Download A PRELIMINARY DESIGN FOR A SMALL

A
PRELIMINARY
DESIGN FOR A
SMALL
CYCLOTRON
Barry King, Jake Roloson,
Sharon Tuminaro, Mark Yuly
Department of Physics
One Willard Avenue
Houghton College
Houghton, NY 14744
1. Abstract
A small cyclotron is being constructed using a 0.5 T permanent
magnet, with 15.2 cm (6.0 inch) diameter pole faces and 3.8 cm (1.5
inch) pole separation. An acceleration chamber containing a single brass
RF electrode is being developed. In this design magnetic field strength
may be modified by adjusting the pole separation using iron pole pieces,
which are sealed to the chamber using high vacuum grease. The chamber
will be filled with low pressure hydrogen gas which will be ionized by
electrons released by a cathode located at the center of the chamber. The
required 3.6 MHz to 11.5 MHz RF power will be supplied by a
commercial RF amplifier. A liquid nitrogen cold trap with a diffusion
pump backed by a forepump will be used to evacuate the chamber.
Energies between 37.5 keV and 87.7 keV for protons and 18.7 keV and
43.8 keV for deuterons should be obtained.
2. Introduction
The cyclotron is a magnetic resonance accelerator. The first
cyclotron was built in 1930 by the late Ernest O. Lawrence with help
from M. S. Livingston. It uses the principle of resonance acceleration,
that is the charged particles move outward in a spiral, traversing a “D”
shaped electrode in resonance with an oscillating electric field. As can
be seen in figure 1, the particles gain energy on each cycle, resulting in
a larger orbital radius. The advantage of a cyclotron is its compact size
and the low voltages used. The motivation is to produce a low energy
particle accelerator to use in a small nuclear physics laboratory.
3. Theory
A charged particle will move in a circle when traveling in
magnetic field perpendicular to its orbit. The centripetal acceleration is
supplied by the Lorentz force, yeilding:
mv 2
 qvB
r
where q is the charge, B is the magnetic field, and m is the mass, r is the
radius and v is the speed of the particle. The frequency with which the
particle revolves is given by
v
qB
f

2r 2m
The beauty of the cyclotron design is the independence of the frequency
on the location of the particle and its speed. In this way it is possible to
connect a hollow copper electrode to a RF amplifier with fixed frequency
defined above. Thus on each successive orbit, the particle will receive a
“kick.” If we look at the classical definition of kinetic energy:
mv 2
T
2
we find that
q 2 B2 R 2
T
2m
where R is the final radius of the particle.
4. Magnetic Field
The magnetic field is uniform ( 0.493 T ) to within one percent,
out to a radius of 6.19 cm ( Figure 3 - Solid Line ). The RF electrode
radius is 7.14 cm ( Figure 3 – Dashed Line ), allowing us to use the full
uniform region of the field. The moveable faraday cup allows us to
collect the particles before entering the non-uniform field and measure
the beam current.
5.
Vacuum System
A liquid nitrogen cold trap and diffusion pump backed by a rotary
forepump will evacuate the acceleration chamber. The vacuum chamber
will be attached to the pumps with a bellows to allow the chamber to be
positioned in the magnetic field. The valves are used to allow the
vacuum chamber to be worked on without letting air into the rest of the
system, and then to be roughed down and re-evacuated.
LN2 Trap – Liquid nitrogen cools any molecules in the trap, and
prevents them from obtaining enough kinetic energy to escape the trap.
Diffusion Pump – Oil is heated in the bottom of the pump, and then
diffused into the upper section where it is cooled by water, and when it
descends it pulls gas molecules that have attached to it.
Electronics – The electronics are designed such that the diffusion pump
cannot be turned on unless the forepump is turned on. The power
supplied to the diffusion pump heater is controlled by a variac, and is
monitored by the volmeter and ammeter shown in figure 5.
6. Chamber Design
The chamber was designed with a single RF electrode, powered
by an RF amplifier through a feedthrough in the chamber wall. Copper
pipes are attached to the side walls of the chamber to allow for gas intake
and evacuation by the vacuum pumps. A small filament releases
electrons which ionize the gas in the center of the chamber. A 5.08 cm x
1.00 cm window attached to the chamber wall will allow observation of
the interior of the chamber. Finally, a faraday cup attached to a bellows
valve opposite the RF electrode will collect the particles. A retarding
grid attached to the front of the faraday cup will eliminate loss of
secondary electrons. The overall design can be seen in Figure 6. The
central chamber and RF electrode will be made of brass, while the
sealing plates, either made of iron or aluminum, will be attached with
vacuum grease ( Figure 8 ).
7. Conclusion
The vacuum system is nearly finished, and we are currently in the
initial phase of constructing the chamber. The gray iron plates will
strengthen the field of our magnet and may allow us to obtain higher
energies. Although this machine will only generate 18.7 keV deuterons,
it might be possible to use the H2(d,n)He3 reaction to yield neutrons with
energies of 2.61 MeV. We could then place a deuterium target in our
faraday cup that would yield a mono-energetic neutron source. The
advantage to this is, while charged particles would need to be extracted,
the neutrons will not interact with the magnetic field or chamber.