The double beam tube consists of a set of Helmholtz coils surrounding a bulb of helium gas at low pressure.
Inside the bulb there are two electron guns. One emits electrons straight into the glass bulb (the radial electron gun), and the other shoots electrons tangentially to the coil. Using the radial electron gun, the range of the electrons is show to be proportional to the accelerating voltage and the energy of the electrons. When a current is passed through the Helmholtz coils, the magnetic field generated acts on the electron. The tangential beam can be bent into a circle.
For a field of flux density
for the electrons to travel in a circle of radius
we have
(1)
The kinetic energy of the electron is equal to
and this is equal to the potential energy gained,
where
is the voltage difference between anode and cathode, so
(2)
From (2)
cancel
from both sides to give
then