Cyclotron Working Principle
It is a device developed by Lawrence and Livingstone and is used to accelerate charged particles like protons and deuterons. This results in the production of high energy beam which is then used for artificial disintegration, etc.
It consists of two D shaped metal boxes (about 21″ in diameter) with their straight sides facing each other. There is a very small gap between these Dee’s faces across which a high potential difference (of order of 105 volts) is applied by a high frequency (10-15 mega cycles per second) oscillator. Thus an alternating electric field is established between Dee’s during one half cycle, one dee is positive and the other is negative while during the next half cycle, the other is positive and one is negative. A source of particle (heavy hydrogen for producing deutrons) is placed between the faces. The whole apparatus is placed between the pole pieces NS of a very strong magnet.
Suppose a deuteron is at the centre of the gap and D1 is at negative potential compared to D2 then deuterons will be accelerated by the electric field between the dees towards D1. Since magnetic field B is perpendicular to the direction of motion of deuteron, a force will act on the particle given by
F = qv x B (where v and B are vectors) = qvB
Consequently, particle moves along a circular path whose radius is given by
So time period and frequency is independent of speed of charge and radius of circular path. If this frequency is equal to the frequency of the oscillator then by the time particle complete half revolution the polarity of the field will change. Deuteron will again be accelerated across the gap, its velocity will increase so that now it will move in a circular path of greater radius but its frequency will not be affected and the process of acceleration continues.
The particle is thus accelerated to gain high velocity. Its kinetic energy increases and when radius of the path reaches upto the value of the radius of the dee (R), beam is deflected by a negatively charged plate. Therefore with r=R, its maximum kinetic energy will be
So the necessary condition for accelerating the deuterons is
f=fo
where f0 is oscillator frequency. This is called resonance condition.
As velocity attained is high, we choose heavier particles e.g., protons, deuterons for acceleration in cyclotron. The reason is that at such high velocities, mass varies with velocity and f will then depend on velocity, upsetting the resonance condition. This variation in mass is more marked in the case of lighter particles. So cyclotron is suitable only for accelerating heavy particle like protons, deuterons a – particles etc.
Electrons can not be accelerated by cyclotrons because the mass of electron is very small and a small increase in energy of electron makes the electrons move with very high speed. As a result of it the electron go quickly out of step with oscillating electric field, it is for these reasons that other accelerating machines such as synchrotron, betatron (for accelerating electrons) have been developed. Cyclotron can not be used for accelerating uncharged particle like neutrons.
But as the speed of the particle has increased, the radius of curvature of the semicircular path increases in accordance with the formula :
r = mv/Bq ( where B is magnetic field , m is mass , v is velocity , q is charge )
For given charge, mass and magnetic field, the radius is proportional to the speed. Clearly, the charged particle begins to move in a larger semicircular path after every passage through the gap. By the time particle reaches the gap successively, electric polarity of Dees keeps changing ensuring that the charged particle is accelerated with an increase in speed. This process continues till the charged particle reaches the periphery and exits through the guide with high energy and bombards a given target being investigated. The description of different segments of the path of accelerated particle is given here :
1: Path is a straight line. Particle is accelerated due to electric force. Speed and kinetic energy of the particle increase.
2: Path is a semicircular curve. Particle is accelerated due to magnetic force. This acceleration is centripetal acceleration without any change in speed and kinetic energy of the particle.
3: Path is a straight line. Particle is accelerated due to electric force in the direction opposite to the direction as in case 1. Speed and kinetic energy of the particle increase by same amount as in the case 1.
4: Path is a semicircular curve of greater radius of curvature due to increased speed. Particle is accelerated due to magnetic force. This acceleration is centripetal acceleration without any change in speed and kinetic energy of the particle.
5: Path is a straight line. Particle is accelerated due to electric force in the direction opposite to the direction as in case 1. Speed and kinetic energy of the particle increase by same amount as in the case 1 or 3.
We see that the particle follows consecutive larger semicircular path due to increase in the speed at the end of semicircular journey. The resulting path of charged particle, therefore, is a spiral path – not circular.
Variable Energy Cyclotron Centre (VECC) is located in Calcutta, India.The Centre building itself houses a 224 cm cyclotron, was the first of its kind in India, having been operational since 1977-06-16. It provides proton, deuteron, alpha particle and heavy ion beams of various energies to other institutions..
Only when the speed of the circulating ion is less than 'c' the speed of light, we find the frequency of revolution to be independent of its speed.
At higher speeds, the mass of the ion will increase and this changes the time period of the ion revolution. This results in the ion lagging behind the electric field and it eventually loses by collisions against the walls of the dees.
*The cyclotron is suitable for accelerating heavy charged particles but not electrons.
*Cyclotrons cannot accelerate in charged particles.
*It is not suited for very high kinetic energy.
any problem please comment
It is a device developed by Lawrence and Livingstone and is used to accelerate charged particles like protons and deuterons. This results in the production of high energy beam which is then used for artificial disintegration, etc.
It consists of two D shaped metal boxes (about 21″ in diameter) with their straight sides facing each other. There is a very small gap between these Dee’s faces across which a high potential difference (of order of 105 volts) is applied by a high frequency (10-15 mega cycles per second) oscillator. Thus an alternating electric field is established between Dee’s during one half cycle, one dee is positive and the other is negative while during the next half cycle, the other is positive and one is negative. A source of particle (heavy hydrogen for producing deutrons) is placed between the faces. The whole apparatus is placed between the pole pieces NS of a very strong magnet.
Suppose a deuteron is at the centre of the gap and D1 is at negative potential compared to D2 then deuterons will be accelerated by the electric field between the dees towards D1. Since magnetic field B is perpendicular to the direction of motion of deuteron, a force will act on the particle given by
F = qv x B (where v and B are vectors) = qvB
Consequently, particle moves along a circular path whose radius is given by
So time period and frequency is independent of speed of charge and radius of circular path. If this frequency is equal to the frequency of the oscillator then by the time particle complete half revolution the polarity of the field will change. Deuteron will again be accelerated across the gap, its velocity will increase so that now it will move in a circular path of greater radius but its frequency will not be affected and the process of acceleration continues.
The particle is thus accelerated to gain high velocity. Its kinetic energy increases and when radius of the path reaches upto the value of the radius of the dee (R), beam is deflected by a negatively charged plate. Therefore with r=R, its maximum kinetic energy will be
So the necessary condition for accelerating the deuterons is
f=fo
where f0 is oscillator frequency. This is called resonance condition.
As velocity attained is high, we choose heavier particles e.g., protons, deuterons for acceleration in cyclotron. The reason is that at such high velocities, mass varies with velocity and f will then depend on velocity, upsetting the resonance condition. This variation in mass is more marked in the case of lighter particles. So cyclotron is suitable only for accelerating heavy particle like protons, deuterons a – particles etc.
Electrons can not be accelerated by cyclotrons because the mass of electron is very small and a small increase in energy of electron makes the electrons move with very high speed. As a result of it the electron go quickly out of step with oscillating electric field, it is for these reasons that other accelerating machines such as synchrotron, betatron (for accelerating electrons) have been developed. Cyclotron can not be used for accelerating uncharged particle like neutrons.
Theory and Working
The charged particle (say a positively charged proton) is released near mid point of the face of one of the Dees. Being in the electric field from one Dee to another, it is accelerated by the electric force in the direction of electric field. As the particle enters the adjoining Dee, the magnetic force, being perpendicular to it, renders the charged particle to move along a semicircular path within the Dee. By the time, it emerges again in the narrow gap separating the two Dees, the electrical polarity of Dees changes so that the particle is again accelerated again with an increase in speed.
But as the speed of the particle has increased, the radius of curvature of the semicircular path increases in accordance with the formula :
r = mv/Bq ( where B is magnetic field , m is mass , v is velocity , q is charge )
For given charge, mass and magnetic field, the radius is proportional to the speed. Clearly, the charged particle begins to move in a larger semicircular path after every passage through the gap. By the time particle reaches the gap successively, electric polarity of Dees keeps changing ensuring that the charged particle is accelerated with an increase in speed. This process continues till the charged particle reaches the periphery and exits through the guide with high energy and bombards a given target being investigated. The description of different segments of the path of accelerated particle is given here :
1: Path is a straight line. Particle is accelerated due to electric force. Speed and kinetic energy of the particle increase.
2: Path is a semicircular curve. Particle is accelerated due to magnetic force. This acceleration is centripetal acceleration without any change in speed and kinetic energy of the particle.
3: Path is a straight line. Particle is accelerated due to electric force in the direction opposite to the direction as in case 1. Speed and kinetic energy of the particle increase by same amount as in the case 1.
4: Path is a semicircular curve of greater radius of curvature due to increased speed. Particle is accelerated due to magnetic force. This acceleration is centripetal acceleration without any change in speed and kinetic energy of the particle.
5: Path is a straight line. Particle is accelerated due to electric force in the direction opposite to the direction as in case 1. Speed and kinetic energy of the particle increase by same amount as in the case 1 or 3.
We see that the particle follows consecutive larger semicircular path due to increase in the speed at the end of semicircular journey. The resulting path of charged particle, therefore, is a spiral path – not circular.
Cyclotron in India
Variable Energy Cyclotron Centre (VECC) is located in Calcutta, India.The Centre building itself houses a 224 cm cyclotron, was the first of its kind in India, having been operational since 1977-06-16. It provides proton, deuteron, alpha particle and heavy ion beams of various energies to other institutions..
Limitations of Cyclotron
Only when the speed of the circulating ion is less than 'c' the speed of light, we find the frequency of revolution to be independent of its speed.
At higher speeds, the mass of the ion will increase and this changes the time period of the ion revolution. This results in the ion lagging behind the electric field and it eventually loses by collisions against the walls of the dees.
*The cyclotron is suitable for accelerating heavy charged particles but not electrons.
*Cyclotrons cannot accelerate in charged particles.
*It is not suited for very high kinetic energy.
