4. Introduction
The cyclotron was one of the earliest types of particle
accelerators, and is still used as the first stage of
some large multi-stage particle accelerators.
One of the most interesting applications of motion of
charge particles in electric and magnetic fields is
Cyclotron.
It is a machine use to accelerate charge particles.
Cyclotrons produce very high energy Charge Particles,
푲. 푬 =
ퟏ
ퟐ
풎풗ퟐ.
E.O Lawrence and M.S Livingston invented this
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machine in 1934.
5. Principle
The Cyclotron works on the principles that:
In Electric Field 퐸 a charged particle is accelerated.
In Magnetic field 퐵 a charged particle can be turned
around.
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 charged
particle between the "Dees" of the magnetic field
region.
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7. DESCRIPTION & DESIGN
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• The cyclotron consists of two flat semicircular
metallic boxes 푫ퟏ & 푫ퟐ called the Dees on account
of their shape like the letter D.
• The two Dees are separated by a narrow parallel
gap.
• A high Frequency of oscillator, which provides an
alternating current is connected between the two
Dees.
8. • Oscillator establishes an alternating electric field in the gap
between the Dees, i.e. the electric field is once directed
towards 푫ퟏ and then towards 푫ퟐ. Thus 푫ퟏ and 푫ퟐ
become alternating positive and negative at the same rate
as the frequency of the oscillator.
• A source is place at the center of the Dees which supplied
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positive ions to accelerate.
• These Dees are mounted inside a vacuum chamber; the
chamber is mounted horizontally between the pole pieces
(N&S) of a huge electromagnet capable of producing a
vertical field.
13. WORKING
The positive ions emitted from the source will
be accelerated in the gap towards the Dee
which is negative at that time.
Let it be 푫ퟐ . Since, there is no electric field
inside the Dees, the positive ion move with
constant velocity along circles of constant
radius under the influence of magnetic field
which is perpendicular the Dees.
If by the time the ions emerge from 푫ퟐ , the
polarity of the applied potential is reversed, the
positive ions will again face the negative Dee
and thus will be again accelerated by the
Electric field in the gap.
Since, there velocity is increased, they will now
move through 푫ퟏ along circular arc of greater
radius as shown in the figure.
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15. • Here, the time passage
to complete the semi –
circle in the 푫ퟏ remains
the same as in 푫ퟐ.
• If the time of travel in
푫ퟏ is equal to half of
the time period of the
oscillator voltage, the
positive ions coming
from 푫ퟏ will find the
reversed field and
hence, they are
accelerated again in the
gap between the Dees.
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푫ퟏ
푫ퟐ
16. 16
• In this way the positive ions move faster
and faster moving in ever – expanding
circles until they reach the outer edge of
the Dees, where they are deflected by
deflector flat and strike the target.
• Here it should be remembered that the
time required for the positive ions to make
one complete turn within Dees is the same
for all speeds and is equal to the time
period of the oscillator.
19. • In magnetic field magnetic force
acts as a centripetal force.
풒풗푩 =
풎풗ퟐ
풓
풓 =
풎풗
풒푩
(1)
• Radius at each turn increase
due to increase in velocity,
therefor its behaves like Spiral
20. 20
Now angular frequency, from
equation (1) we get,
풗 =
풒풓푩
풎
풓흎 =
풒풓푩
풎
풂풔 풗 = 풓흎
흎 =
풒푩
풎
(2)
풂풔 흎 = ퟐ흅풇 So the frequency is
21. 21
풇 =
풒푩
ퟐ흅풎
(3)
Now time period T, 푎푠 풇 =
ퟏ
푻
푻 =
ퟐ흅풎
풒푩
(4)
Frequency and Time period is
independent of radius.
22. The ions will have maximum energy
when it travels at the boundary of the
Dee. If the outside radius of the Dee is
R, then according to equation (1), the
maximum velocity 풗풎 of the ion may be
written as:
풗풎 =
풒푹푩
풎
(5)
And so the maximum kinetic energy of
the ion will be given by
푬풎 =
ퟏ
ퟐ
풎풗풎
ퟐ =
푹ퟐ풒ퟐ푩ퟐ
ퟐ풎
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23. It cannot accelerate neutron, because
neutron do not have any charge.
The energy of charged particles emerging
from cyclotron, is limited due to variation of
mass with velocity, i.e.,
풎 =
풎ퟎ
ퟏ −
풗ퟐ
풄ퟐ
Where 풎ퟎ is the rest mass, m is the mass in
motion when velocity is v and c is the
velocity of light.
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24. 24
풇 =
풒푩
ퟐ흅풎
=
풒푩 ퟏ−
풗ퟐ
풄ퟐ
풎ퟎ
Thus, the frequency of rotation of charged particle
decreases with increase of velocity.
Consequently, the charge particle takes a longer
time to complete semicircular path. Now the
particle continuously goes on lagging behind the
alternating potential differences till a stage is
reached when it is no longer be accelerated further.
It cannot accelerate electron. The mass of electron
is so small that the frequency 풇 =
풒푩
ퟐ흅풎
is very high,
due to which velocity increase so rapidly that it
becomes out of step very soon.
25. It is used for experiment
in nuclear physics, where
high energy collisions are
required.
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