Figured out why the
magnetic cage, combined with ion guns isn’t a problem for
Well, at least I’ve managed to fool myself into thinking it isn’t a problem.
In the use of the cage structure as both an ion gun and inertial containment
field, it’s important not to have any of the cage structure generate magnetic
fields. The reason is that if there is current flowing through the wires,
the ions which are driven by this same structure (the grids operating as an ion
gun) will be crossing the generated magnetic fields generated from these
currents at right angles. Current flowing through a wire generates a
really simple field, shown on the right.
Thus, any ion accelerated by these electrodes will cross the magnetic field
lines at right angles and thus their momentum will be given a transverse
component. Transverse components of the ion momentum increases the minimal
radius the ions approach in the center.
In the magnetic cage, the
ions are injected parallel to field lines. So there will be
spiraling of the ions down the field lines (shown
in the figure on the right). So I was thinking about the ion injection in
the magnetic cage. The faces are open, so there’s this big vacuum gap in
the magnetic field. I went to the handy-dandy
magnetic flux calculator page where I could find out what the flux would be
at the distance x from the centerline of a rectangular bar magnet face. I
know this is not the correct approximation to use, as what I actually need to
measure is the flux at some distance perpendicular to poles of the magnet.
But it’s there and I’m just trying to get a feel anyway.
The inscribed circle of a pentagon for the icosidodecahedron cage with the
four inch radius I’m using is approximately 2 inches . So if I use my
NdFeB grade 35 magnets (.107" x .107" x 2"), I get a flux of about 8 gauss.
If I use grade 5 ceramic magnets, I get a flux of 3 gauss also (the ceramic
magnets are thicker). So continuing down the path to hell I’m paving with
my over simplified model, the flux at the center of the pentagon faces should be
anywhere from 6 to 16 gauss, plus or minus a few gauss. In the current
design, the ions will be injected into the faces with a minimum energy of 2 KV.
I say minimum, as the are also being accelerated by the massive negative space
charge in the center of the cage. The
ion gun itself is accelerating the
ions at 2 KV, so I’m not counting the acceleration due to the space charge at
the center of the cage.
cage structure is also held at the negative potential the electrons are injected
with, but because of the way the guns are constructed and mounted around the
spherical vacuum chamber, the particles don’t see much of the fields produced by
the cage – they’re shielded by the vacuum chamber fields (which is coupled to
the 2 KV oscillating field of the ion gun. So calculating the actual
fields and particle energies at various points in the system is actually pretty
complicated. My simple model is that the ions will have energies at least
2000 volts when their at the center of the pentagon faces.
The gyro radius of a deuteron ion at 2000 volts is something like 2
meters. So there’s going to be an angular velocity kick of 4.3899E+05
meters / sec. A fairly hefty kick, if only a brief one, as the ion passes
through the center of the face. And this kick is proportional to the angle at
which the ion beam is misaligned down the radius of the system – hopefully very
small. A simple model of this should be easy enough to analyze with some
finite element modeling. I only have the cheesy student editions of
programs with no magnetic field capability. If anyone out there has access
to a FEM for charged particle optics with magnetics, the first approximation
model should be fairly straight forward. I’d be interested in seeing the
analysis. Until then, I think I’ve managed to fool myself that the
transverse momentum introduced by the magnetic fields of the cage are miniscule.
Again, if someone knows better, please let me know…
The reason why the magnetic fields wreck so much havoc when the grid is also
used as the ion gun is that the magnetic fields are very strong close to the
wires carrying the current. If things are working correctly, the
accelerated ions pass very close to the wires that form the cage, and thus the
ion guns. The ions also cross the fields at orthogonal paths and thus get
maximum kick as they cut the field lines. Since the cage structure also
ionizes the deuterium, there’s every reason to suspect that quite a bit of
current will be flowing in the grid wires of the cage – i.e. lot’s of amps.
So the magnetic fields, if un-cancelled, will be mighty strong.
I wonder if deviation due to this current flow might be a significant
limitation in the glow discharge fusor designs that have built to date.
The current flowing will cause magnetic fields which will perturb the desired
radial vector of the ion. Maybe this is one of the reasons that fusors
with ion guns have higher yields – they have less intrinsic distortion in the
radial focusing of the ions. It might be interesting to calculate what
this effect might be given the operating parameters of the various glow
discharge fusors built so far. It might be that simply using double
conductors for the grids that cancel out the magnetic fields might significantly
improve the yields of these systems.