CYCLOTRON
1.
INTRODUCTION
A cyclotron is used for accelerating positive ions, so that they acquire energy large enough to
carry out nuclear reactions. Cyclotron was designed by Lawrence and Living stone in 1931 in
order to overcome the drawbacks of the linear accelerator. In a cyclotron, the positive ions cross
again and again the same alternating electric field and thereby gain the energy. It is achieved by
making them to move along spiral path under the action of a strong magnetic field. It is also
known as magnetic resonance accelerator.It makes use of the magnetic force on a moving charge
to bend moving charges into a semicircular path between accelerations by an applied electric
field. The applied electric field accelerates electrons between the "dees" of the magnetic field
region. The field is reversed at the cyclotron frequency to accelerate the electrons back across the
gap.
2.
HISTORY
The cyclotron was conceived in Germany in the 1920s. At Aachen University in 1926, the
cyclotron was proposed by a co-student of Rolf Wider, who rejected the idea as too complicated
to construct. In 1927, Max Steenbeck developed the concept of the cyclotron at Siemens, but a
misunderstanding prevented him from publishing and building the apparatus. The first cyclotron
patent was filed by Hungarian physicist Leo Szilard in 1929, while working at Humboldt
University of Berlin.
The first cyclotron was developed and patented by Ernest Lawrence in 1932 at the University of
California, Berkeley. He used large electromagnets recycled from obsolete Poulsen arc radio
transmitters provided by the Federal Telegraph Company. A graduate student, M. Stanley
Livingston, did much of the work of translating the idea into working hardware.[17] Lawrence
read an article about the concept of a drift tube linac by Rolf Widerøe,[18][19] who had also been
working along similar lines with the betatron concept. At the Radiation Laboratory of the
University of California at Berkeley Lawrence constructed a series of cyclotrons which were the
most powerful accelerators in the world at the time; a 69 cm (27 in) 4.8 MeV machine (1932), a
94 cm (37 in) 8 MeV machine (1937), and a 152 cm (60 in) 16 MeV machine (1939). He also
developed a 467 cm (184 in) synchrocyclotron (1945). Lawrence received the 1939 Nobel prize
in physics for this work.
The first European cyclotron was constructed in Leningrad in the physics department of the
Radium Institute, headed by VitalyKhlopin (ru). This Leningrad instrument was first proposed in
1932 by George Gamow and Lev Mysovskii (ru) and was installed and became operative by
1937.[20][21][22] In Nazi Germany a cyclotron was built in Heidelberg under supervision of
Walther Bothe and Wolfgang Gentner, with support from the Heereswaffenamt, and became
operative in 1943.
3.
PRINCIPLE OF CYLOTRON
It is based on the principle that a positive ion can acquire sufficiently large energy with a
comparatively smaller alternating potential difference by making them to cross the same electric
field time and again by making use of a strong magnetic field.
Cyclotron works on the principle that a charged particle moving normal to a magnetic field
experiences magnetic lorentz force due to which the particle moves in a circular path.
A charged particle can be accelerated to very high energies by making it pass through a moderate
electric field a number of times. This can be done with the help of a perpendicular magnetic field
which throws the charged particle into a circular motion, the frequency of which does not
depend on the speed of the particle and the radius of the circular orbit.
4.
CONSTRUCTION
It consists of a hollow metal cylinder divided into two sections D1 and D2 called Dees, enclosed
in an evacuated chamber. The Dees are kept separated and a source of ions is placed at the centre
in the gap between the Dees. They are placed between the pole pieces of a strong electromagnet.
The magnetic field acts perpendicular to the plane of the Dees. The Dees are connected to a high
frequency oscillator.
4.1
COMOPONENTS
As shown in figure, a cyclotron consists of the following main parts

It consists of two small, hollow, metallic half-cylinders D1 and D2 called dees as they are
in the shape of D.

They are mounted inside a vacuum chamber between the poles of a powerful
electromagnet.

The dees are connected to the source of high frequency alternating voltage of few
hundred kilovolts.
The beam of charged particles to be accelerated is injected into the dees near their centre,
in a plane perpendicular to the magnetic field.

The charged particles are pulled out of the dees by a deflecting plate (which is negatively
charged) through a window W.
The whole device is in high vacuum (pressure ∼10−6 mm of Hg) so that the air
molecules may not collide with the charged particles.
5.
THEORY
Let a particle of charge q and mass m enter a region of magnetic field B→ with a velocity v→
normal to the field B→. The particle follows a circular path, the necessary centripetal force begin
provided by the magnetic field. Therefore,
Magnetic force on charge q = Centripetal force on charge q
or
qvBsin90o=mv2r or r=mvqB
Period of revolution of the charged particle is given by
T=2πrv=2πv.mvqB=2πmqB
Hence frequency of revolution of the particle will be
fc=1T=qB2πm
Clearly,this frequency is independent of both the velocity of the particle and the radius of the
orbit and is called cyclotron frequency or magnetic resonance frequency.This is the key fact
which is made use of in the operation of a cyclotron.
WORKING
Suppose a positive ion,say a proton,enters the gap between the two dees and finds dee D1 to
be negative.It gets accelerated towards deeD1.As it enters the deeD1,it does not experience
any electric field due to shielding effect of the metallic dee. The perpendicular magnetic field
throws it into a circular path.At the instant the proton comes out of deeD1,,it finds deeD1
positive and deeD2. It moves faster through D2 describing a larger semicircle than before. Thus
if the frequency of the applied voltage is kept exactly the same as the frequency of revolution
of the proton,then every time the proton reaches the gap between the two dees, the electric
field is reversed and proton receives a push and finally it acquires very high energy. This is
called the cyclotron’s resonance condition. The proton follows a spiral path. The accelerated
proton is ejected through a window by a deflecting voltage and hits the target.
MAXIMUM K.E OF THE ACCELERATED IONS :
The ions will attain maximum velocity near the periphery of the dees. If v0 is the maximum
velocity acquired by the ions and r0 is the radius of the dees, then
mv20r0=qv0B or v0=qBr0m
The maximum kinetic energy of the ions will be
K0=12mv20=12m[qBr0m]2
or
K0=q2B2r202m.
7.
7.1
TYPES OF CVLOYTONS
CLASSICAL CYCLOTRONS
The key to the operation of a cyclotron is the fact that the orbits of ions in a uniform magnetic
field are isochronous; that is, the time taken by a particle of a given mass to make one complete
circuit is the same at any speed or energy as long as the speed is much less than that of light. (As
the speed of a particle approaches that of light, its mass increases as predicted by the theory of
relativity.) This isochronicity makes it possible for a high voltage, reversing in polarity at a
constant frequency, to accelerate a particle many times. An ion source is located at the centre of
an evacuated chamber that has the shape of a short cylinder, like a pillbox, between the poles of
an electromagnet that creates a uniform field perpendicular to the flat faces. The accelerating
voltage is applied by electrodes, called dees from their shape: each is a D-shaped half of a
pillbox. The source of the voltage is an oscillator—similar to a radio transmitter—that operates
at a frequency equal to the frequency of revolution of the particles in the magnetic field. The
electric fields caused by this accelerating voltage are concentrated in the gap between the dees;
there is no electric field inside the dees. The path of the particle inside the dees is therefore
circular. Each time the particle crosses the gap between the dees, it is accelerated, because in the
time between these crossings the direction of the field reverses. The path of the particle is thus a
spiral-like series of semicircles of continually increasing radius.
7.2.
NANOTRON
superconducting,cold iron, cryogen free‘portable’ deuteriumCyclotron
7.3
ISOTRON
for short lived PET isotope production:

Protons or heavy ions


30-100 MeV
Synchrocyclotron or isochronous cyclotron is possible
7.4
GIGATRON
1 GeV, 10 mA protons for airborne active interrogation
7.5
MEGATRON
600 MeV muoncyclotron (requires a gigatron to producemuons and a reverse cyclotron muon
cooler for capture for accel.)
LIMITATIONS
Maintaining a uniform magnetic field over a large area of the Dees is difficult.
At high velocities, relativistic variation of mass of the particle upsets the resonance condition.
1.According to the Einstein’s special theory of relativity, the mass of a particle increases with the
increase in its velocity as
m=m01−v2/c2√
Where mo
is the rest mass of the particle. At high velocities,the cyclotron frequency (fc=qB/2πm)
will decrease due to increase in mass. This will throw the particles out of resonance with the
oscillating field. That is,as the ions reach the gap between the dees, the polarity of the dees is not
reversed at that instant. Consequently the ions are not accelerated further.
The above drawback is overcome either by increasing magnetic field as in a synchrotron or by
decreasing the frequency of the alternating electric field as in a synchro-cyclotron.
2. Electrons cannot be accelerated in a cyclotron.A large increase in their energy increases their
velocity to a very large extent.This throws the electrons out of step with the oscillating field.
3.Neutron,being electrically neutral,cannot be accelerated in a cyclotron.
USES OF CYCLOTRON:
1.The high energy particles produced in a cylinder are used to bombard nuclei and study the
resulting nuclear reactions and hence investigate nuclear structure.
2.The high energy particles are used to produce other high energy particles,such as Neutrons by
collisions.These fast neutrons used in atomic reactions.
3.It is used to implant ions into solids and modify their properties or even synthesis new
materials.
4.It is used to produce radioactive isotopes which are used in hospitals for diagnosis and
treatment.
Particle energy
Since the particles are accelerated by the voltage many times, the final energy of the particles is
not dependent on the accelerating voltage but on the strength of the magnetic field and the
diameter of the accelerating chamber, the dees. Cyclotrons can only accelerate particles to speeds
much slower than the speed of light, nonrelativistic speeds. For nonrelativistic particles, the
centripetal force
where
is the particle's mass,
required to keep them in their curved path is
its velocity, and
provided by the Lorentz force
where
is the radius of the path. This force is
of the magnetic field
is the particle's charge. The particles reach their maximum energy at the periphery of
the dees, where the radius of their path is
the radius of the dees. Equating these two forces
So the output energy of the particles is
Therefore, the limit to the cyclotron's output energy for a given type of particle is the strength of
the magnetic field
, which is limited to about 2 T for ferromagnetic electromagnets, and the
radius of the dees
, which is determined by the diameter of the magnet's pole pieces. So very
large magnets were constructed for cyclotrons, culminating in Lawrence's 1946
synchrocyclotron, which had pole pieces 4.67 m (184 in) (15.3 feet) in diameter.
Synchrocyclotron
Main article: Synchrocyclotron
A synchrocyclotron is a cyclotron in which the frequency of the driving RF electric field is
varied to compensate for relativistic effects as the particles' velocity begins to approach the speed
of light. This is in contrast to the classical cyclotron, where the frequency was held constant, thus
leading to the synchrocyclotron operation frequency being
,
where
is the classical cyclotron frequency and
again is the relative velocity of the
2
particle beam. The rest mass of an electron is 511 keV/c , so the frequency correction is 1% for a
magnetic vacuum tube with a 5.11 kV direct current accelerating voltage. The proton mass is
nearly two thousand times the electron mass, so the 1% correction energy is about 9 MeV, which
is sufficient to induce nuclear reactions.
Isochronous cyclotron
An alternative to the synchrocyclotron is the isochronous cyclotron, which has a magnetic field
that increases with radius, rather than with time. Isochronous cyclotrons are capable of producing
much greater beam current than synchrocyclotrons, but require azimuthal variations in the field
strength to provide a strong focusing effect and keep the particles captured in their spiral
trajectory. For this reason, an isochronous cyclotron is also called an "AVF (azimuthal varying
field) cyclotron".[24] This solution for focusing the particle beam was proposed by L. H. Thomas
in 1938.[24] Recalling the relativistic gyroradius
, one can choose
and the relativistic cyclotron frequency
to be proportional to the Lorentz factor,
. This results in the relation
which again only depends on the velocity
, like in the non-relativistic case. Also, the
cyclotron frequency is constant in this case.
The transverse de-focusing effect of this radial field gradient is compensated by ridges on the
magnet faces which vary the field azimuthally as well. This allows particles to be accelerated
continuously, on every period of the radio frequency (RF), rather than in bursts as in most other
accelerator types. This principle that alternating field gradients have a net focusing effect is
called strong focusing. It was obscurely known theoretically long before it was put into
practice.[25] Examples of isochronous cyclotrons abound; in fact almost all modern cyclotrons
use azimuthally-varying fields. The TRIUMF cyclotron mentioned below is the largest with an
outer orbit radius of 7.9 metres, extracting protons at up to 510 MeV, which is 3/4 of the speed of
light. The PSI cyclotron reaches higher energy but is smaller because of using a higher magnetic
field.