Chapter IV. Betatrons
The betatron is a circular device that accelerates electrons: beta rays as they were originally
called in early observations of radioactivity. Following the success of the cyclotron it seemed
that the betatron, and the synchrotron which was to come later, should also be called “-tron”
to show that they too were accelerators.
Betatrons made a slow start. The cyclotron was the first practical accelerator for more
than a few MeV and it accelerated heavy particles like protons and deuterons — but it would
not work with electrons. We saw in Chapter II how even protons, at 30 MeV when they come
close to the speed of light, no longer remain in step with the RF in a cyclotron. The electron,
being almost 2000 times lighter than a proton, is, at any particular energy, much closer to the
velocity of light and therefore loses synchronism at a few keV.
Electrons were not very interesting at that time; physics was concentrating on how
neutrons and protons were bound together in the nucleus. A force, which we now call the
“strong force,” seemed to attract neutrons and protons, overcoming the repulsion of the
electrical charges of the protons, which, left to themselves, would have made the nucleus fly
apart. It seemed natural to use a particle that would exert this force — neutron or proton — as
a probe and not the electron, which seemed only to have electrical properties.
Of course electrons had been used to produce x-rays from a copper target for medical
diagnosis since the days of Roentgen, but the electron energy required was not very high. If
you look at the knobs and dials on your dentist’s x-ray machine you will see it is calibrated to
produce up to 100 kV: a voltage quite within the range of an electrostatic generator. Later on
there was a need for intense, higher energy electron beams to produce harder x-rays that
would penetrate the body and treat tumors. In Chapter II we mentioned that at the Berkeley
laboratory in the early 30s Sloan had used a resonant transformer to provide 800 keV
electrons for this purpose. This was not a betatron but a transformer whose secondary
winding was an open circuit. Electrons experiencing a fraction of a wavelength of the
oscillating high voltage in the gap were thrown off at high energy.
When the quantum theory predicted that atoms would emit and absorb x-rays and that
these would reveal the energy levels of the atom, a controlled source of x-rays was required;
but here again the energies needed to excite the K level electrons are only of the order of a
few keV.
And so for many years there seemed no pressing need for high energy electron
accelerators. Although betatrons, first discussed as early as 1922 (under the name of “beam
transformer”), would have filled the gap, it was only in 1942 that the idea was taken up again
to accelerate electrons in the energy range 5 MeV to 300 MeV. The popularity of the betatron
was short-lived for, by 1948, electron synchrotrons had been developed which were more
compact, lighter, and therefore less expensive. Synchrotrons could easily be built for a higher
energy than the betatrons they superseded. Nowadays only a few betatrons are built — as a
portable source of hard x-rays.
Those who built betatrons had to tackle and overcome a number of technical
difficulties that were the keys to building other circular machines (synchrotrons and colliders)
which followed. Betatrons, though they had no accelerating cavities and used magnetic
induction to accelerate electrons, were the first circular machines to have a rising field that
was kept in step with the rising energy of a pulse of electrons. Unlike cyclotrons that
produced a constant stream of beam, the electrons in a betatron were accelerated in a series of
pulses — just as they are in the synchrotrons that followed. To keep the particles on a circular
orbit as they were accelerated, designers had to understand how they would oscillate, from
side to side and up and down about the ideal circular path. These oscillations, which are just
as important for today’s synchrotrons and storage rings, are still called “betatron
oscillations,” their frequency the “betatron frequency” and their magnitude the “betatron
amplitude.” If they get into resonance with field errors, that is called a “betatron resonance”
— homage to the basic understanding contributed by the designers of the betatrons.
IV.1 Early History
The name “betatron” is relatively new and does not appear until Kerst revived the idea in the
1940s. Two decades earlier they were called “beam transformers” or “ray transformers.” It
was J. Slepian who, in 1922, had the idea of employing magnetic induction to accelerate
electrons. He took his idea from the voltage transformer to be found in all common household
appliances: the same device that powers the lap-top on which this book is being typed. In an
electrical transformer, an alternating current in the primary coil generates an alternating
magnetic field in a soft iron magnetic core. Both the primary and secondary coils are wound
on the same magnetic core so that the changing field excites alternating current in the
secondary.
Slepian’s idea was simply to replace the secondary winding with a free stream of
electrons flowing in a ring-shaped vacuum chamber, which, like the secondary of a normal
transformer, was threaded by the core. The current that flows in a normal transformer’s
secondary is driven by the voltage induced in the coil from end to end. At each point in the
coil there is an electric field (the gradient of this voltage) that drives the electrons along the
copper wire of the coil. There would be a similar voltage, V, around any circular path around
the magnetic core. Suppose the secondary coil were replaced by a donut-shaped vacuum
chamber. Any free electrons in the donut would feel the corresponding electric field and start
to circulate, gaining an energy, eV, on each turn. It was also argued that the device would be
very efficient since the losses in a normal transformer’s core are very small.
Slepian’s first thoughts were patented in 1927 while he was working at the
Westinghouse Electric Company and although his work was purely theoretical, it stimulated
some sporadic experimental work over the next two decades. In his device, electrons were
held in a circular orbit by the magnetic field between two poles of an electromagnet — just
like in the cyclotron that was to follow. The electromagnet was in fact the core of the
transformer and carried magnetic flux lines through the orbit of the electrons. It was just
opened up enough to slide in the donut-shaped vacuum chamber. The primary winding of the
transformer was the same coil that excited the electromagnet. Thus the field between the
poles both guided the electrons in a circle and accelerated them. With some clever matching
of flux and field the orbit radius would remain the same.
In the fall of 1922 and before any experimental work was initiated, Rolf Wideroe,
while still an undergraduate, was having similar ideas. He called his device a “ray
transformer” (“beta ray transformer” might have been a better description). In his device
there were two coils, one to provide the magnetic field necessary to keep the electrons
circulating at a fixed radius and the other to produce the flux which varies in time and
accelerates the electrons. His principal contribution to the concept was to think carefully
about the relation between the two fields. He found that in order for the guide field to
increase at a rate which keeps pace with the required rate of acceleration, it should have
exactly half the value you would expect in a simple dipole magnet carrying the same flux.
This “Wideroe condition” is essential for a betatron.
Wideroe described the whole concept of a betatron in his notes in 1923, and applied
for a patent. This would have predated Slepian’s work but there is no record that Wideroe
pursued his application to the end. In the autumn of 1925, Wideroe wanted to develop the
concept as an experiment for his doctor’s degree, but his thesis advisor encouraged him to
look for another topic!
In 1926, Wideroe moved to Aachen, where he was able to start experimental work on
his ray transformer. He built a device that was to reach an energy of 6.8 MeV but
unfortunately it never worked, probably because electrons charged up the glass walls of the
accelerating ring.
At the same time (1927) and far away in the Bureau of Terrestrial Magnetism, in
Washington, Breit and Tuve were also experimenting with an induction device. They were
motivated by the desire to make bursts of x-rays. Their machine did not satisfy the Wideroe
condition, but they were content to let the electrons spiral inwardly as the magnetic field
increased. However, they did realize the importance of focusing; shaping the field near the
orbit such that, if an electron deviated slightly from its design trajectory, it would experience
a force that would make it return to the correct trajectory. For vertical (axial) focusing this
required a magnetic field that decreased with increasing radius. This feature was exactly the
opposite of what had been foreseen in Slepian’s design but it proved to be correct and has
been incorporated into the design of all subsequent circular accelerators: cyclotrons,
betatrons, synchrotrons, etc. The experimental work of Breit and Tuve probably resulted in a
working machine, but the detection techniques for bursts of x-rays were so rudimentary that
one does not really know. In any case, about this time, the success of electrostatic machines
(described in Chapter I) brought the efforts on induction accelerators to an end.
Meanwhile in Britain, E.T.S. Walton was also pursuing the concept of an inductionbased circular accelerator. His outstanding theoretical work verified the concept of the
Wideroe condition and, more importantly, quantified the radial focusing condition that had
been first appreciated by Breit and Tuve. He also did extensive experimental work, but had
difficulty with the injection of the electrons. Like other workers, he had made no provisions
for the extraction of electrons other than forcing them to hit a target and produce x-rays. His
experimental work was not rewarded with success, but his theoretical contributions were
important for all further circular machines.
A number of other ideas were put forward in this period. In 1936, Jassinsky proposed
adding electrostatic fields to supply radial focusing, a concept that would only work at low
energy. Also in 1937, M. Steenbeck, of the Siemens Company in Berlin, applied for a patent
on a circular induction accelerator which was very similar to Wideroe’s. Steenbeck claimed,
subsequently, that in 1935 he was able to accelerate 1.8 MeV electrons although there is no
indication in the patent that he realized the need for conducting walls, nor is there description
of any experimental work. His experiments were not pursued.
In 1938 G.W. Penny applied for a patent for a device very similar to Wideroe’s, but
with electrostatic focusing. F.R. Abbott, at the University of Washington, built a device that
had all the elements that one needed to make a betatron (including conducting walls), but for
unknown reasons the device never worked and his efforts were never described in a
publication.
Also never published was the work of James L. Tuck and Leo Szilard at Oxford
University. Both of them carefully designed the machine, although it was Tuck who did the
experimental work. The device was designed to reach an even higher energy than that of
Breit and Tuve. The work of Tuck and Szilard was the most complete in technical detail and
the most likely to succeed of all the various attempts we have described. However, the advent
of World War II brought the work to a halt, and the device was never operated.
IV.2 The Kerst Betatron
In 1939, Donald Kerst at the University of Illinois extended Walton’s work on the theoretical
motion of electrons in spatially varying and time dependent fields. This analysis, due to Kerst
and Robert Serber, paved the way for the first successful betatron and provided a solid basis
for the analysis of particle motion in all future circular accelerators. Serber was a first-class
theorist and J. Robert Oppenheimer’s right-hand man in Berkeley in the 30s. Later he became a
theorist at Los Alamos, where he is famous for developing a handbook, which every newcomer
read, that described the key physics of atomic bombs. However, the basic ideas were all due to
Kerst, and Serber’s role was “only” to elegantly formulate the considerations.
Kerst was not to be put off by the previous unsuccessful attempts to build betatrons
(See sidebar for Kerst). He persevered and on July 15, 1940 operated the first successful
betatron. (See Fig. 4.1.) This was a circular tube of radius 7.5 cm, producing electrons with
energy of 2.3 MeV. The initial x-rays from this device were equivalent to 100 millicuries of
radium; later this was increased to the equivalent of a few grams of radium. One can imagine
the impact that this development made in medicine as well as in non-destructive material
testing (for example, looking for flaws in welds). Kerst then took a year’s leave from the
University of Illinois in 1940–41 and went to the General Electric Laboratories where he
designed two betatrons: a 20 MeV machine and a 100 MeV machine. (See Fig. 4.2.) During
the World War II days, Kerst built a 4 MeV portable betatron for inspecting unexploded
bombs in the field. He was also at Los Alamos where, according to the official history, his
“technical achievements are amongst the most impressive (at the laboratory).” Among these
was a 20 MeV betatron that was used to study the dynamics of bomb assembly implosions.
IV.3 The Wideroe Betatron — Second Attempt
Reports of Donald Kerst’s success reached Wideroe in Trondheim in the autumn of 1941.
Wideroe immediately returned to his earlier ideas on the “ray-transformer.” He wrote a rather
extensive review paper that was published in 1943.
In the spring of that year and while living in Nazi Germany, he was asked to go to
Berlin and work for their war effort. At that time his brother had been sentenced to 10 years
in jail for helping refugees escape from the Nazis and there were hints that his brother’s term
would be shortened. The Nazis didn’t disclose their purpose to Wideroe until 1944, but it
emerged that they were interested in using the x-rays from a betatron as a long-range deathray to kill enemy pilots or detonate their bombs. There was little chance that this would
succeed.
Meanwhile work started on what was known as the Hamburg Betatron. This 15-MeV
machine, financed by the German Aviation Ministry, was completed in 1944 and produced xrays equivalent to about 30 grams of radium. A much larger 200 MeV machine was designed
but never built. Wideroe’s brother’s prison term was not shortened and he had to wait to the
end of the war when he was liberated by the Americans. After World War II, Wideroe was
himself imprisoned, this time by his own country, Norway, for collaboration with the Nazis.
The Norwegians incorrectly suspected that he had invented and worked on the V2 rockets.
He was released once they realized that the betatron work had not resulted in any practical
weapon.
IV.4 The Years after World War II
After the war, Kerst returned to the University of Illinois and there, in 1950, after building an
80 MeV machine, he completed the largest betatron ever built — a 300 MeV machine —
used for the study of particle physics.
At this time there was considerable industrial interest in betatrons, both for medical
purposes and for non-destructive material testing. Their commercial production was in the
hands of General Electric, Westinghouse, Allis-Chalmers, Brown Boveri, Siemens-Reiniger
and Philips. Their machines were in the range of 30 MeV and many were sold as a safer
alternative to an intense radium source. Their obvious advantages were that they could be
turned off when not required, and that the beam could be directed to a particular spot.
The use of these machines to provide electrons and hence x-rays for the radiation
treatment of cancer patients pioneered the widespread use of accelerators in medicine. In
Chapter XI we will read that cyclotrons had been used for medical treatment even prior to
World War II, but their use was very limited and always involved bringing the patient to a
physics laboratory. More than 200 betatrons were built after World War II and installed in
hospitals in many locations in more than 20 countries. Nowadays, of course, these betatrons
have given way to linear machines. The new linacs are cheaper, m
Perhaps the last time we hear of a betatron in accelerator research was when one was
converted by Goward and Barnes into the first “proof of principle” synchrotron (see Chapter
V). Nowadays, except for those still produced as portable x-ray sources (See Fig. 4.3),
betatrons are only of historical interest.