Underlying principle of cyclotron
Working
Schematic diagram
Obtaining the expression for the cyclotron frequency
Cyclotron works on the principle that kinetic energy of the charged particle is increased when they move in crossed oscillating electric and magnetic fields again and again.
When charged particle enters inside the metal boxes, no electric field acts on it, the magnetic field however acts on the particle and makes it go round on a circular path inside the metal boxes, every time when particle moves one dee to another it is acted upon by the electric field and the sign of electric field changes alternatively in turn with the circular motion of the particle, hence particle is accelerated, which in turn increases the kinetic energy of it.
‌

mv2

r

‌=qvB
r‌=‌

mv

qB

Frequency,
v‌=‌

v

2πr

‌=‌

v

2π(‌ mv qB )

=‌

qB

2πm

Thus, frequency is independent of the speed ' v ' and radius ' r '.