14
An Introduction to Beam Physics
FIGURE 1.9: Design sketch of the use of the Van de Graaff generator as
a particle accelerator. (From R. J. Van de Graaff, US Patent 1,991,236, 1931
[18].)
create a field-free interior, a new charge can be brought in from the belt on
the inside of the sphere without experiencing any opposing fields, and thus
large amount of charges can be accumulated on the sphere, resulting in very
high potentials. The mechanism of the Van de Graaff generator is shown in
the left part of Fig. 1.8 and the complete machine is shown in Fig. 1.9. The
sketches are from the original patent on the device [18]; see also [20].
In passing it is worthwhile to remark that while the newly added charge
does not experience a field when moving from the belt to the inside of the
sphere, it certainly experiences a field while approaching the sphere and being
attached to the belt. Thus the potential energy contained on the charged
sphere does not come for free. It is generated through the mechanical work
that is necessary to move the belt and the attached charges toward the sphere.
The charged sphere is connected to a metal enclosure containing the ion
source, thus elevating the source to the potential of the charged sphere, which
can then be utilized for the acceleration of the particles.
The main practical limitation of the Van de Graaff accelerator is the necessity to prevent sparks. This is achieved on the one hand by sheer size,
because at the same potential difference, larger size means less electric field
strength. On the other hand, it is important to inhibit the spark formation process. Microscopically, sparks form in a gas when small numbers of
charged particles have a mean free path length that is long enough so they can
attain energies sufficient to ionize other particles upon collision, resulting in
an avalanche. This can be avoided by choosing inert gases like He (helium)
or SF 6 (sulfur hexafluoride), and on the other hand applying high pressure to
reduce the mean free path length.
An Introduction to Beam Physics
FIGURE 1.9: Design sketch of the use of the Van de Graaff generator as
a particle accelerator. (From R. J. Van de Graaff, US Patent 1,991,236, 1931
[18].)
create a field-free interior, a new charge can be brought in from the belt on
the inside of the sphere without experiencing any opposing fields, and thus
large amount of charges can be accumulated on the sphere, resulting in very
high potentials. The mechanism of the Van de Graaff generator is shown in
the left part of Fig. 1.8 and the complete machine is shown in Fig. 1.9. The
sketches are from the original patent on the device [18]; see also [20].
In passing it is worthwhile to remark that while the newly added charge
does not experience a field when moving from the belt to the inside of the
sphere, it certainly experiences a field while approaching the sphere and being
attached to the belt. Thus the potential energy contained on the charged
sphere does not come for free. It is generated through the mechanical work
that is necessary to move the belt and the attached charges toward the sphere.
The charged sphere is connected to a metal enclosure containing the ion
source, thus elevating the source to the potential of the charged sphere, which
can then be utilized for the acceleration of the particles.
The main practical limitation of the Van de Graaff accelerator is the necessity to prevent sparks. This is achieved on the one hand by sheer size,
because at the same potential difference, larger size means less electric field
strength. On the other hand, it is important to inhibit the spark formation process. Microscopically, sparks form in a gas when small numbers of
charged particles have a mean free path length that is long enough so they can
attain energies sufficient to ionize other particles upon collision, resulting in
an avalanche. This can be avoided by choosing inert gases like He (helium)
or SF 6 (sulfur hexafluoride), and on the other hand applying high pressure to
reduce the mean free path length.