Question

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W protons? MC Maximum ho 15. You are working as a medical assistant at a proton beam CR facility, where high-speed protons are used to bombard cancer cells. The protons are accelerated with a cyclotron, which you find very interesting because of your background in physics. You are explaining this to a patient who has some familiarity with cyclotrons. She asks, "How many revolutions does a proton make in the cyclotron before it reaches its exit kinetic energy?" You are taken aback, both by the high qual- ity of her question and the fact that you never thought of such a question before. You tell her you will try to get her an answer before she finishes her treatment today. When you are finished preparing her for treatment, you go into the cyclotron room and look at the machine. Only three num- bers are available on the machine labeling: the exit energy K = 250 MeV, the radius at which the protons exit, r = 0.850 m, and the accelerating potential difference between the dees, AV = 800 V. You go back to the patient prepared to give her a total number of times the protons go around the cyclotron before exiting. 16. Singly charged uranium answer question ion and UCIONished e shere. Your fact ick, both hes hell her you you nev C a no

Answer 1

In general, a Cyclotron is a device used to accelerate charged particles to very lage kinetic energies by using or applying both electric and magnetic fields. Actually, it consists of two flat semi-cylindrical metallic containers in shape of 'D'. They are mounted inside an evacuated chamber held in between the pole pieces of powerful electromagnet. An alternating voltage of frequency f is applied across the gap between the dees.  

what is happening, basically is A positively charged particles like a proton, alpha particle or a positive ion which is released from the source at the center of dees, gets accelerated to the any one of the dee( depending upon the polarity, negative or positive). Due to applied magnetic field B, the positive particle moves along a semicircular path inside the Dee. The frequency f of the applied AC is adjusted such that when that positive particle or ion arrives at the other Dee it will be at maximum negative potential so that the charged particle is further accelerated due to attraction. The ion moves along a semicircular path inside another Dee. This process is repeated with increasing velocity and increasing radius of the semicircular orbit. When the radius of this orbit becomes equal to the radius R of the dees, the charged particle or ion is deflected out of the circular path. In this way we obtained the beam of high energy particles.

provided Kinetic Energy Expression The Required Centripetal force is by the magnetic force muk=qXB R Radius of this path R= my | Bq m-is mass of ion of particle ve velocity of . . B. Magnetic field q- charge n on os pantele (* The total path length (semicircompatt) = TR The time taken t to travesse the semianale t = Tm I Bq @ This time taken is Theendent of both vand a This is because the increase in length of the path due to larger Radius is exactly Compensated by increase in velocity of the ion - - U= GqR

If R is the Radius of the dee, the maximum velocity at the periphery is Umax = BqR m and the maximum KE KEmax = 1 m vanax = 1 m(BER)" 2m Maximum Kinetic energy KEmax = 1 B²q²R² ② Cyclotron frequeny & No of Renshatin the time taken by the ion to travesse any Semicircular path is geven by t= TEM Time taken to complete Rand - B9 The frequency of osullahir Required to keep the ion in phase is the reciprocal of the time in which the particles make me Revolution (This is what we call it Cycliom - T= 21tm frequency) f = Be

IT 21m 11 = to Be We may easily show that KE = 2m ² f² R² f = KE am M2R2 for our case KE= 250 MeV R=0.850m AV= 800v 250x100x1.6x1019 2X16X10-27 XT² X 10.8502 250x10681681019 V 2x16x1027 xit²x (0850) 2 ~ 4.2x107
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