving in a magnetic field experiences a force f= q*VxB. This force is
perpendicular to both the mag field and the direction of motion. If it is a uniform magnetic field charged particles move in circles, and the frequency is called the cyclotron frequency.
You can essentially decompose the velocity into a component parrallel to the mag field, and a component perpendicular. The later is like an orbital velocity, the former (parallel to the field) velocity is unaffected. So your electrons would turn sideways rather than go straight at the wires.
But in a real plasma, the charged particles will occasionally collide, and new orbits established after every collision. I think (but its been decades for me) as a result they will drift in the direction of the electric field anyway. I don't know if this happens in a fast enough time span to seriously affect the device. But in oder for the fusion device to work, the hydrogen (or Helium-3) nuclei have to be colliding with each other. So the system will not
be lossless. I presume the scientists in charge have worked this all out.
A: The idea is that the magnetic fields contain the electrons in the center. Yes there will be losses, but the containment factor is the key to current research. Is it enough to build a sufficient population of electrons to create a large enough negative potential well to in turn attract ions (fusion fuel) at a high enough velocity and density that they will collide and fuse as they accellerate towards the center of the volume from opposing directions. The current state of the research states that confinement is proven. The step in progress is the next after confinement, and that is scaling. In the current project, the magnetic field is being increased by a factor of 8 (.1T to .8T) to verify the predicted containment scaling. If the scaling is proven, the next step would be to build a unit at the predicted breakeven size, which is about ten times the currently tested diameter. They will increase the magnet torus from 30cm to 3Meters (or 15cm radius to 1.5Meter radius, as is commonly discussed). The primary loss in a fusor is collisions with the central grid. The polywell eliminates this grid by use of the magnetic fields.
A: It should be stressed that electrons are very very easy to trap in the magnetic confinement region created by the arrangement of magnetic coils in Polywell.  The electrons in the trap interact with the magnetic fields and actually bend the lines of force into a spherical magnetic chamber with small regions where the lines of force lead outwards. This happens because electrons by themselves are diamagnetic.  
Some positive ions (protons, deuterium nuclei, B11 nuclei, etc.) will drift into the well also.  Electrons and ions can escape the well, but travel along the magnetic lines of force and get fed back into the well.  The high voltage static electric field continuously draws electrons into the trap, and the ions are attracted to them.  
The pocket of trapped plasma is called quasi-neutral because there are always just a bit more electrons than ions.  Ions are also injected from far outside the well and are accelerated to a high speed by the electric field toward the quasi-neutral (on the negative side of neutral) gas in the pocket.  Because these ions are fed in from far outside the well, their speed is so high at the center of the trap, that if a collision does occur, then fusion will happen.  
The gas pressure used is so very low that "thermalization" does not happen.  "Thermalization" is when gas particles randomly collide and create a Boltzmann distribution.  Because the gas pressure is very very low, hardly any non-fusion, high speed, accelerated, incoming ion with trapped ion collisions occur.  Therefore the accelerated ions maintain their speed.  
Ions that do not fuse will just fly out the other side of the potential well, slow down, and fall back in again.  The see-saw effect of falling in, flying out and falling back into the well can be maintained by adding a small oscillation to the generally static electric field which resonates with the particular species of ion that is desired to be accelerated into the cloud of "target" ions.  If the population of gas particles in the trap gets too dense, "thermalization" will occur.  The accelerated ions get slowed down by too many non-fusion collisions, and fusion stops.
A: I guess some more remarks are necessary with regard to electrons being inside and outside the "grid".  If you studied Physics in High School and/or College, you may recall one exercise where you integrate the electric force inside a charged hollow sphere.  The net force on a charged particle inside that sphere integrates out to zero.  In Polywell, the "grid" is a set of 6 charged tori in a cubical arrangement.  While that is not exactly a hollow sphere, some distance inward from the tori, the static electric field will tend to blend toward spherical symmetry.  Even with a cubical charged shell, the forces on a charged particle inside will be small.  What happens is that the potential inside a charged hollow container is a constant level everywhere inside, so forces are the "same" in all directions.  The more spherical the container, the more uniform that potential level will be. In the case of Polywell, the closer to center inside the "grid", the more spherical symmetry the electric field will exhibit.  Outside the "grid", and the farther away from the center, the more the electric field appears as a point charge.  So anywhere inside the "grid", there will be a very lowered electric force at least, and of that, less and less force due to lack of perfect spherical symmetry the closer to center an ion may come. Outside the grid, there will be some force acting more like a point charge the farther away.
Remember that there are positive ions inside the electrostatic trap as well.  The quasi-neutral plasma having positive ions in the mix, will also  tend to smooth out whatever electric forces remain.  What keeps the plasma in the trap are mostly the magnetic fields.  The plasma is held in the trap as a "target" so high speed ions coming from far outside the magnetic trap and accelerated by the electric field can collide with an ion in the trap.
For the other question, the magnets are not used to "repel" electrons exactly.  Rather, in a magnetic field, electrons are constrained to travel along magnetic lines of force.  The electrons are prevented from grounding on the positively charged metal "grids" by simply being constrained to travel along magnetic lines of force that never intersect the "grids".  That is why the "grids" were made to conform to the contour of the magnetic lines of force.  The use of magnetic coils inside circular cross-section toroidal static charged metal "grids" was Bussard's solution to electron loss.  If you read about his earlier experiments, you will see that the EMC2 team was having great difficulties with electron loss because they were using tori with a square cross-section. There are even pictures on the internet that show the burn marks on the shell where electrons following magnetic lines of force were channeled right into the toroid casing and "grounded".  So the solution was to create a torus with a cross-section that is more conformal to the magnetic lines of force.  The electrons then travel along magnetic lines of force that never (well, at lest fewer) intersect the metal shell of the charged torus, and having less of a path to ground, the electron loss was greatly reduced.  I would guess that future toroid shells may evolve into a sort of teardrop or maybe egg-shaped cross-section to conform even more closely to the contour of the magnetic lines of force.
