500 9 Particle Physics – I
9.86 A synchro-cyclotron has a pole diameter of 4 m and a magnetic field of
1 .5Wm−^2 (15,000 G). What is the maximum energy that can be transmitted
to electrons which are struck by protons extracted from this accelerator?
[University of Bristol 1968]
9.87 If the frequency of the dee voltage at the beginning of an accelerating sequence
is 20 Mc/s, what must be the final frequency if the protons in the pulse have
an energy of 469 MeV?
[University of Durham 1963]
9.2.13 Synchrotron. ....................................
9.88 At what radius do 30 GeV protons circulate in a synchrotron if the guide field
is 1 W m−^2
9.89 Calculate the orbit radius for a synchrotron designed to accelerate protons to
3 GeV assuming a guide field of 14 kG
[University of Durham 1962]
9.90 What percentage depth of modulation must be applied to the dee voltage of
a synchrotron in order to accelerate protons to 313 MeV assuming that the
magnetic field has a 5% radial decrease in magnitude.
[University of Durham 1962]
9.91 An electron synchrotron with a radius of 1 m accelerates electrons to 300 MeV.
Calculate the energy lost by a single electron per revolution when it has
reached maximum energy.
[Andhra University 1966]
9.92 Show that the radiusRof the final orbit of a particle of chargeqand rest mass
m 0 moving perpendicular to a uniform field of magnetic inductionBwith a
kinetic energyntimes its own rest mass energy is given by
R=m 0 c(n^2 + 2 n)^1 /^2 /qB
9.93 Protons of kinetic energy 50 MeV are injected into a synchrotron when the
magnetic field is 147 G. They are accelerated by an alternating electric field
as the magnetic field rises. Calculate the energy at the moment when the mag-
netic field reaches 12,000 G (rest energy of proton=938 MeV)
[University of Bristol 1962]
9.94 A synchrotron (an accelerator with an annular magnetic field) accelerates pro-
tons (mass numberA=1) to a kinetic energy of 1,000 MeV. What kinetic
energy could be reached by deuteron (A= 2) or^3 He (A = 3 , Z =2)
when accelerated in this machine? Take the proton mass to be equivalent to
1,000 MeV.
[University of Durham 1970]