The machine has four conductive plates
mounted on insulating supports, making two variable capacitors that can
change capacitance in alternate way, as the two central plates are moved
in the direction of one or of another of the two fixed plates at the
left and right sides of the device. At the ends of the movement the
central plates touch each a contact. The plate closer to one external
plate touches a grounded contact, and the other touches a contact going
to the same external plate. The picture below shows how the charges in
the plates ideally increase, starting from an initial charge in one
external plate.
Charge multiplication
Starting from the initial configuration (a), the first cycle ends in (c)
with the charges in plates
A and
B doubled. The next
cycle, however, due to the charge present in plate
D in (d),
results in 5 times more charge. The sequence for the charge in plate
A
is then
Q, 2
Q, 5
Q, 13
Q, 34
Q,
89
Q, 233
Q, and so on. In plate
D the
corresponding charges (when in the positions at left) are 0, -
Q,
-3
Q, -8
Q, -21
Q, -55
Q, -144
Q,
and so on. By dividing one charge by the previous in the same plate,
it's seen that the multiplication factor at plate
A starts at
2 and tends to 2.618 after several cycles. In plate
D it
starts from infinity and falls also to 2.618 after several cycles. The
machine is then more than a "doubler".
Note that this ideal multiplication factor is only achieved if the
capacitance variation is large, and the self-capacitances of the plates
when isolated are significantly smaller than the maximum capacitance
between a pair of plates.
A variation of this same machine is described in a patent [1], with the
two variable capacitors varying simultaneously instead of in
complementary way. In that way the multiplication factor is smaller, and
the self-capacitances of the fixed plates must be large, or discrete
capacitors must be attached to them. The machine described here works
also with diodes instead of switches, as in the patent.
Construction
The 15 cm plates are made of fiber boards covered with thick aluminum
foil, glued to them with contact glue. The insulating supports are made
of HDPE boards, and the contacts with aluminum wire. A brass guide bar
keeps the central plates in position as the central part is moved back
and forth, with the help of a handle attached to the central structure.
The ground terminals are interconnected below the base by a metal strip
(actually not necessary, but improves a bit the performance, as the MDF
base is not very conductive). Two acrylic disks are glued to the to
outer disks as spark shields and movement limiters. Two electrometers
are mounted at the two fixed plates for visualization of the charge.
Top view.
The mechanical system is not very good, having significant friction.
Little wheels could be added to the central structure to facilitate the
movement, or the plates could be mounted differently, in a rotating
structure.
Operation
The machine is self-starting, and gets charged quite suddenly after a
few cycles, reaching about ±10 kV. At the limit corona from the
connection wires, imperfect edges of the aluminum foil, and the
electrometers limits the voltage growth, and can be heard and even seen
in the dark. The insulation of the supports is not very good, due to
their large surface area, and the machine loses the charge in little
time.