9.2 Problems 501
9.95 A synchrocyclotron accelerates protons to 500 MeV.B=18 kG,V=10 kV
andφs= 300. To find
(a) the radius of the orbit at extraction
(b) Energy of ions for acceptance
(c) the initial electric frequency limits
(d) the range of frequency modulation
9.96 Explain how a synchrotron accelerates particles. What is the main energy loss
mechanism in these devices? How much more power is needed to maintain a
beam of 500 GeV electrons in a synchrotron of radius 1 km than to maintain a
beam of protons of the same energy? Is this feasible?
[University of Aberyswyth 2003]
9.97 Protons are accelerated in a synchrotron in the orbit of 10 m. At one moment in
the cycle of acceleration, protons are making one revolution per microsecond.
Calculate the value at this moment of the kinetic energy of each proton in MeV.
[University of Bristol 1961]
9.98 Electrons are accelerated to an energy of 10 MeV in a linear accelerator, and
then injected into a synchrotron of radius 15 m, from which they are acceler-
ated with an energy of 5 GeV. The energy gain per revolution is 1keV
(a) Calculate the initial frequency of the RF source. Will it be necessary to
change this frequency?
(b) How many turns will the electron make?
(c) Calculate the time between injection and extraction of the electrons
(d) What distance do the electrons travel within the synchrotron?
9.2.14 Linear Accelerator ................................
9.99 Protons of 2 MeV energy enter a linear accelerator which has 97 drift tubes
connected alternately to a 200 MHz oscillator. The final energy of the pro-
tons is 50 MeV (a) What are the lengths of the second cylinder and the last
cylinder (b) How many additional tubes would be needed to produce 80 MeV
protons in this accelerator?9.100 The Stanford linear accelerator produces 50 pulses per second of about 5×
1011 electrons with a final energy of 2 GeV. Calculate (a) the average beam
current (b) the power output.
9.101 A section of linear accelerator has five drift tubes and is driven by a 50 Mc
oscillator. Assuming that the protons are injected into the first drift tube at
100 kV and gain 100 kV in every gap crossing
(a) What is the output energy after the fifth drift tube?
(b) What is the total length of the whole section? (Ignore the gap length)
[AEC 1966 Trombay]