Question

Cyclotrons are electrostatic accelerator used in place of linear accelerator to save space. These accelerators are used in research and to produce medial isotopes. Determine the maximum possible kinetic energy of a He+ ion accelerated in a 5 m diameter cyclotron with a magnetic field of 1.5 Tesla. what do the cyclotron need to be changed, and by how much, if the required velocity of the particle was 90% that of the speed of light? Comment on your findings.

Answer 1

KE max=? He+ ion. Radius = 2,5 m B = 1.5 T

F = B q v = mv^2/r

v = Bqr/m = 1.5 T x 1.6 x 10^(-19 ) C x 2.5 m/ [6.7 x 10^(-27) Kg

KE = 0.5 x 6.7 x 10^(-27) Kg x {1.5 T x 1.6 x 10^(-19 ) C x 2.5 m/ [6.7 x 10^(-27) Kg]} ^2

= 2.686 x 10^(-11) J

—————-==

v = 0.9 C

r = mv/Bq

r = m0 x v / Bq (1-v^2/c^2)

= (6.07*10^(-27)*0.9*3*10^8 )/ ( 1.5 * 1.6 * 10^(-19)*(1-0.9^2)) = 35.9 Meters

So you need larger Dees for the Cyclotron.

If you. want cyclotron radius to be same, you may need higher B value.

B = mo v / r q (1-v^2/c^2)

= 6.7 x 10^(-27) Kg x 0.9 C / [ 1.5m x 1.6 x 10^(-19) C x (1- 0.9^2)

= 39.7 T

so B value needs to be increased.