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Phys13news
UNIVERSITY OF
WATERLOO
Department of Physics & Astronomy
University of Waterloo
Waterloo, Ontario, Canada
N2L 3G1
Fall 2014
Number 149
St. Elmo’s Fire
Cover:
From the Editor
St Elmo’s fire is a continuous,
luminous electrical discharge in the
atmosphere. Primarily from elevated
objects above the Earth’s surface.such
as steeples, airplanes, ship masts, etc..
Picture Courtesy Robert Jones at
“How it Works”
Contents
Weird and Wonderful Manifestations
Manifestations of Electro-magnetism:
Past and Present………………….....3
Michael Faraday: The Formation of
a Scientist and his Greatest
Discovery……………………..…..6
The
Cyclotron:
Principles
of
Operation and Uses in Modern
Society……………………….….....9
The Electron Microscope ..…….....14
After some five years of absence as editor and
publisher of Phys13news, we again have the pleasure of
providing stories of interest. We continue with a
historical perspective of some of the important
electromagnetic phenomena that was started in the
previous issue. Although, we’ve had a three-issue
hiatus, please be assured that your subscriptions will be
honoured to include future issues as necessary. It is our
long term goal that within the next year we will switch
to an online publication without user fees. Moreover, I
would like to encourage the involvement of High School
teachers in the future content of Phys13news,
particularly with respect to teaching material that they
may have found useful and rewarding.
Guenter Scholz
Phys13news is published four times a year by the
Department of Physics and Astronomy at the University
of Waterloo. Our policy is to publish anything relevant
to high school and first-year university physics, or of
interest to high school physics teachers and their senior
students. Letters, ideas and articles of general interest
with respect to physics are welcomed by the editor. You
can reach the editor by paper mail, fax or email.
Paper:
Phys13news
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University of Waterloo
Waterloo, ON N2L 3G1
Fax:
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Editor:
Guenter Scholz
Editorial Board:
Avery Broderick, Richard Epp, Bae-Yeun
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Chris O’Donovan
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Printing:
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The SIN Bin……………………………….……….…16
Phys13news / Fall 2014
Page 2
Weird and Wonderful Manifestations of
Electromagnetism: Past and Present
Madeleine Bonsma
Institute for Quantum Computing
Since ancient times, people have been amazed,
frightened, confused, and awed by the effects of
electrical and magnetic influences around them. From
common occurrences like lightning, magnetic attraction,
and static electricity to the rare Saint Elmo's Fire,
electromagnetism can produce a host of stunning natural
phenomena. Historically, many of these bewildering
events were poorly understood and often attributed to
the supernatural. With the scientific revolution came a
physical understanding of electromagnetism and its
effects in the world. Some of these phenomenon, both
common and unusual, are identified and outlined and
their historical and modern understanding contrasted.
Magnetism and Static Electricity
Magnetism is one facet of electromagnetism that
has been put to use for millennia. Mentions of lodestone,
a naturally occurring magnetic iron ore, was used as a
compass in China, as far back as 2500 B.C. (2). Static
electricity, too, has no doubt been observed for a long
time. Thales of Miletus, a Greek philosopher in about
600 B.C., is credited with first noticing static electricity
in the form of rubbed amber attracting light objects.
Early scholars often associated the properties of
lodestone and amber, even to the point of confusing the
two (l). The actual relationship between them was not
known for some time. The several thousands of years
between first observations to a logical understanding is a
fascinating illustration of our interactions with natural
phenomena.
Introduction
As a species, our knowledge and understanding of
the world over time is a monotonically increasing
function and it is interesting and valuable to look back
at previous points in the history of science and take
note of the ideas and methods at the forefront of
learning in those times. It is tempting, from our lofty
and privileged place in "the future", to consider early
theories and explanations, now often obviously wrong
or unscientific. But as Home points out in “The
Effiuvial Theory of Electricity” (1), early investigators
of electricity began from a somewhat different way of
looking at the world and so their ideas deserve some
respect. Pattern-seekers throughout history have
generally had the same goal, and with this in mind I
will try not to be over-critical of past understandings
of the natural world.
It is a valid and worthwhile pursuit to study
knowledge from previous eras. Here I am only
concerned with presenting stories from the history of
electromagnetism for informational and entertainment
purposes. Also, it should be noted that explanations
for most natural phenomena throughout time are a
continuum, not a step function, and so I will usually
choose just a few interesting historical approaches to
contrast with present understanding.
Magnetism and static electricity are two ideas that
have been theoretically unified o n l y relatively
recently, however their manifestations have been
observed for thousands of years.
Phys13news / Fall 2014
FIG. 1: Illustration of the discovery of the Leyden jar.
An assistant in the lab of Pieter von Muschenbroek holds
a water-filled jar, charged by the electrostatic machine
on the right. A charge accumulates in the water and
on the hand of the assistant, who receives a powerful
shock when he touches the metal wire hanging into the
jar with his free hand.
After many years of intellectual and artistic
stagnation, the dawn of the enlightenment brought
about a revolution in the sciences as well (4). New
discoveries in electricity and electrostatics came thick
and fast, each one more wondrous and unprecedented
than the one before. The invention of charge storing
mechanisms (such as the Leyden jar, a primitive
capacitor - Fig. 1) and the discovery that electricity
could be transmitted (even by humans) prompted
dramatic experiments and demonstrations of the power
of electricity. For example, the prevailing theory at the
time of the invention of the Leyden jar in the
Page 3
mid-1700s was that electricity was a fluid of some
sort and variations on this theme such as one-fluid or
two-fluid theories were proposed and supported at
different times and in different places. Another
remarkable direction of early electromagnetic theory
came through William Gilbert and Johannes Kepler.
Gilbert's discovery of earth's magnetic field led him
and others, including Kepler, to suppose that gravity
and the motion of the planets in the solar system could
be explained with magnetic forces. This is now known
to be spectacularly wrong, but the trajectory of their
thought was logical nonetheless.
bottom of the cloud as well as between the cloud and the
ground.
When this difference becomes great enough (about
3 megavolts), the result is equivalent to a capacitor
breakdown on a large scale,
The insulating air
(dielectric) within the cloud or between cloud and
ground becomes ionized, violently and rapidly
conducting electricity between the "plates" of the
cloud­ ground capacitor.
Today, we benefit from hundreds of years of
hindsight on the fascinating experiments of the early
electricians. There were many contributors to the
current understanding of electro-magnetism, but James
Clerk Maxwell is usually credited with ultimately
unifying electricity and magnetism. The Lorentz force
law and the four equations bearing Maxwell's name
neatly summarize all of classical electrodynamics.
Electricity and magnetism were then understood to be
fundamentally intertwined, a changing magnetic field
induces an electric field and a changing electric field
induces a magnetic field (3).
Lightning and St. Elmo’s Fire
Of all the electromagnetic phenomena, lightning
must have been one of the most spectacular to people of
the ancient world. Lightning is mentioned in the Biblical
plague of hail, and in many other places in the Bible it is
used as an indicator of the presence of God.
Lightning (and thunder) have a prominent place in
many mythologies. Anaximander, a student of Thales of
Miletus also around 600 B.C., is credited with this
statement about stormy occurrences: "Thunders,
lightnings, presters, and whirlwinds are caused by the
wind enclosed in a thick cloud, which, by reason of its
lightness, breaketh forth violently, the rupture of the
cloud maketh a crack, and the divulsion by reason of the
blackness causeth a flashing light" (4). Stephen Gray, an
English scientist in the early 1700s, noted the similarity
between crackling electrical sparks and rumbling
thunder and lightning, and Benjamin Franklin is widely
credited with proving that lightning is an electrical
discharge following his kite experiments (2).
Although lightning is not fully understood even
today, its general mechanism is known. Powerful air
currents in thunderclouds cause particles in the cloud
(droplets of water) to collide and acquire a charge.
Negatively charged particles accumulate at the bottom of
the cloud and positive charges rise to the top, creating an
immense potential difference between the top and
Phys13news / Fall 2014
FIG. 2: Illustration of St. Elmo's Fire atop a sailing
ship's masts.
St. Elmo's Fire (Fig. 2) is a rarer sight than
lightning, but must have evoked similar fear and wonder
in onlookers. In European weather lore, the flame-like
glow was often taken as an omen for bad weather by
sailors, and sometimes as a sign of the helpful presence
of a deity. Home lists St. Elmo's Fire as one of just four
electrical phenomena that were well known by early
civilizations (1).
Today, St. Elmo's Fire is seen around airplanes,
masts of sailing ships, towers, treetops or other tall,
pointed, conducting objects. The phenomenon is
actually a corona discharge that occurs primarily in
stormy weather due to the increased atmospheric
Page 4
electric field strength during storms. Corona discharge
is an electrical discharge that emanates from
conducting objects when the electric field near their
surfaces approaches 100,000 V/ m. Pointed objects are
especially prone to corona discharge because the
intensity of an electric field at a charged spherical
surface is inversely proportional to the surface's radius
of curvature.
The Aurora
Like lightning, the Auroras Borealis (Fig. 3)
and Australis was observed by early humans,
primarily at far northern and southern latitudes.
Indeed we find many mentions of the aurora in Norse,
Inuit, and Australian stories and mythology.
Aristotle's explanation for the aurora stemmed from
the four elements of earth, air, fire, and water and
thought that the sun's heat caused a vapour to rise
from the surface of earth, collide with fire and
burst into flame. Another early Norwegian
account of the aurora suggested that it is caused
by fire circling the globe, or from the sun's rays
reaching the sky from below the horizon, or even
burning glaciers. Into the late 1700’s, the theory
persisted that the aurora might somehow be
reflected sunlight but this was finally disproved
when in 1827 it was observed that light from the
aurora was not polarized (4).
Modern scientific understanding of the aurora is
in many ways more fantastical than even early
civilizations could have dreamed. The sun, a great
ball of reacting and colliding gas, emits a steady
stream of charged particles - the solar wind. These
charged particles are deflected by earth's magnetic
field towards the poles and collide with gas
molecules in earth's upper atmosphere, between 100
km to 200km above the surface. Where the
concentration and speed of these particles is large
enough, because of a high solar activity or the
geometry of earth's field, the collisions between
molecules in the atmosphere and the solar wind
wi l l produce bright electrical discharges that are
coloured depending on the type of gas involved in
the collision (4). We observe a mystical, ethereal
light caused by the sun, but not the sun's light. The
empirical facts are as astounding as the mythologies
and historical explanations for the aurora.
Conclusion
Electricity and magnetism are embedded in some
way in nearly every aspect of the universe we live in,
and while to ancients and early scientists the
connections were not always apparent, our forebears
Phys13news / Fall 2014
FIG. 3: Photograph of aurora borealis taken near
Fairbanks, Alaska.
noticed and studied these natural phenomena with awe
and wonder. As our reliance on the scientific method
increased, our empirical understanding of these
phenomena too has increased and provided insights into
the underlying order and structure behind these
observations. New understanding was sometimes hinted
at by previous thoughts but was just as often vastly
different from what anyone imagined.
References
[1] R. W. Home, The Effluvial Theory of Electricity
(Arno Press, Inc., 1981).
[2] H. W. Meyer, A History of Electricity and
Magnetism
(Massachusetts
Institute
of
Technology, 1971).
[3] T. L. Hankins, Science and the Enlightenment
(Camb. Univ, Press, 1985).
[4] H. Falck-Ytter, The Auroro: The northern lights in
mythology, history, and science (Floris Books,
1985).
Page 5
Michael Faraday: The Formation of a
Scientist and his Greatest Discovery
Peter Mundy
Alumni, University of Waterloo
Michael Faraday was born on 22 September 1791 in
Newington Butts, London, England to James and
Margaret Faraday, a blacksmith and maidservant
respectively (l). His upbringing was a somewhat
ordinary one for the tum of the 19th century in England
when food prices were exceptionally high and many
families were barely managing to survive. As one may
expect for this time in history Faraday's elementary
education was far below present day standards and, in
his own words, was an education "consisting of little
more than the rudiments of reading, writing, and
arithmetic". At the age of fourteen Faraday became an
apprentice bookbinder and bookseller under the tutelage
of George Riebau and it was in this role that, for the
next seven years, Faraday would educate himself by
reading a myriad of books (1).
In the years surrounding and including 1812, to
further his own education and his interest in science,
Faraday attended lectures by the renowned chemist
Humphry Davy as well as the scientist John Tatum. The
lecture topics were numerous and included electricity
and optics, two particular subjects that would feature
prominently in Faraday's academic career. He would
take notes during these lectures and from these notes he
compiled a three hundred page book (able to do so from
his apprenticeship as a bookbinder) which he then sent
to Davy himself. This was arguably a turning point in
the young Faraday's life that set his future career in
motion as, after damaging his eyesight in a nitrogen
trichloride experiment, Davy decided to hire Faraday to
be his secretary at the Royal Institution (2). This was
the beginnings of his scientific journey.
In his position as secretary, and his later position as
chemical assistant, Faraday was surrounded by science
and scientists. During the period of 1813 to 1815 he
accompanied Davy on a tour of Europe as his scientific
assistant and it was on this tour that he was exposed to
many scientific ideas and prominent scientists. During
the 1810’s Faraday learnt much about science and being
a scientific assistant. Here he developed the habit that
would enable him to become a great scientific
experimentalist by verifying for himself the science
which he had read and was trying to understand. Of
himself he says "I could not imagine much progress by
reading only, without experimental facts and trials".
The year of 1819 was the end of Faraday's allotted
time at the Royal Institution and for the next several
years he used his education in chemistry to perform
Phys13news / Fall 2014
miscellaneous jobs for companies such as the East India
Company, an explosives manufacturer. For them he
analyzed samples of explosives to determine their water
content (6). These job opportunities, while providing the
necessary finances, also occupied Faraday's time that he
would rather have spent on research. Scientists today
may resonate with his feeling that, "Much of [my time]
is unfortunately occupied in very common place
employment and this I may offer as an excuse (for want
of a better) for the little I do in original research".
Work on electromagnetic interaction did not
originate with Faraday but had been studied by the
Danish scientist Hans Christian Oersted and the French
scientist Andre-Marié Ampère. Investigating the theory
of electromagnetic interaction in 1821, Davy and
William Hyde Wollaston conducted an experiment to
test Wollaston's theory that "the existence of a helical
current ought to make a current-carrying wire revolve
around its own axis when a permanent magnet was
brought close to it" (8). Faraday was not present for this
experiment but later investigated this experiment as he
was invited by the editor of the Annals of Philosophy,
Richard Phillips, to write an historical account of
electromagnetism, an emerging field of science. In
writing this account Faraday conducted the relevant
experiments in electromagnetism that he explained.
Faraday's discovery in September of 1821 that "rotation
of a wire in voltaic current round a magnet, and of a
magnet round the wire" showed that Wollaston's theory
that the wire should revolve around its own axis was
incorrect (9). His discovery was made by inventing the
apparatus shown in Fig. 1. On the left hand side of the
diagram can be seen a vertical magnet that is allowed to
rotate around the suspended fixed wire and on the right
hand side can be seen a vertical fixed magnet with a
wire that is allowed to rotate around it and electrical
current flowed through this apparatus. The gravity of
this discovery and the experimental apparatus used
cannot be overstated; Faraday had invented the first
electric motor.
Over the next decade Faraday's work was rather
varied and little documentation exists to have a full
picture of all his work. What is known is that he spent a
sizeable portion of his time developing the highest
quality glass that he was able to. This borosilicate of
lead was the same glass that he would use later on in his
studies of the interaction between light and
electromagnetism. 1827 saw the publishing of his first
book titled “On Chemical Manipulation (3)”, a thorough
laboratory manual for lack of a better phrase. With each
passing year Faraday was granted more honors from
various scientific societies and his fame within the
academic world of science increased and also evidenced
by his relief from his duty of lecturing at the Royal
Institution "because of his occupation in research" (3).
Page 6
knew that when electricity flowed through this copper
wire the needle would detect the flow of electric current.
Faraday connected the other coil of copper wire on the
torus to a battery and as this connection was made or
broken, the needle detected a flow of current. Magnetic
induction had been demonstrated for the first time.
Fig. 1: Apparatus, now known as the homopolar motor
(10), invented by Faraday to investigate the theory of
electromagnetic rotation.
His previous work on electromagnetism as well as
his investigation of Ampère's electromagnetic theory
were the building blocks of an important experiment that
Faraday conducted on 29 August 1831. Ampère's
electromagnetic theory is summed up excellently by
Williams and is quoted directly: "Magnetic forces were
the result of the motion of the two electric fluids;
permanent magnets contained these currents running in
circles concentric to the axis of the magnet and in a
plane perpendicular to this axis" (1).
The
aforementioned experiment by Faraday led to his
greatest discovery, the theory and demonstration of
electromagnetic induction. It is difficult to overstate the
importance and brilliance of this discovery in that it is
foundational in modern electromagnetic theory.
Faraday's experiment can simply be expressed in
words: A changing magnetic field produces an electric
field. Although he had a good understanding of the
experimental setup and theory, what he lacked was a
mathematical formulation that physicists demand. This
was not to appear until James Clerk Maxwell's 1873
publication, A Treatise on Electricity and Magnetism,
the modem form of which are the four eponymous
partial differential equations (PDE’s) (4).
A contemporary statement of Faraday's law states:
"the induced electromotive force in any closed circuit is
equal to the negative of the time rate of change of the
magnetic flux through the circuit". In Maxwell's
mathematical formalism Faraday's law reads
∇×Ε = −
∂B
∂t
(1)
where E, as usual, denotes the electric field vector and
B, the magnetic field vector. This PDE can also be
expressed in integral form as
∂B
−∫
⋅ da
�∫ E × dl =
∂t
(2)
where dl is the differential line element vector and da is
the differential area vector element.
Faraday's law has many useful applications in
everyday life, most notable are the electrical generator
and transformer.
From Faraday's law one can
qualitatively see that by changing the magnetic field
with time in a closed circuit, an electric field is induced
in the circuit - the essence of the electrical generator.
Fig. 2: A diagram of the experimental setup used in
Faraday’s discovery of electromagnetic induction (5).
Coil A is the coper wire connected to the battery and
coil B is the wire that has an electric current induced in
it. The G symbol is a galvanometer which in this
experiment was the magnetized needle.
The experiment consists of a soft iron torus with
two copper wires wound around the torus as shown in
Fig. 2. One of these copper wires extended in length in
its unwound form and was positioned over the top of a
parallel, magnetized needle and, due to his earlier
experiments with electromagnetic rotation Faraday
Phys13news / Fall 2014
Faraday invented the first electrical generator in
1831, shown below in Fig. 3, and has been named in his
honor as Faraday disc.
Throughout his career Faraday studied electromagnetism and gave the scientific community
experimental evidence on which theories could be built
or elaborated. Some of his later works included the
studies of diamagnetism, the plane polarization of light
and the the Faraday cage.
In his later years Faraday's health waned and
his last experiment was conducted in 1861. Faraday
himself explains his fading memory (and reason for
retirement) as an "Inability to draw upon the mind for
Page 7
treasures of knowledge it has previously received".
The Cyclotron: Principles of Operation and
Uses in Modern Society
Kayla J. Sutton
Department of Physics and Astronomy,
Fig. 3: A drawing of a Faraday disc, also known as a
homopolar generator. It is a DC electrical generator
that utilizes the Lorentz force to convert kinetic energy
to electrical energy.
Michael Faraday, from humble beginnings,
showed a keen interest in science and experimental
discovery that served him well throughout his
exemplary academic career. His interest was first
stimulated as an apprentice bookbinder in his
teenage years and his commitment to science is
seen in his large collection of notes from
scientific lectures. For the duration of his career he
readings
by
sought to verify his scientific
conducting his own experiments and it was this
experimentalist nature coupled with his hardworking attitude that surely helped him to
experimentally discover electromagnetic induction
in 1831. Towards the end of his life Faraday's
relentless work ethic caught up with him and
overwork led to his failing health. The impactful
nature of his discoveries and subsequent inventions,
particularly electromagnetic induction and the
electrical generator, place Faraday firmly in the
league of extraordinary experimental scientists. As
the prominent physicist Ernest Rutherford once
said, "When we consider the magnitude and extent
of his discoveries and their influence on the
progress of science and of industry, there is no
honour too great to pay to the memory of Faraday,
one of the greatest scientific discoverers of all time".
1. L. P. Williams, Michael Faraday, a Biography by L
P. Williams, (Simon and Schuster, 1971),.
2. http://en.wikipedia.org/wiki/Michael_Faraday,
retrieved 12/1/2013.
3. W. Jerrold, Michael Faraday: Man of Science, p. 79.
4. http://en.wikipedia.org/wiki/James _Clerk
_Maxwell, retrieved 12/1/2013.
Phys13news / Fall 2014
The cyclotron is a type of particle accelerator that
involves charged particles accelerating along a spiral
trajectory outwards from a central point. The trajectory
of the particles is created in part by a static magnetic
field, as well as a rapidly alternating electric field. Since
the speed at which the particles are accelerating
approaches the speed of light, relativistic effects must be
taken into account when finding the particles frequency
of oscillation. This phenomenon has led to the
development of the synchrocyclotron, a cyclotron whose
frequency compensates for relativistic effects. The
classical cyclotron was invented by Earnest Lawrence of
the University of California, Berkeley, who patented his
device in 1932. Since its inception, cyclotrons have
spawned other types of particle accelerators such as the
synchrotron, and the magnetron. Today, cyclotrons are
used to create high-energy particle beams for nuclear
physics applications, as well as in the medical physics
industry where they are used in particle therapy and in
the creation of radioisotopes for PET imaging.
Introduction
From the beginning of nuclear physics research,
learning about subatomic particles has had great appeal
for the scientific community. Thus the need for particle
accelerators, a machine that uses electromagnetic fields
to accelerate charged particles as well as confine them to
a beam. Particle accelerators exist as electrostatic
accelerators, which accelerate particles with static
electric fields, and oscillating field accelerators. One of
the most well-known oscillating field accelerators is the
cyclotron that uses a radio frequency oscillator to vary
the electric field accelerating the charged particles.
Today the cyclotron is just one member of a family of
field particle accelerators that have been developed
since the 1920’s.
Invention of the Cyclotron
Particle accelerators can be either electrostatic,
accelerating particles with static electric fields, or
oscillating field accelerators known as the cyclotron.
They use a radio frequency oscillator to vary the electric
field accelerating the charged particles, and the first idea
for these was conceived by Dr. Ernest Orlando
Lawrence, born August 8 1901, a Chemist. He obtained
an undergraduate degree in chemistry from the
University of South Dakota in 1922. Later he switched
into the field of physics, obtaining a Master's degree in
physics from the University of Minnesota in 1923, and a
Page 8
Ph.D. from Yale in 1925 (1). Lawrence then worked
as an assistant professor and research fellow at Yale,
before settling at the University of California,
Berkeley as an associate professor in 1928. Two years
later Lawrence became the youngest full professor in
at the University of California, where he remained for
his career (1).
Milton Stanley Livingston (3). His goal for the
cyclotron was to validate his notion of simply
accelerating charged particles to very high velocities,
without the use of extremely high voltages or extremely
large apparatus (l), by accelerating particles in a
circular path with an alternating electric field.
Lawrence’s intention was to accelerate the particles for
research to gain a better understanding of the nucleus
(3). Lawrence's technical name for the machine he was
building was the 'Magnetic Resonance Accelerator', it
was the laboratory slang of 'Cyclotron' that became the
more popular name for the machine (3). The first
working model of the cyclotron was only four inches in
diameter, and made to test the resonance accelerator
principles. Nevertheless, it had the ability to accelerate
hydrogen ions up to 80,000 eV (3). The next model
was 10 inches in diameter and accelerated ions up to 1
MeV, marking the first time in history that particles of
this energy had been created (3). Further development
led to cyclotrons of 27 to 37 inches in diameter,
achieving up to 8 MeV, all within the first 5 years of
the device's existence. Development finally slowed
around 1945 as particles were beginning to achieve
relativistic speeds and problems encountered at these
speeds then led to the development of the
synchrocyclotron (l).
Fig. 1: Ernest O. Lawrence
It was in 1939, about ten years after the building of
the first cyclotron, that Lawrence won the Nobel Prize in
Physics "for the invention and development of the
cyclotron, and for results obtained especially with regard
to artificial radioactive elements" (2).
In 1929 Lawrence first came up with an idea for a
'Magnetic Resonance Accelerator' (2). His ideas were
sparked by a paper by Norwegian scientist Rolf
Wideroe, which
discussed
'Kinetic
Voltage
Transformation'.
Wideroe’s paper described an
apparatus that he used to accelerate particles by either
using a radiofrequency (RF) field or an electric field
created by an alternating current within the
radiofrequency range (l). The apparatus consisted of a
long glass tube with an ion source, a small electrode
connected to the radiofrequency current oscillator, and
a deflection plate to handle the accelerated particles
(l). In Wideroe's experiment sodium and potassium
ions were accelerated to speeds with a kinetic energy
equal to twice the applied voltage by travelling along
two electrodes between which the oscillating electric
field was applied (3). After reading Wideroe's paper,
Lawrence started to think about the notion of using an
alternating electric field to accelerate the ions. He came
up with the idea to have the ions travel in a circular path
so that they may traverse the same electric field and
gain energy multiple times (3). This would be much
better than the current approach of traversing the
magnetic field once and using higher voltages to reach
larger ion speeds.
Work began on the first cyclotron in 1930 while
Lawrence worked with a new graduate student,
Phys13news / Fall 2014
Physical Description of the Cyclotron
The cyclotron is designed to accelerate particles in a
circular path by using the behavior of charged particle in
electromagnetic fields. The apparatus consists of two
electromagnet poles consisting of hollow electrode
chambers (called ‘dees’ or ‘Ds’ due to their similarity in
shape to the letter D), an alternating radiofrequency
current source, an ion source, a deflecting plate, and a
target (1). A simplified diagram of the cyclotron is
shown below in Figure 2, along with the circular path
that the charged particles will take. The two D
electrodes are positioned between the north and south
electromagnet poles so that the magnetic field created
between the poles is perpendicular to the plane of the
D’s. The D’s are separated by a narrow gap across
which the particles are accelerated.
Also in the chamber between the poles is the ion
source and the deflecting plate, but not shown in Fig. 1.
This chamber is evacuated so that there are no air
particles to scatter the charged particles. The chamber
also needs to be strong enough not to distorted in the
vacuum, it has to be made of non-magnetic materials to
Page 9
not disturb the field created by the electromagnet and,
finally, it must have a high electrical conductivity to
allow large currents to flow (3).
consequence of the magnetic field, and the particle’s
acceleration is caused by the electric field.
Charged particles in a magnetic field will be
accelerated in circular motion pattern. This motion is the
result of force acting on the particles due to the magnetic
field. This force is described by the Lorentz Force Law,
given by equ. (1). Q is the charge of the particle, 'v' is
the ion’s speed, and 'B' is the magnetic field inside the
cyclotron. A uniform magnetic field is created by the
electromagnet poles, perpendicular to the plane of the
D’s.
F = Q (v × B)
mag
(1)
The uniform electric field created in the gap between
the D’s accelerates the particles, allowing them to gain
kinetic energy a s they traverse the gap (I).
1. Cyclotron Frequency
Fig. 2: Simplified Cyclotron Schematic.
The ion source, ocated near the centre of the gap
between the D’s, releases ions towards one of the D’s to
begin their circular journey. In most cyclotrons today
(as of 1962) ions are instead created via cathode
discharge. This discharge is collimated by the magnetic
field and the gas is ionized to create the ions which can
then be accelerated by the cyclotron (3).
The alternating radio frequency current source
creates a potential difference between the two D’s which
creates an electric field between them in the accelerating
gap. Because the current is alternating means that one D
has a positive voltage, while the other is negative, and
they switch back and forth with a particular frequency
(1). This is critical for the movement of the ions, see the
section below on 'Electricity and Magnetism Principles
of Operation'.
The deflector plate exists only on one of the two
electrodes, the leftmost one in Figure 1. Its purpose is to
prevent the beam of ions travelling around the D, once
they reach the outer circumference the electrode. The
deflector then pulls the ions out of their cyclotron path
and directs them to a tripedal external target. This is
done by creating another electric field in the deflector
plate region that attracts the ions and forces them to
abandon their circular motion (3).
Electric and Magnetic Principles of Operation
The cyclotron operation is based on the forces of a
uniform magnetic and electric field on the charged
particles. The spiral motion of the charged particle is a
Phys13news / Fall 2014
The frequency of the circular motion of the
charged particles of the cyclotron is important in its
operation. This frequency is found from knowing that
the magnetic force applied to the particles that cause
their centripetal acceleration:
F
= ma
mag
Where 'a' is the particle’s centripedal acceleration and
'm' is the particle’s mass. If we let 'R' be the radius of
the circular motion and 'v' be the particle speed, we can
rewrite the equation as follows (note that in equ. (1), the
magnetic field and the motion of the particle are
orthogonal, eliminating the cross product):
v2
QvB = m
R
From here we can substitute the angular frequency, ω,
fo r v / R and solve for the cyclotron frequency:
QB = m
v
R
QB = mω
QB = m2π f
f =
QB
2π m
(2)
(3)
The frequency, f, is that of the particles as they
travel around the cyclotron. Notice that the frequency is
independent of the speed of the particles. This is
important because as the particles accelerate, and their
Page 10
frequency changes, they will continue to remain on the
same orbit independent of their velocity (1).
Types of Cyclotrons
1.
2. Particle Energies in a Cyclotron
The electric field in the cyclotron exists in the
region between the two D’s and as the charged particles
enter this region, they travel from one D electrode to
another, depending on the charge of the particle.
Positively charged particles will move towards the
negative electrode and if the particles are negatively
charged they will move towards the positive electrode
(1). As a charged particle moves through the electric
field, the field does work on it and the particle gains
energy
U= Q∆V
(4)
As the particle continues to gain energy by
repeatedly travelling across the electric field, its kinetic
energy increases and consequently so will its speed.
As the speed of the particle increases, we can see from
equ. (2), so will the radius of the orbit the particle
travels. This means that after the particle repeatedly
travels across the electric field region and gains speed,
and continues to be forced into a circular path by the
magnetic field, the radius of this path will increase
following every orbit.
It is this pattern of particle movement (from the first
D, through the electric field gap, into and around the
second D, again through the electric field gap and back
to the first D) that is made possible by the alternating
radio frequency current which continually switches the
D’s with the positive and negative potential. The time it
takes the particle to travel from the start of one D to the
end is f/2 where f is the cyclotron frequency. During
this time the voltage across the gap is also switched
because the current also alternates at ½ the cyclotron
frequency. Alternating the current with the same
frequency as the cyclotron frequency, and therefore the
particle frequency, allows the particles to continue
traveling from D to D since each time the charged
particle reaches the gap, the voltage switches and it will
be forced through the electric field toward the following
D.
As the particles move from D to D, continually
gaining kinetic energy from their interaction with the
electric field, they continually increase their radius of
travel, and they eventually reach the maximum radius of
travel allowed for that cyclotron. The particles will now
exit the cyclotron having gained maximum kinetic
energy, from Equ. 2, as:
KEmax
( QBRmax )
=
Phys13news / Fall 2014
2m
2
(5)
Positive and Negative Ion Cyclotrons
The first cyclotrons were designed and tested using
hydrogen ions as the charged particles to be
accelerated (3). Although only positive ions were used
for some time, cyclotron principles apply to both
positive and negative ions, the only thing that would
differ between them being the direction of travel through
the electric field. Negative ion cyclotrons were also
build starting in 1966, but did not become widely used
until the 1980’s.
2.
Relativistic Cyclotrons
It was earlier implied, in equ. (3), that the frequency
of the cyclotron (and therefore of the particle travel and
of the alternating current) remains constant. This was
true for most early apparatus, but as the technology
became more advanced and the particles began to reach
relativistic speeds, the constancy of the frequency
becomes problematic because equ. (3) does dependent
on the particle mass which as particle speeds approach
the speed of light will change dramatically. Equ. 6
below describes the change in mass at relativistic speeds
and Equ. 7 shows the changes to the cyclotron
frequency, f 0 , is the original cyclotron frequency.
m0
mrelativistic =
2
v
f0 1 −  
c
(6)
f relativistic
=
v
f0 1 −  
c
2
(7)
As the speed of the particle, 'v', approaches the
speed of light, 'c', the relativistic mass increases relative
to the rest mass, m0. This means that at these speeds, in
order for the cyclotron to properly operate,
compensations must be made.
One way to account for the changing cyclotron
frequency was patented by Edwin McMillan in 1947 (6),
who called it the synchrocyclotron, but it is also called a
frequency
modulated
cyclotron
(l).
The
synchrocyclotron, in essence, varies the driving RF
frequency which oscillates the electric field to match the
changing frequency of the particles.
Another method of compensating for the relativistic
mass of the particle is called the isochronous cyclotron,
or the azimuthally varying field cyclotron. Instead of
accounting for the relativistic effects by changes to the
RF frequency, this kind of cyclotron instead changes the
magnetic field. Instead of a constant field, the magnetic
poles are altered to vary the field radially around the
circle to keep the particles reaching the acceleration gap
Page 11
at the appropriate time at the original cyclotron
frequency despite their increasing speeds and masses.
The magnetic field variation balances the relativistic
mass increase, so that the frequency of the particles can
remain the same. The changes to the electromagnetic
pole are shown below in Fig. 3.
Fig. 3: Isochronous Cyclotron Electromagnet
Uses in Modern Society
3.
Research
Cyclotrons are often used in nuclear physics
research as a source of high energy particle beams.
They can help gain insight into the properties of
elementary particles.
Moreover, these high energy beams can also used to
create nuclear reactions when the beams are targeted on
other particles. As well, cyclotrons are used in solid
state and condensed matter physics research areas. In
the latter, cyclotrons are used as sources of radiation and
neutrons to help in understanding the properties of
semiconductors. Most importantly, cyclotrons are used
in medical physics, both practically and in research.
4.
Particle Proton Therapy
One practical medial physics application of the
cyclotron is in proton therapy which uses positively
charged ions (protons in particular) accelerated by a
cyclotron and directed at a tumor in the body. The high
speed protons bombarding the tumor will release the
majority of their kinetic energy as they collide
inelastically with the tumor, giving it a radiation dose
that helps in its destruction. By using a collimated beam
allows the treatment to be localized and reduces damage
to surrounding tissues.
5.
3. PET Imaging
Another medical application of the cyclotron is in
positron emission tomography, or PET, which is a type
of medical imaging process. The process involves
detecting radiation emitted by positron emitting
radionuclides after they have been injected into the
body. The radionuclides are produced via a reactor and
a cyclotron. In clinical studies the most common
Phys13news / Fall 2014
radionuclides that are created and used in PET imaging
are: 11C, 13N, 18F, 15O (4). These are chosen due to
their short half-lives making them easier to detect, and
safer for use in the human body.
The first step in PET imaging is the creation of
radionuclides with a cyclotron that accelerates particles
to very high speeds and then aims these high velocity
particles at an elemental target. This bombardment of
particles onto an elemental target produces unstable
isotopes of that element, called radionuclides. A
radionuclide is an atom with an unstable nucleus that
emits radiation in order to become stable. They are also
known as a radioactive isotope, or a radioisotope (4).
They undergo radioactive decay by emitting a gamma
ray or another type of subatomic particle. Finally, these
radionuclides are also known as tracers because, when
they are attached to a biologically active molecule that
then travels throughout the body and the radiation
emitted from the tracer can then be detected in the body
by using PET imaging (4).
Conclusion
From research in nuclear physics, to everyday
clinical uses, the cyclotron is an integral part in modem
physics. Cyclotrons, as well as other types of particle
accelerators, were first invented to give insight into
subatomic particles, and have come a long way from
their early colloquial name of atom smashers.
Although the cyclotron makes use of what some
consider today to be basic principles of electricity and
magnetism along with the behavior of charged particles
in electromagnetic fields, there is nothing basic about its
history and development. After its invention by Ernest
Lawrence, many other scientific researchers and
engineers have worked together to create and develop
these particle accelerators, and are used all over the
world today.
References
(I) T. Koeth, "Rutgers Cyclotron," Rutgers State
University of New Jersey, 27 March 2003. [Online].
http://www.physics.rutgers.edu/cyclotron/welcome.
shtm. [Accessed December 2013].
(2) N. Media, "Ernest Lawrence," The Nobel
Foundation, 1999. [Online]. http://www.nobelprize.
orglnobel_prizes/physics/laureates/I939/lawrencebio.html. [Accessed December 2013].
(3) M. S. Livingston, Particle Accelerators; L. I. Schiff,
Ed., McGraw-Hill Book Company, 1962.
(4) "Ernest Lawrewnce and M. S. Livingston,"
American
Physical
Society,
2013.
http://www.aps.org1programs/outreach/history1hist
oricsites/lawrencelivingston.cfm.
[Accessed
December 2013].
Page 12
The Electron Microscope
Guenter Scholz
Department of Physics and Astronomy
Phys13news / Fall 2014
Page 13
Phys13news / Fall 2014
Page 14
Phys13news / Fall 2014
Page 15
The SIN Bin
Rohan Jayasunderan
Department of Physics and Astronomy
A problem corner intended to stimulate some reader participation. The best solutions to the problem will receive
mention in the upcoming issue. Please send your favorite problems and solutions to the editor.
SIN Bin #149
Kalle Anka Scrooge needs to increase his investment in a factory for black hole-powered garbage disposal units. To
do this he has an ingenious idea on how to conserve his hard-earned cash, by changing the power delivered to a lightbulb.
He connects a battery together with a lightbulb that has a 10 ohm internal resistance, between points A and B as shown,
and determines the current through the lightbulb. Determine this current, as a factor times the current in a simple circuit
consisting of only the battery and the lightbulb. Assume that all resistances equal 10 ohms.
(a)
(b)
(c)
(d)
(e)
8/15
8/7
1/5
1/2
1
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