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A betatron is a type of cyclic
particle accelerator
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.
Large accelerators are used for fundamental research in particle ...
. It is essentially a
transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
with a
torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.
If the axis of revolution does not tou ...
-shaped vacuum tube as its secondary coil. An alternating current in the primary coils accelerates
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s in the vacuum around a circular path. The betatron was the first machine capable of producing electron beams at energies higher than could be achieved with a simple
electron gun
An electron gun (also called electron emitter) is an electrical component in some vacuum tubes that produces a narrow, collimated electron beam that has a precise kinetic energy. The largest use is in cathode-ray tubes (CRTs), used in nearly ...
, and the first circular accelerator in which particles orbited at a constant radius.
The concept of the betatron had been proposed as early as 1922 by
Joseph Slepian
Joseph Slepian
(February 11, 1891 – December 19, 1969)
was an American electrical engineer known for his contributions to the developments of electrical apparatus and theory.
Born in Boston, MA of Jewish Russian immigrants, he studied ma ...
.
Through the 1920s and 30s a number of theoretical problems related to the device were considered by scientists including
Rolf Wideroe,
[
] Ernest Walton
Ernest Thomas Sinton Walton (6 October 1903 – 25 June 1995) was an Irish physicist and Nobel laureate. He is best known for his work with John Cockcroft to construct one of the earliest types of particle accelerator, the Cockcroft–Walton g ...
, and
Max Steenbeck
Max Christian Theodor Steenbeck (21 March 1904 – 15 December 1981) was a German physicist who worked at the '' Siemens-Schuckertwerke'' in his early career, during which time he invented the betatron in 1934. He was taken to the Soviet Uni ...
.
The first working betatron was constructed by
Donald Kerst
Donald William Kerst (November 1, 1911 – August 19, 1993) was an American physicist who worked on advanced particle accelerator concepts (accelerator physics) and plasma physics. He is most notable for his development of the betatron, a novel ...
at the
University of Illinois Urbana-Champaign
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the University ...
in 1940.
History
After the discovery in the 1800s of
Faraday's law of induction
Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic inducti ...
, which showed that an
electromotive force
In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transd ...
could be generated by a changing
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
, several scientists speculated that this effect could be used to accelerate charged particles to high energies.
Joseph Slepian
Joseph Slepian
(February 11, 1891 – December 19, 1969)
was an American electrical engineer known for his contributions to the developments of electrical apparatus and theory.
Born in Boston, MA of Jewish Russian immigrants, he studied ma ...
proposed a device in 1922 that would use permanent magnets to steer the beam while it was accelerated by a changing magnetic field. However, he did not pursue the idea past the theoretical stage.
In the late 1920s,
Gregory Breit
Gregory Breit (russian: Григорий Альфредович Брейт-Шнайдер, ''Grigory Alfredovich Breit-Shneider''; July 14, 1899, Mykolaiv, Kherson Governorate – September 13, 1981, Salem, Oregon) was a Russian-born Jewish Am ...
and
Merle Tuve
Merle Anthony Tuve (June 27, 1901 – May 20, 1982) was an American geophysicist who was the Chairman of the Office of Scientific Research and Development's Section T, which was created in August 1940. He was founding director of the Johns Hopkins ...
at the
Bureau of Terrestrial Magnetism constructed a working device that used varying magnetic fields to accelerate electrons. Their device placed two
solenoidal magnets next to one another and fired electrons from a gun at the outer edge of the magnetic field. As the field was increased, the electrons accelerated in to strike a target at the center of the field, producing X-rays. This device took a step towards the betatron concept by shaping the magnetic field to keep the particles focused in the plane of acceleration.
In 1929,
Rolf Wideroe made the next major contribution to the development of the theory by deriving the ''Wideroe Condition'' for stable orbits. He determined that in order for the orbit radius to remain constant, the field at the radius must be exactly half of the average field over the area of the magnet. This critical calculation allowed for the development of accelerators in which the particles orbited at a constant radius, rather than spiraling inward, as in the case of Breit and Tuve's machine, or outward, as in the case of the
cyclotron
A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. Lawrence, Ernest O. ''Method and apparatus for the acceleration of ions'', filed: Janu ...
.
Although Wideroe made valuable contributions to the development of the theory of the Betatron, he was unable to build a device in which the electrons orbited more than one and a half times, as his device had no mechanism to keep the beam focused.
Simultaneously with Wideroe's experiments,
Ernest Walton
Ernest Thomas Sinton Walton (6 October 1903 – 25 June 1995) was an Irish physicist and Nobel laureate. He is best known for his work with John Cockcroft to construct one of the earliest types of particle accelerator, the Cockcroft–Walton g ...
analyzed the orbits of electrons in a magnetic field, and determined that it was possible to construct an orbit that was radially focused in the plane of the orbit. Particles in such an orbit which moved a small distance away from the orbital radius would experience a force pushing them back to the correct radius. These oscillations about a stable orbit in a circular accelerator are now referred to as ''betatron oscillations''.
In 1935
Max Steenbeck
Max Christian Theodor Steenbeck (21 March 1904 – 15 December 1981) was a German physicist who worked at the '' Siemens-Schuckertwerke'' in his early career, during which time he invented the betatron in 1934. He was taken to the Soviet Uni ...
applied in Germany for a patent on a device that would combine the radial focusing condition of Walton with the vertical focusing used in Breit and Tuve's machine. He later claimed to have built a working machine, but this claim was disputed.
The first team unequivocally acknowledged to have built a working betatron was led by Donald Kerst at the University of Illinois. The accelerator was completed on July 15, 1940.
Operation principle
In a betatron, the changing magnetic field from the primary coil accelerates electrons injected into the vacuum torus, causing them to circle around the torus in the same manner as current is induced in the secondary coil of a transformer (
Faraday's law).
The stable orbit for the electrons satisfies
:
where
:
is the flux within the area enclosed by the electron orbit,
:
is the radius of the electron orbit, and
:
is the magnetic field at
.
In other words, the magnetic field at the orbit must be half the average magnetic field over its circular cross section:
:
This condition is often called ''Widerøe's condition''.
Etymology
The name "betatron" (a reference to the
beta particle
A beta particle, also called beta ray or beta radiation (symbol β), is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, β ...
, a fast electron) was chosen during a departmental contest. Other proposals were "rheotron", "induction accelerator", "induction electron accelerator", and even "''Außerordentlichehochgeschwindigkeitselektronenentwickelndesschwerarbeitsbeigollitron''", a suggestion by a German associate, for "Hard working by golly machine for generating extraordinarily high velocity electrons" or perhaps "Extraordinarily high velocity electron generator, high energy by golly-tron."
Applications
Betatrons were historically employed in
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
experiments to provide high-energy beams of electrons—up to about 300
MeV
In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacu ...
. If the electron beam is directed at a metal plate, the betatron can be used as a source of energetic
x-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
s, which may be used in industrial and medical applications (historically in
radiation oncology
Radiation therapy or radiotherapy, often abbreviated RT, RTx, or XRT, is a therapy using ionizing radiation, generally provided as part of cancer treatment to control or kill malignant cells and normally delivered by a linear accelerator. Radia ...
). A small version of a betatron was also used to provide a source of hard X-rays (by deceleration of the electron beam in a target) for prompt initiation of some experimental
nuclear weapon
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions ( thermonuclear bomb), producing a nuclear explosion. Both bom ...
s by means of photon-induced fission and
photofission
Photofission is a process in which a nucleus, after absorbing a gamma ray, undergoes nuclear fission and splits into two or more fragments.
The reaction was discovered in 1940 by a small team of engineers and scientists operating the Westing ...
in the bomb core.
The Radiation Center, the first private medical center to treat cancer patients with a betatron, was opened by Dr.
O. Arthur Stiennon in a suburb of
Madison, Wisconsin
Madison is the county seat of Dane County and the capital city of the U.S. state of Wisconsin. As of the 2020 census the population was 269,840, making it the second-largest city in Wisconsin by population, after Milwaukee, and the 80th-lar ...
in the late 1950s.
''Wisconsin alumnus'', Volume 58, Number 15 (July 25, 1957)
Limitations
The maximum energy that a betatron can impart is limited by the strength of the magnetic field due to the saturation of iron and by practical size of the magnet core. The next generation of accelerators, the synchrotron
A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed p ...
s, overcame these limitations.
References
External links
{{Commons category, Betatrons
The Betatron at UIUC
Accelerator physics
German inventions of the Nazi period