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CBSE > > Cyclotron
Cyclotron Working Principle
cycloton-head
It is a device developed by Lawrence and Livingstone and is used
to accelerate charged particles likeprotons
and deuterons. This results in the production of high energy
beam which is then used for artificial disintegration,
etc.
It consists of two D shaped metal boxes (about
21″ in diameter) with their straight sides facing each other.
There
is a very small gap between these Dee’s faces across which a
high potential difference (of order of 105 volts) is
applied by a high frequency (10-15 mega cycles per second)
oscillator. Thus an alternating electric field is
established between Dee’s during one half cycle, one dee is
positive and the other is negative while during the
next half cycle, the other is positive and one is negative. A
source of particle (heavy hydrogen for producing
deutrons) is placed between the faces. The whole apparatus is
placed between the pole pieces NS of a very
strong magnet.
cyclotron4
click on images to zoom
Suppose a deuteron is at the centre of the gap and D1 is at
negative potential compared to D2 then deuterons will
be accelerated by the electric field between the dees towards
D1. Since magnetic field B is perpendicular to the
direction of motion of deuteron, a force will act on the
particle given by
F = qv x B (where v and B are vectors) = qvB
Consequently, particle moves along a circular path whose radius
is given by
cyclotron-2
So time period and frequency is independent of speed of charge
and radius of circular path. If this frequency is
equal to the frequency of the oscillator then by the time
particle complete half revolution the polarity of the field
will
change. Deuteron will again be accelerated across the gap, its
velocity will increase so that now it will move in a
circular path of greater radius but its frequency will not be
affected and the process of acceleration continues.
The particle is thus accelerated to gain high velocity. Its
kinetic energy increases and when radius of the path
reaches upto the value of the radius of the dee (R), beam is
deflected by a negatively charged plate. Therefore
with r=R, its maximum kinetic energy will be
cyclotron
So the necessary condition for accelerating the deuterons is
f=f o
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Cyclotron Explained with Equations
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8/20/2019 Cyclotron Working Principle
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cyclotron5
where f0 is oscillator frequency. This is called resonance
condition.
As velocity attained is high, we choose heavier particles e.g.,
protons, deuterons for acceleration in cyclotron. The
reason is that at such high velocities, mass varies with
velocity and f will then depend on velocity, upsetting
theresonance condition. This variation in mass is more marked in
the case of lighter particles. So cyclotron is suitable
only for accelerating heavy particle like protons, deuterons
a – particles etc.
Electrons can not be accelerated by cyclotrons because the mass
of electron is verysmall and a small increase
in energy of electron makes the electrons move with very high
speed. As a result of it the electron go quickly out
of step with oscillating electric field, it is for these reasons
that other accelerating machines such as synchrotron,
betatron (for accelerating electrons) have been developed.
Cyclotron can not be used for accelerating uncharged
particle like neutrons.
Cyclotron in India
Variable Energy Cyclotron Centre (VECC) is located in Calcutta,
India.The Centre building itself houses a 224 cm
cyclotron, was the first of its kind in India, having been
operational since 1977-06-16. It provides proton, deuteron,
alpha particle and heavy ion beams of various energies to other
institutions.
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