Download cyclotron

The cyclotron is a particle accelerator. It is mainly used to accelerate
positively charged ions.
Charged particle is allowed to pass through electric and magnetic fields
acting right angles to each other continuously.
kinetic energy of the particle increases in the electric field and direction of
the particle changes in the magnetic field.
It consists of 2 D-shaped chambers connected to high voltage radio
frequency oscillator. The whole arrangement is placed in a uniform
magnetic field acting in right angles to the chambers.
Source of ions which are to be accelerated is
placed between the 2 D-shaped chambers.
When the power supply is on the ion
experiences a force in the electric field
which is set up between the 2 chambers. It
accelerates and enters into the chamber
which is at low potential (-ve). Inside the
chamber electric field is 0 but the magnetic
field changes the direction of the particle
into semi-circular path. By the time it
completes the semi circular path, polarity of
the chambers change. Hence, charged
particle enter into other chamber with
grater velocity.it performs greater semicircular path in the chamber. This process
continues till the particle is ejected out with
a strong deflection.
Moving charge experiences force in the magnetic field for its circular motion.
Therefore centripetal force
mv²/r = qvBsinθ
mv/r = qBsin90
v= qBr/m ……………….(1)
T/2 = πr/v
T = 2πr/v
T = 2πrm/qbr [from (1)]
T = 2πm/Bq
Form the eqns for time period we cay say that it is independent of velocity and
radius of the orbit.
Frequency = I/t = Bq/2πm
K.E = ½ mv²
= ½ mq²B²r² [from(1)]
K.E = q²B²r²/2m
This particle accelerator cannot be used to accelerate electrons or
negatively charged ions to high energy particles.
As the electrons are small, soon these electrons reach the speed of
light, hence the mass changes.
As the mass changes the frequency will not match with the frequency of
the supply.
Finally, this leads to an explosion.