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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 Department of Physics and Astronomy University of Waterloo Waterloo, ON N2L 3G1 Fax: E-mail: 519-746-8115 [email protected] Editor: Guenter Scholz Editorial Board: Avery Broderick, Richard Epp, Bae-Yeun Ha, David Hawthorn, Matteo Mariantoni, Chris O’Donovan Publisher: Judy McDonnell Printing: UW Graphics 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. 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