500
9 Particle Physics – I
9.86 A synchro-cyclotron has a pole diameter of 4 m and a magnetic field of
1.5 W m
−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 radius R of the final orbit of a particle of charge q and rest mass
m 0 moving perpendicular to a uniform field of magnetic induction B with a
kinetic energy n times its own rest mass energy is given by
R = m 0 c (n
2
+ 2n)
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 magnetic 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 protons (mass number A = 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]
9 Particle Physics – I
9.86 A synchro-cyclotron has a pole diameter of 4 m and a magnetic field of
1.5 W m
−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 radius R of the final orbit of a particle of charge q and rest mass
m 0 moving perpendicular to a uniform field of magnetic induction B with a
kinetic energy n times its own rest mass energy is given by
R = m 0 c (n
2
+ 2n)
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 magnetic 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 protons (mass number A = 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]