Linear Accelerator

Introduction

Acceleration is called the rate of variation of velocity or the difference in velocity per unit of time. A cyclotron is a device for generating high-speed ions. Lawrence and Livingston built this device. The synchronous acceleration principle is used. Nuclei are attacked using particles like electrons and protons accelerated by an accelerator. A particle accelerator is used as a pre-accelerator to first accelerate the particles to a certain voltage before injecting the accelerator particles. As a charged particle travels through solids, a series of ionized and excited atoms appear in its path. These can be detected or counted. Detectors work based on this principle. Most of the detectors pass charged particles through the material.

What is a linear accelerator?

Ions are accelerated along a linear path by voltage differences across electrodes along the path. Accelerators are used to increase the kinetic energy of ions and electrons. Nuclei are attacked using particles like electrons and protons accelerated by an accelerator. A linear particle accelerator uses an electromagnetic field to accelerate charged particles to nearly the speed of light and contain them in well-defined radii. Large accelerators are used for fundamental research in particle physics.

Working principle

By applying an oscillating electric field to the series channel, the charged particle can be terminated. This new theory is called resonance acceleration. Here low voltage pulses are given at the right time. A linear accelerator is of this type. So resonance acceleration is the principle of the linear accelerator.

Construction and operation

A linear accelerator consists of several cylindrical electrodes placed in a vacuum-filled elongated chamber. These tubes are called drift tubes. In the longitudinal direction of this pipe, the flow is in a straight line. The length of each tube is consistently greater. The odd-numbered tubes are connected to one end of the R.F. Oscillator and the even- numbered tubes are connected to the other end of the R.F. Oscillator. Hence successive tubes have a counter-electric field. Ions from one end of the discharge tube pass through the axis of the cylindrical electrodes and are accelerated when they reach the gap between the two cylinders. Because there is a constant voltage inside the cylinder, the ions are not accelerated while inside the tube.

Linear Accelerator

Thessaloniki, Greece - Novemper 21, 2018: Official opening of the first linear accelerator technology IMRT, IGRT, VMAT of the Department of Radiotherapy Oncology at Theagenil Hospital in northern Greece

Let the positively charged particle move from left to right. The ion is accelerated as it passes through the first cylinder and reaches the gap between the first and second cylinders. Now cylinder 2 becomes positive voltage. If v is the voltage and e is the charge of the particle,

$$\mathrm{ev\:=\:\frac{1}{2}\:mv_1^2}$$

$$\mathrm{v_1\:=\:\sqrt\frac{2ev}{m}}$$

The ion moves uniformly with this velocity in the second tube. The length of the tube should be so arranged that the time taken to travel the length of the tube is half the duration of A.C. voltage. So when the pulse reaches the 2nd, and 3rd inter-tube gap the electric field changes. Hence, the particle is accelerated and reaches the third tube. In this, the velocity of the particle 𝑣2 can be given as

$$\mathrm{e.2v\:=\frac{1}{2}\:mv_2^2}$$

$$\mathrm{v_2^2\:=\:\sqrt\frac{4ev}{m}}$$

$$\mathrm{v_2^2\:=\:2\sqrt\frac{4ev}{m}}$$

$$\mathrm{=\:\sqrt2\:\sqrt\frac{2ev}{m}}$$

$$\mathrm{v_2\:=\:\sqrt2v_1}$$

As it moves through the tube with high velocity, the time taken to pass through it is constant. The length of the tube has been increased accordingly. The time taken for the particle to cross each cylinder should be half the period of the A.C. voltage. Thus the longitudinal ratio of the tubes is 1:√2:√3;... and the particles are accelerated to reach the gap in time and the energy increases. The total number of tubes is ‘n’ and if the reverse voltage of the A.C. source is v, then the energy gained by the particle is equal to the energy gained by acting on the particle at one time nv volts.

If the frequency of the oscillation is t, 2T=f. So, time to cross the nth pipeline,

$$\mathrm{T\:=\:\frac{1}{2f}\:=\:\frac{L_n}{v_n}}$$

$$\mathrm{but\:v_n\:=\:\frac{2nev}{m}}$$

$$\mathrm{\therefore\:L_n\:\frac{v_n}{2f}\:=\:\sqrt\frac{2nev}{m}\:\frac{1}{2f}}$$

$$\mathrm{L_{n}\:=\:\frac{(\frac{nev}{2m})^{\frac{1}{2}}}{f}}$$

From the above equation, we can calculate the length of the nth pipe. Two disadvantages of a linear accelerator are as follows, (1) its length is very high. (2) The ionic current is of low concentration.

Types of linear accelerator

The most common types are the Cockcroft - Walton generator and Van de Graff generator

Cockcroft - Walton generator

The principle of this high voltage device is very simple. When capacitors in parallel are charged with low voltage and then discharged in series, the value of the discharge voltage is the sum of the charges on each capacitor. The construction of this device is shown in the figure.

The capacitors in this device are set up in the column. Due to the oscillating advantages of the voltage supplied by the transformer and the automatic switch nature of the rectifiers, the charge is loaded to the top of the column. Both these rectifiers conduct current during the first half cycle. Current conducts during the next half-cycle. These rectifiers do not conduct current during the next half cycle. Now the feedback capacitors

charge is shared with the other capacitors through the next two rectifiers. This process continues until all the capacitors are fully charged. In this case, the voltage difference between the lower and upper ends of the column is equal to the sum of the voltages of each capacitor. Therefore, the required high voltage can be obtained by increasing the number of capacitors in both the conductors, hence it is called a voltage multiplier. The output will be taken between DD.

Van de Graff generator

When a charged particle passes through an electric field created between two electrodes by a high voltage, it is accelerated to a high voltage. It is based on this principle developed by Van de Graff. It can be used to get up to 4 million volts. This high voltage can be used to accelerate charged particles.

The charged particle to be accelerated is generated by the gas discharge ion source I. This source is placed in an accelerator tube T in shell S. the accelerator tube is vacuumed and consists of several insulated cylinders arranged in series with small gaps. A high voltage is applied near the ion source at the upper end of this tube and the end is grounded. A potential gradient appears from the upper end of the tube to the tube to the lower end. Ions moving from top to bottom are accelerated in the gap between the cylinders. The electric field in this gap concentrates the particles into a beam. This beam is made to fall on a target G placed at the bottom of the tube.

Applications

• Particles such as electrons and protons can be accelerated to several million electron volts using a linear accelerator.

• The advantage of a linear accelerator is that it does not require any kind of magnet to direct the particle.

• The particles coming out of these automatically align well and form a beam so that the target can be hit directly with it.

Conclusion

A cyclotron is a device for generating high-speed ions. Lawrence and Livingston built this device. The synchronous acceleration principle is used. Nuclei are attacked using particles like electrons and protons accelerated by an accelerator. A linear particle accelerator uses an electromagnetic field to accelerate charged particles to nearly the speed of light and contain them in well-defined radii. Large accelerators are used for fundamental research in particle physics. Particles such as electrons and protons can be accelerated to several million electron volts using a linear accelerator. The advantage of a linear accelerator is that it does not require any kind of magnet to direct the particle. The most common types are the Cockcroft - Walton generator and Van de Graff generator.

FAQs

1: What is the Geiger Muller counter?

The Geiger-Muller counter was set up in 1908 by Rutherford and Keiger to count alpha particles emitted at a given time from radioactive material. In 1928, Geiger and Muller revised this system.

2: Explain Betatron

Betatron is used to accelerate an electron to very high energy. Because beta particles are electrons, this accelerator is called a Betatron. It can be used to accelerate electrons to 300 MeV.

3: What are the uses of a scintillation counter?

Inorganic Phosphor-equipped scintillation counters are highly efficient for detecting protons, deuterons, and alpha particles. Calcium tungstate is used as a phosphor to detect gamma rays.

4: What is the principle of the Cloud chamber?

When air saturated with water vapor is suddenly expanded adiabatically, the temperature drops suddenly. If there is any dust in the air, water droplets appear. Water droplets do not appear in dust-free air. But if there are any charged particles in the air, waves appear. Wilson’s cloud chamber is a constrictor for the formation of droplets of ions. Ions are produced by passing particles such as alpha and beta through the chamber.

5: What are detectors?

As a charged particle travels through solids, a series of ionized and excited atoms appear in its path. These can be detected or counted. It is based on this principle that the detectors work.