LINAC (Linear Accelerator)

What is LINAC?
It is a device which is used to accelerate the charged particles in straight line and also increase the
energy of charge particles. In LINAC the positively charge particles are accelerated by passing through
the AC radio frequency electric field.

Working Principle:
1.
The electric field inside a hollow cylinder is zero. Hence the motion of charge particle inside
the cylinder is with uniform velocity.
2.
In half cycle of AC field, the charge particle is accelerated and in the remaining half cycle it
moves with constant speed. Thus repeatedly the particle is accelerated in steps with help of
a alternating current.
LINAC
In this figure showing how a linear accelerator works. In this example the particles accelerated (red dots) are
assumed to have a positive charge. The graph V(x) shows the electrical potential along the axis of the
accelerator at each point in time. The polarity of the RF voltage reverses as the particle passes through each
electrode, so when the particle crosses each gap the electric field (E, arrows) has the correct direction to
accelerate it. The figure shows a single particle being accelerated each cycle; in actual linacs a
large number of particles are injected and accelerated each cycle.
Working:
When the R.F. oscillator is switched on,the positively charged particle is accelerated by C1 when C1
is negative.There is no increase in the velocity when it moves inside the tube C1.The length of the
tube C1 is so adjusted that it reaches at the end of the C1 when C2 became negatively charged(time
taken to travel the length C1 equals to half of the time period of R.F. oscillator) so that the particle is
accelerated within the gap of C1 and C2.Again the length of the tube C2 is so adjusted that it reaches
at the end of C2 when the C3 became negatively charged.Thus positive charge particle is again
accelerated within the gap of C2 and C3.In this way the positively charged paricle is again and again
accelerated in multiple gaps.
The Maximum Energy Gained by Charged Particle:
If the voltage applied between the electrodes is V volts, and the charge on each particle is q then each particle
gains an equal increment of energy of qV electron volts when passing through each gap. Thus the output
energy of the particle is
E = nqV electron volts , where n is the number of accelerating electrodes
in the machine.
The Maximum Velocity Gained by Particle:
1
2
The final kinetic energy of particle after passing the nth tube = m𝑣 2 = nqV
𝟐𝒏𝒒𝑽
𝒎
𝒗𝒏 = √
⟹ 𝒗𝒏 ~ √𝒏
Length of Drift Tubes:
Time taken to travel the nth tube of length equals to half of time period,T of R.F. oscillator
i.e. t =
𝑇
2
Thus the length of tube n ,
=
1
2𝑓
; where f is the frequency of R.F. oscillator.
Ln = Vn × t
Substituting the above values, we get:
𝑳𝒏 =
𝟏
𝟐𝒇
𝟐𝒏𝒒𝑽
𝒎
√
⇒ 𝒍𝒏 ~ √𝒏
Therefore, the length of the drift tube C1, C2, C3………Cn must be the order of √1 : √2 : √3………….√𝑛 .
Advantages and Disadvantages of LINAC: