# Linear Accelerator Construction and Working I Principle I 3 advantages.

Linear accelerators overcome the problem of maximum potential difference that can be held by the charged shell by the repeated acceleration of Ions through small potential difference. In this article, we are covering Linear Accelerator Construction and Working.

## What is a Linear Accelerator

Linear accelerator is a device that accelerates particles in a straight line by means of an oscillating electric field which provides either a series of boosting (accelerating) kicks in the correct phase at a series of electrodes gap or accompanies the particles as a traveling wave. Linear accelerators are abbreviated as Linacs

## Linear Accelerator Principle

An oscillating electric field is applied across the electrodes joined in series. The charged particle when passed through them is accelerated if the frequency of the applied field is in resonance with the motion of the particle.

## Linear Accelerator Construction and Working

### Linear Accelerator Construction

The schematic diagram of the linear accelerator is shown below. It consists of a series of metallic hollow cylinders called electrodes (E) or drift tubes of successively increasing length arranged coaxially within a tube (G).

Alternate electrodes are connected to the two terminals of the high-frequency oscillator i.e., the even-numbered electrodes are connected to one terminal while the odd-numbered electrodes are connected to the second terminal of the oscillator.

### Linear Accelerator Working

The positive ions produced at S are made to enter the arrangement of electrodes. The ions are accelerated toward E1 and after entering this electrode they move with constant velocity as there is no field inside it.

Now if the length of the electrode E1 is such that the iron emerges from it at the moment when the phase of the alternating voltage has reversed, the iron will be further accelerated towards the electrode E2  by the potential between E1 and E2.

Then the ions enter the electrode E2 and move with a constant velocity which is greater than that the velocity of iron in E1. The length of each electrode is adjusted in such a way that the time taken by the ions within the electrodes is equal to half of the period of the oscillator and evidently the length of the successive electrode is increased.

Therefore, the ions gain additional energy at each gap. By using a number of electrodes, the final energy of the iron is made to correspond to a potential difference many times that used for one acceleration( i.e. potential difference across one gap).

## Phase Stability in Linear Accelerators

For phase stability, particles must cross the gaps in a phase that corresponds to the rising part of the radiofrequency field cycle.

Let us suppose a particle crossing the gap has a phase angle ϕA with respect to the radio frequency field and maintains it along the next gap.

Another particle with a phase angle ϕB which is less than ϕA will be less accelerated. Similarly, a particle with a phase angle ϕC which is more than ϕA will be more accelerated.

This shows that the particle at B will traverse the drift tube slowly and the particle at C will traverse the drift tube quickly to be in phase at the next gap. Thus, particles corresponding to point A in phase have stability.

But this phase stability condition means that the particles will have a diverging tenancy. The shape of the field line at the gaps between the drift tubes is shown in the figure.

A non-axial particle experiences a focussing force F1 on entering the gap and a defocussing force F2 on leaving the gap. Since the particle crosses the gap in the increasing part of the cycle of the radiofrequency field, the overall field increases with time and so the defocusing force F2 predominates.

This difficulty can be solved by distorting the electric field lines in the right-hand half gap by the introduction of a metallic grid at each drift tube and entrance to eliminate the unwanted curvature of the field lines. The grid though focusses the particles yet reduces the beam intensity.

Another technique is to use electric quadrupole lenses along the axis of the tube.

## Advantages of the Linear Accelerator

• It gives a well-collimated beam of ions.
• It is quite economical for obtaining very high-energy particles.
• The particles are able to reach very high energies without the need for extremely high voltages.

## Drawbacks of Linear Accelerator

• It is inconveniently long in size.
• The intensity of the ionic current is low.
• The main drawback is that, because the particles travel in a straight line, each accelerating segment is used only once.