cyclotron

Certificate This is ti certify that this project submitted by Mohd Aleem Class 11th science to department of Physics, Sir Bilal school Firozabad was varied under my guidance and supervision of Mr. Rajkumar Katara during the academic year 2014-15

Teacher In- Charge

ACKNOWLEDGEMENT It has been a highly enlightening experience to study In Sir Bilal School, Firozabad during 2014-15. It has been possible to achieve the perfect blend of the valuable experience gained from the school and the indispensable Knowledge gathered from theoretical studies. Moreover, the much discipline and culture have been collected carefully over the period of my schooling. I thank Mr. Rajkumar Katara for choosing me to undertake this project and for his guidance to overcome difficulties faced by me while completing the project. My special gratitude to Mrs. Sheeba, Principal Sir Bilal School, Whose constant encouragement to undertake special assignment not only inspired me to complete this project but also made me proud student of the school. I am also thankful to my parents for helping and guiding me in completing this project successfully without whose valued help this project could not have been completed - Mohd Aleem

Index . Introduction . Principle . Construction . Theory . Cyclotron Frequency . Maximum Energy of the positive lons

Introduction An accelerator is used for accelerating charges particle so that they acquire energy large enough to carry out the nuclear reaction. Historically linear accelerator was develop accelerate charge particles but its main drawback is that it length has to very large. If the charge particle are to be accelerated to a very high energy. It is because the cylindrical tubes of increasing lengths have to be used as a charged particle gains more and energy. Cyclotron was designed by Lawrence and Livingstone in 1931 in order to overcome the drawback of the linear accelerator. It is suitable for accelerating heavy charged particles such as proton, α- particles and positive ions. In a cyclotron the positive ions cross again and again the same alternating [radio frequency] Electric field and thereby gain the energy. It is achieved by making them to move along spiral circular paths under the action of a strong magnetic field. It is also known as magnetic resonance accelerator.

Principal It is based on the principal that a positive ion can acquire sufficiently large energy with a comparatively smaller alternating potential difference by making it to cross the same electric field time and again by making use of a strong magnetic field.

CONSTRUCTION It consists of two D-shaped hollow semicircular metal chamber D1 and D2 called dees. The two dees are placed horizontally with a small gap separating them. The dees are connected to the source of high frequency electric field. The dees are containing a gas at a low pressure of the order of 10-3 mm mercury. The whole apparatus is placed between the two is placed between the two poles of a strong electromagnet N/S. The magnetic field acts perpendicular to the plane of dees. The positive ions are produced in the gap between the two dees by the ionization of the gas. To produce proton hydrogen gas is used while for producing alpha particle helium gas Is used.

THEORY Consider that a positive ion is produced at the centre of the gap at the time, when the dees D1 is att positive potential and the dee D2 is at a negative potential. The positive ion will move from dee D1 to dee D2. As the magnetic field acts normally to the motion of the positive ion the positive ion experience force. The force on the positive ion due to magnetic field provides the centripetal force to the positive ion and it is deflected along a circular path.if B is strength of the magnetic field and m, v and q are respectively the mass velocity and charge of the ion them. B q v=m Here r is the radius of the semi circula path along which the position will move inside the dee D2. Thus, r= After moving along the semi circular path inside the D2 the positive ion reaches the gap between the two dees. At this stage the polarit of the dees just reverses due to alternatin * electric field i.e. D1 become negative and D2 become positive. The positive ion again gian energy as it is attracted by the D1. After moving along the semi circular path inside the dee D1 the positive ion again reaches the gap and it again and again the energy. This process repeats itself time and again. It is because the positive ion spends the same time inside a dee irrespective if its velocity or the radius of the circular path. It can be proved as below. t = length of the semi circular path Using the equation we have

As required the time which a positive ion of mass m and charge q spends inside a dee is inside independent of its velocity and radius of the semi

circular path. It may again be pointed out that decrease in time spent inside a dee due to increasing velocity of positive ion is path. Due to this condition the positive ion always crosses the alternating electric field across the gap between the two dees in correct phase.

CYCLOTRON FREQUENCY Under the action of the given magnetic field (B fixed) the given positive ion (e/m fixed) will cover the semi circular path in a fixed time only if t in equation is equal to T/2, where T is the time period of the electric field.

The cyclotron angular frequency Also cyclotron frequency

It is also known as magnetic resonance frequency (non relativistic)

MAXIMUM ENERGY OF THE POSTIVE IONS Let V max be the velocity acquired by the positive ion, when it moves along the largest circular path i.e. path of radius equal to the radius R of the dees.Then Bqvmax=

Therefore maximum kinetic energy gained the positive ion

The maximum energy acquired by the positive ion can be expressed in another form as obtained below: If V is the potential difference applied between the does and N is the number of time the positive ion crosses the gap between the two dees before leaving the dees then,

Obviously N=2n where n is the number of rotation complete by the positive ion before the radius of its circular path become equal to that of the dees. Limitation of cyclotron . Where a charged particle is accelerated its mass also start increasing with increase in its speed. When its speed becomes comparable to that of light the mass of the charged particle becomes quite large as compared to its restmass. If m0 is rest mass then mass of charges particle when moving whith speed v is given by m=

Therefore as v increase t also incres i.e. the charged particle starts taking more and more time to complete the semi circular path inside dee. Since electric field changes the polarity of the dees after a fixed interval, the change particle starts lagging behind the electrin field and it is ultimately lost by colliding against the walls of the dees. However this problem is overcome in the following two ways (a) As v increase decrease. Therefore B is increased in such a manner that the factor B and hence t always remains constant. Such a cyclotron in which the strength of magnetic firld is adjusted to overcome the problem due to relavistic variation in mass of the positive ion is called sunchroton. (b) The frequency of revolution of charged particle inside the dess may be expressed as V=Bq It follows that as v increase decrease and hence v decrease. If frequency of the electric field is adjusted to b=e always equal to frequency of revolution of the charged particle them such a cyclotron is called sunchro- cyclotron of frequency modulated cyclotron. 2. Cyclotron is used to accelerate heavy charged particles such a protons it is not suitable for accelerating electrons. The reason is that due to small mass the speed of electron increase rapidly. Likewise due to the quick relatives variation in their mass the electron get out of step with the oscillating electrin field.

BIBLOGRAPHY 1. 2. 3. 4.

NCERT Text Book abc Physics Comprehensive Physics University physics