1 Accelerators, Colliders and Their Application
5
Unlike almost all accelerators that followed, the ray transformer relied entirely
upon the inductive effect of a varying magnetic field. It is the rate of change of
flux, φ, in the yoke which establishes an accelerating potential difference around
the beam’s path. The windings, that of the C-magnet and of the primary of the
transformer, W 1 , give independent control of the guide field and accelerating flux.
Wideröe calculated that electrons circulating in a ring of only 10 or 20 cm
diameter could reach several MeV within one quarter wave of the AC excitation
of the transformer. He had to use Einstein’s newly discovered theory of special
relativity to correctly describe the motion of particles close to the speed of light.
He also found an important principle which ensures that the beam radius does not
change as it accelerates. To ensure constant radius during acceleration the total flux
linking the beam including that generated by both sets of the coils, B a, must be twice
that generated by the left hand coil pair which produces the field keeping the beam
in a circular orbit, B g .
˙
B a = 2 ˙
B g
Unfortunately, Wideröe was dissuaded from building the ray transformer by
difficulties with surface fields and by his professor, who wrongly assumed the beam
would be lost because of gas scattering. However, his Ray Transformer and the 2
to 1 ratio, now known as the Wideröe principle, were important discoveries which
were put into practice 15 years later when D.W. Kerst and R. Serber [6] built a series
of betatrons.
Wideröe went on to develop a second basic acceleration method to overcome the
electrostatic limitation: the drift tube linac.
1.2.3 Repetitive Acceleration
There are two broad classes of accelerator characterized by the way they achieve
repetitive acceleration and which overcome the insulation problems of the electrostatic machines. The simplest concept is that of the linear accelerator. Particles
pass though cavities excited by radio frequency generators. They arrive on the
threshold of each cavity with the energy they have already received and gain a
further increment in energy from the electric field in the cavity which points in
their direction of motion. Each cavity performs the function of the gap between the
anode and cathode of an electrostatic accelerator but, unlike the electrostatic case,
the increments of energy may be added together without developing a huge voltage
to ground in any part of the apparatus. Of course, there is a limit to the voltage
(energy increment) each cavity can apply and the length of the device becomes
very long for energies above 1 GeV. Nevertheless, a linac has become the only way
of accelerating highly relativistic electrons which radiate a large fraction of their
energy when bent into a circular path.
5
Unlike almost all accelerators that followed, the ray transformer relied entirely
upon the inductive effect of a varying magnetic field. It is the rate of change of
flux, φ, in the yoke which establishes an accelerating potential difference around
the beam’s path. The windings, that of the C-magnet and of the primary of the
transformer, W 1 , give independent control of the guide field and accelerating flux.
Wideröe calculated that electrons circulating in a ring of only 10 or 20 cm
diameter could reach several MeV within one quarter wave of the AC excitation
of the transformer. He had to use Einstein’s newly discovered theory of special
relativity to correctly describe the motion of particles close to the speed of light.
He also found an important principle which ensures that the beam radius does not
change as it accelerates. To ensure constant radius during acceleration the total flux
linking the beam including that generated by both sets of the coils, B a, must be twice
that generated by the left hand coil pair which produces the field keeping the beam
in a circular orbit, B g .
˙
B a = 2 ˙
B g
Unfortunately, Wideröe was dissuaded from building the ray transformer by
difficulties with surface fields and by his professor, who wrongly assumed the beam
would be lost because of gas scattering. However, his Ray Transformer and the 2
to 1 ratio, now known as the Wideröe principle, were important discoveries which
were put into practice 15 years later when D.W. Kerst and R. Serber [6] built a series
of betatrons.
Wideröe went on to develop a second basic acceleration method to overcome the
electrostatic limitation: the drift tube linac.
1.2.3 Repetitive Acceleration
There are two broad classes of accelerator characterized by the way they achieve
repetitive acceleration and which overcome the insulation problems of the electrostatic machines. The simplest concept is that of the linear accelerator. Particles
pass though cavities excited by radio frequency generators. They arrive on the
threshold of each cavity with the energy they have already received and gain a
further increment in energy from the electric field in the cavity which points in
their direction of motion. Each cavity performs the function of the gap between the
anode and cathode of an electrostatic accelerator but, unlike the electrostatic case,
the increments of energy may be added together without developing a huge voltage
to ground in any part of the apparatus. Of course, there is a limit to the voltage
(energy increment) each cavity can apply and the length of the device becomes
very long for energies above 1 GeV. Nevertheless, a linac has become the only way
of accelerating highly relativistic electrons which radiate a large fraction of their
energy when bent into a circular path.