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Ernest Lawrence
Información personal
Nombre de nacimiento Ernest Orlando Lawrence Ver y modificar los datos en Wikidata
Nacimiento 8 de agosto de 1901 Ver y modificar los datos en Wikidata
Canton (Estados Unidos) Ver y modificar los datos en Wikidata
Fallecimiento 27 de agosto de 1958 Ver y modificar los datos en Wikidata (57 años)
Palo Alto (California, Estados Unidos) Ver y modificar los datos en Wikidata
Sepultura Chapel of Memories Columbarium and Mausoleum Ver y modificar los datos en Wikidata
Residencia Berkeley y Estados Unidos Ver y modificar los datos en Wikidata
Nacionalidad Estadounidense
Familia
Cónyuge Mary K. «Molly» (Blumer) Lawrence
Educación
Educado en
Supervisor doctoral William Francis Gray Swann Ver y modificar los datos en Wikidata
Información profesional
Ocupación Físico, físico nuclear y profesor universitario Ver y modificar los datos en Wikidata
Área Física Ver y modificar los datos en Wikidata
Conocido por invención del ciclotrón
Empleador Universidad de California en Berkeley Ver y modificar los datos en Wikidata
Estudiantes doctorales Edwin Mattison McMillan
Chien-Shiung Wu
Milton Stanley Livingston
Kenneth Ross Mackenzie
John Reginald Richardson
Miembro de
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De: BARILOCHENSE6999 Enviado: 09/08/2024 00:38
Libro Brotherhood of the Bomb: The Tangled Lives and Loyalties of Robert  Oppenheimer, Ernest Lawrence, and De Herken, Gregg - Buscalibre

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Ernest Lawrence

Ernest Lawrence

Lived 1901 – 1958.

Ernest Lawrence invented the cyclotron, for which he was awarded the 1939 Nobel Prize in Physics. Cyclotrons in his laboratories were used to discover a large number of new chemical elements and isotopes – millions of lives have been saved using these radioisotopes. Lawrence’s work initiated the age of “big science.”

 

Beginnings

Ernest Orlando Lawrence was born on August 8, 1901 into a middle-class family in the small prairie-town of Canton, South Dakota, USA. His father was Carl Gustavus Lawrence, a superintendent of schools and history teacher. His mother was Gunda Regina Jacobson, a mathematics teacher. Both were of Norwegian ancestry.

Ernest attended elementary and high school in Canton, except for four years spent in South Dakota’s capital, Pierre. The family moved to Pierre because his father’s job took them there when Ernest was aged 9 – 13. Ernest was tall and thin, and he picked up the nickname ‘skinny,’ which he didn’t mind.

Ernest became a seriously knowledgeable radio-ham. He built a shortwave transmitter and shared his enthusiasm for wireless communications with two rather remarkable friends. One was his junior brother John, who became one of the founders of nuclear medicine; the other was Merle Tuve, whose forebears were also Norwegian, and who became a very eminent physicist.

Ernest’s parents were rather devout members of the Lutheran Church. His mother was vehemently opposed to her son to going to the state university, fearing he might be led astray there! He enrolled in medicine at the University of South Dakota in Vermillion in 1919 without his mother’s knowledge. Although a medical student, his passion for building radio transmitters did not slacken. He approached Lewis Akeley, the Dean of Engineering, about setting up a campus radio station.

Akeley, who had once been a professor of chemistry and physics, was so impressed by the young radio enthusiast’s expertise in electronics that he persuaded him to forget about premedical studies and switch to physical sciences instead. So Ernest majored in physical science. And he also started South Dakota’s first ever radio station!

Luis Alvarez“On the wall of Lawrence’s office, Dean Akeley’s picture always had the place of honor in a gallery that included photographs of Lawrence’s scientific heroes: Arthur Compton, Niels Bohr, and Ernest Rutherford.”

 

LUIS ALVAREZ
Nobel Prize in Physics Winner 1968
 

Ernest Lawrence graduated at age 21 with a Bachelor’s Degree, then joined his childhood friend Merle Tuve at the University of Minnesota, where he completed a Master’s Degree in Physics in two years. In 1925 he obtained his Ph.D. in Physics from Yale University.

Ernest Lawrence’s Contributions to Science

The Cyclotron

Alpha-particle bombardments
By 1929 Lawrence had been an associate professor of physics at the University of California at Berkeley for a year.

Until then, physicists used radioactive elements as a source of high energy particles. Alpha-particles, escaping at high speeds from radioactive nuclei, offered scientists like Ernest Rutherford a way to bombard chemical elements with high energy atom-sized particles. This had led to a number of groundbreaking discoveries, including the discoveries of the proton and the atomic nucleus.

Particle Accelerators
In 1929 Lawrence picked up a copy of a science journal to read during a particularly tedious meeting he had to attend. The journal included a paper by Rolf Widerøe, one of the pioneers of a new concept in physics – particle accelerators, or atom-smashers.

Particle accelerators promised scientists a way of using electricity to produce atom-sized particles moving at high speeds. Unlike radioactive sources of particles, the amount of energy carried by particles from accelerators could be fine-tuned to produce specific results.

This was an especially exciting field, because it seemed certain that momentous new discoveries would emerge from the use of accelerators.

Accelerated particles could be crashed into target atoms, producing debris from which information about the tiny, unseen world of the atomic nucleus could be obtained. Also, it was possible that new types of atoms and chemical elements could be produced.

Rolf Widerøe had envisioned a device in which high voltages would be used to accelerate particles in a straight line.

Miniaturizing an Accelerator
Lawrence thought that, if it were to produce very high energy particles, Widerøe’s device would be too long to fit in a typical laboratory.

And he instantly had his big idea: instead of accelerating particles in a straight line, he would use electromagnets to accelerate them in a spiral path, gathering ever more speed and energy until they smashed into their target. His device would be smaller and cheaper than Widerøe’s.

Cyclotron Patent

Diagram from Lawrence’s cyclotron patent. Charged particles are injected into the center of the cylinder and are accelerated by a high frequency alternating voltage. Magnets above and below the cylinder create the magnetic field that causes the particles to follow a spiral path. While moving in a spiral, the particles repeatedly encounter the accelerating voltage from the electrodes and so are repeatedly accelerated. The elegant result is that the amount of energy given to the particles is many times greater than they would get from following a straight line path with a single applied voltage. Particles spiral outward at ever greater speeds until they crash into a target.

The first cyclotron Lawrence built was only 4 inches (10 cm) across and cost $25. And it worked! It accelerated ions of hydrogen molecules to an energy of 80,000 electron volts.

It is ironic that Lawrence’s big idea was for low-cost miniaturization of an accelerator. Soon enough, he would be the pacesetter in high-cost “big science.”

Ever Bigger
Lawrence saw the great potential of his device, and others did too – he now got funding to develop both linear accelerators and cyclotrons. He was thrilled with how things had turned out. His work allowed him to revisit those idyllic, happy, childhood days of building wireless transmitters with sympathetic friends. Except now he could indulge his passion for electronic equipment on an epic scale.

And the icing on the cake was that at 29 years old, he was promoted to become the University of California’s youngest full professor.

By mid-1931 he had an 11-inch cyclotron operating using a 2 ton magnet and was planning a 27-inch cyclotron using an 80 ton magnet!

Lawrence’s cyclotron patent was granted in 1934. Although he’d patented the device, he encouraged other research laboratories to build cyclotrons, gave them assistance when they got stuck, and never charged any royalties for his invention. He was also generous with new radioactive materials produced in his laboratory, giving samples to other laboratories to help them out.

Albert Einstein, however, had reservations about the usefulness of research using particle accelerators, declaring:

Albert Einstein“You see, it is like shooting birds in the dark in a country where there are only a few birds.”

 

ALBERT EINSTEIN
Interview at AAAS meeting, 1934
 

Since atoms are mainly empty space, Einstein was correct in his analogy. What he overlooked is the fact that accelerators would soon reach a point where they had a very rapid rate of fire and a virtually unlimited supply of bullets!

 
60-inch cyclotron

The 60-inch cyclotron, completed in 1939, at the Lawrence Radiation Laboratory, Berkeley. This device features two magnets weighing a total of almost 200 tons. Glenn Seaborg and his coworkers used this particle accelerator to discover five new chemical elements: plutonium, curium, americium, berkelium, and californium.

Lawrence provided scientists with the finest ever tool for discovering the secrets of the atom. Scientists like Glenn Seaborg and Albert Ghiorso would use Berkeley’s cyclotrons to greatly expand the number of elements in the periodic table.

Glenn Seaborg“His cyclotron is to nuclear science what Galileo’s telescope was to astronomy … his buoyant optimism spread to everyone around him and accounted for the attainment of many an ‘impossible’ objective.”

 

GLENN SEABORG
Nobel Prize in Chemistry Winner 1951
 

Missing out on Discoveries
In the early 1930s Lawrence and his growing team, although making great efforts to make new discoveries using their cyclotrons, were not very successful.

  • They could have discovered transmutation of lithium to helium by proton bombardment, but didn’t. This ‘splitting of the atom’ was discovered in 1932 by John Cockcroft and Ernest Walton, at the University of Cambridge in the UK, for which the pair received the 1951 Nobel Prize in physics.
  • They could have discovered nuclear fusion, but didn’t. This was discovered in 1934 by Ernest Rutherford and Mark Oliphant, also at the University of Cambridge in the UK. Oliphant used a particle accelerator to fire deuterium ions at substances such as ammonium chloride and found he had produced helium-3 and tritium. (In fact, Lawrence’s team in Berkeley had carried out a similar experiment but had – to Lawrence’s ultimate considerable embarrassment – misinterpreted the results, wrongly believing they had discovered that deuterons disintegrate.)
  • They could have discovered how to synthesize artificial radioactive elements by alpha-particle bombardment, but didn’t. This was discovered in 1934 by the Joliot-Curies at the Curie Institute in Paris, France, for which they received the 1935 Nobel Prize in Chemistry. Lawrence was particularly dismayed when he heard about this, because he realized it was something his own laboratory could have achieved easily.
Ernest Lawrence“We have had these radioactive substances in our midst for more than half a year. We have been kicking ourselves that we haven’t had the sense to notice that the radiations given off do not stop immediately after turning off the bombarding beam.”

 

ERNEST LAWRENCE
February 1934
 

Although it was maddening to have missed out on some incredibly exciting discoveries, Lawrence was not fazed. His greatest ambition was to build ever more powerful accelerators, because he felt that ultimately these accelerators would yield secrets of nature not available at lower energies.

Ernest Lawrence“I have gotten over feeling badly. We would be eternally miserable if our errors worried us too much because as we push forward we will make plenty more.”

 

ERNEST LAWRENCE
February 1934
 

And discoveries did begin to flow using Lawrence’s cyclotrons. In 1939 Luis Alvarez and Robert Cornog used the 60-inch cyclotron to study helium-3. Theoreticians had said helium-3 would be radioactive. Actually, it proved to be stable. And then Alvarez and Cornog used the 37-inch cyclotron to produce tritium, which theoreticians said would be stable, but was actually radioactive. In the same year, Edwin McMillan and Philip Abelson used the 60-inch cyclotron to produce and so discover the new element neptunium. Many more discoveries would follow.

Cancer Treatments

Lawrence’s cyclotrons were soon making a difference to people’s lives. In 1921 the American people had raised $100,000 for Marie Curie to purchase a mere 1 gram of radium for research and cancer treatments. Radioactive elements for cancer treatments were shockingly expensive.

With his cyclotron, Lawrence realized he could fine-tune the production of radioactive isotopes.

In 1934 he realized that sodium-24 could be an ideal, non-toxic source of gamma rays for cancer radiotherapy. He used one of his cyclotrons to convert normal rock salt into sodium-24 by deuteron bombardment. Soon, for about $2 worth of salt and power, he had made the medical equivalent of radium that had cost $100,000 in 1921!

Lawrence continued his efforts to make radioisotopes for cancer therapy. While carrying out this work researchers in his laboratory discovered carbon-14, oxygen-15, fluorine-18, and thallium-201.

Technetium-99m, now used worldwide in tens of millions of medical procedures every year, was also discovered in his laboratory. Technetium-99m’s use has saved millions of lives.

Keeping it in the Family
In 1936 Lawrence invited his brother John, from Yale University’s medical faculty, to Berkeley to cooperate in trials using the cyclotron and its products in medical treatments. The result was huge success, to the extent that John Lawrence is now known as the father of nuclear medicine.

In 1937 Lawrence’s mother was diagnosed with inoperable cancer and given just a few months to live. Ernest and John decided to attack her tumor using an incredibly powerful x-ray machine that Ernest and his team had built and installed at the University of California’s medical school. The result was that his mother was completely cured. She actually went on to outlive Ernest.

Cyclotrons and Cancer Today
In addition to producing radioisotopes for cancer treatments, cyclotrons are still in use today producing proton beams, which yield neutron beams, which are used to attack cancers directly.

The Nobel Prize

Ernest Lawrence was awarded the Nobel Prize in Physics in 1939 for his invention of the cyclotron and the discoveries made with it. He and his team conquered a huge number of colossal engineering problems to achieve their results.

Luis Alvarez“The important ingredients of his success were native ingenuity and basic good judgment in science, great stamina, an enthusiastic and outgoing personality, and a sense of integrity that was overwhelming.”

 

LUIS ALVAREZ
Nobel Prize in Physics Winner 1968
 

Ever Bigger Science and the Bomb

By 1940 Lawrence was planning a 184-inch cyclotron, which needed 4500 tons of magnets. The Rockefeller Foundation put up over a million dollars to get the project started. Lawrence’s research was growing fast in scale and ambition. It had become big science.

It is a testament to Lawrence’s energy and persuasive skills that he was able find funding. He was helped by the fact that governments around the world were becoming increasingly interested in releasing the enormous amount of energy scientists had realized was present in the atomic nucleus.

184-inch cyclotron during construction

Lawrence’s 184-inch cyclotron during construction. The era of big science had begun.

With the world’s most advanced accelerators and the discovery in 1940 of plutonium using the Berkeley 60-inch cyclotron, Lawrence was destined to play a leading role in the Manhattan Project – the project that built the world’s first nuclear weapon and would push science to ever greater scales of operation.

Lawrence developed a new device, the calutron, to separate isotopes of uranium. The calutron was a hybrid of the cyclotron and a mass spectrometer. Calutrons were employed to produce the uranium-235 that was used in the Little Boy atomic bomb dropped on Hiroshima in August 1945.

Lawrence's Calutron

Lawrence’s calutron invention was used to separate isotopes of uranium.

Ernest Lawrence“The atomic bombs will surely shorten the war, and let us hope that they will effectively end war as a possibility in human affairs.”

 

ERNEST LAWRENCE
Speaking in early 1945
 

The largest cyclotron Lawrence built for research purposes was the 184-inch (4.67 meter) cyclotron completed in 1942. Protons could be accelerated to energies in excess of 100 MeV.

Today, the age of big science that began with Lawrence marches onward. Ever bigger, ever more expensive, ever more powerful devices continue to reveal the extent and depth of the subatomic world.

In 2015, CERN’s Large Hadron Collider operated in a circular tunnel almost 17 miles (27,000 meters) long underneath Switzerland. Particle energies reached 6.5 TeV – about 65,000 times more powerful than Lawrence’s 1942 device.

Some Personal Details and the End

Lawrence married Mary Kimberly Blumer in May 1932. The daughter of the Dean of Yale’s Medical School, she was always known as Molly. Molly had a Bachelor’s Degree in Bacteriology and met her future husband on a blind date. The couple had six children.

Ernest Lawrence died at the age of 57 on August 27, 1958 in a hospital in Palo Alto, California following surgery for intestinal problems.

Less than a month after his death, the University of California renamed two of the university’s nuclear research laboratories in his honor: the Lawrence Livermore National Laboratory and the Lawrence Berkeley National Laboratory. Today both continue as world-leading research centers.

Three years after his death, element 103 was discovered, produced for the first time in a particle accelerator at the Lawrence Berkeley National Laboratory. The element was named lawrencium in honor of the man who had made its discovery possible.

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Please use the following MLA compliant citation:

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Further Reading
Glenn Seaborg
E. O. Lawrence – Physicist, Engineer, Statesman of Science.
Science, 128 (3332), p1123-1124, Nov 7 1958

Luis W. Alvarez
Ernest Orlando Lawrence – A Biographical Memoir
National Academy of Sciences, Washington D.C., 1970

J. L. Heilbron, Robert W. Seidel
Lawrence and His Laboratory: A History of the Lawrence Berkeley Laboratory, Volume 1
University of California Press, 1989

Jeffrey E. Williams
Donner Laboratory: The Birthplace of Nuclear Medicine
Nucl Med., 40:16N-20N, 1999

Science and Technology Review
Lawrence Livermore National Laboratory, 2001

Paul Halpern
Collider: The Search for the World’s Smallest Particles
John Wiley & Sons, 2009

Michael Hiltzik
Big Science: Ernest Lawrence and the Invention that Launched the Military-Industrial Complex
Simon and Schuster, 2015


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De: BARILOCHENSE6999 Enviado: 09/08/2024 00:44
Lawrence & Oppenheimer | J. Robert Oppenheimer, Ernest Lawrence

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De: BARILOCHENSE6999 Enviado: 09/08/2024 00:49
Ernest Lawrence Quote: “The atomic bombs will surely shorten the war, and  let us hope that they will effectively end war as a possibility in hum...”

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De: BARILOCHENSE6999 Enviado: 09/08/2024 00:51
TodoFP on X: "Efeméride de hoy 8 de agosto: Ernest Lawrence  https://t.co/PkpDeSS4on" / X

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De: BARILOCHENSE6999 Enviado: 09/08/2024 01:15
Cosmological Astrophysics - One evening in 1929, while sitting in the  library at the University of California, Berkeley, an American man (an  associate professor that time) glanced over a journal article by #

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De: BARILOCHENSE6999 Enviado: 09/08/2024 01:28
An American Genius: The Life of Ernest Orlando Lawrence, Father of the  Cyclotron (English Edition) eBook : Childs, Herbert: Amazon.es: Tienda  Kindle

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Ernest Lawrence - Biography, Facts and Pictures

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De: BARILOCHENSE6999 Enviado: 09/08/2024 01:56
Ernest Lawrence
Información personal
Nombre de nacimiento Ernest Orlando Lawrence Ver y modificar los datos en Wikidata
Nacimiento 8 de agosto de 1901 Ver y modificar los datos en Wikidata
Canton (Estados Unidos) Ver y modificar los datos en Wikidata
Fallecimiento 27 de agosto de 1958 Ver y modificar los datos en Wikidata (57 años)
Palo Alto (California, Estados Unidos) Ver y modificar los datos en Wikidata
Sepultura Chapel of Memories Columbarium and Mausoleum Ver y modificar los datos en Wikidata
Residencia Berkeley y Estados Unidos Ver y modificar los datos en Wikidata
Nacionalidad Estadounidense
Familia
Cónyuge Mary K. «Molly» (Blumer) Lawrence
Educación
Educado en
Supervisor doctoral William Francis Gray Swann Ver y modificar los datos en Wikidata
Información profesional
Ocupación Físico, físico nuclear y profesor universitario Ver y modificar los datos en Wikidata
Área Física Ver y modificar los datos en Wikidata
Conocido por invención del ciclotrón
Empleador Universidad de California en Berkeley Ver y modificar los datos en Wikidata
Estudiantes doctorales Edwin Mattison McMillan
Chien-Shiung Wu
Milton Stanley Livingston
Kenneth Ross Mackenzie
John Reginald Richardson
Miembro de
Firma

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De: BARILOCHENSE6999 Enviado: 09/08/2024 17:05

 UFO Engine idea - flying cyclotron

 
Hi guys,
I was wondering for a log time, how to create some engine that works in space, without loosing any fuel/material in jet.
It there would be a method to use only electric power to generate thrust, that do not violate momentum conservation rule...

I know that there is EMdrive idea, but I do not want to discuss it here, since it is not confirmed jet.
I invented my own idea and I claim, that it does not break momentum conservation rule.

In simplest words the idea is to use cyclotron and send it to the space :-)

Cyclotron will give us circulating plasma consisted of negatively charged particles, accelerated to very high velocities and rotating on the circulated path.
Of course in space when we accelerate plasma, cyclotron will also gather some rotational move in opposite direction than plasma.

Here is the view from the top
Click image for larger version

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When we already have plasma circulating with very high speed, then in some places (called Thrust Generators) we activate magnetic field in the plane of the cyclotron, but perpendicular to the plasma's move. Magnetic field makes plasma's path curved up to the cover. Then plasma hits up cover and bounce back following curved path.

Here is the picture how it would look like
Click image for larger version

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And now, the point.
1. Magnetic field does not make work over plasma. It curves plasma's path without any centrifugal acceleration or force going down, that would give momentum down to the cyclotron.
2. But when plasma hits the cover of the Thrust Generator it transfers its momentum and bounce back to the cyclotron. So the thrust is only in up direction.

What do you think about such engine, transformating rotational kinetic energy into thrust?

P.S.
May be this is the reason, why UFO observers almost always describe UFO as rotating plate?...
..breakthrough is not just next ordinary step...
https://forum.cosmoquest.org/forum/the-proving-grounds/against-the-mainstream/134160-ufo-engine-idea-flying-cyclotron

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De: BARILOCHENSE6999 Enviado: 09/08/2024 17:16

Cyclotron

 

cyclotron is a type of particle accelerator invented by Ernest Lawrence in 1929–1930 at the University of California, Berkeley,[1][2] and patented in 1932.[3][4] A cyclotron accelerates charged particles outwards from the center of a flat cylindrical vacuum chamber along a spiral path.[5][6] The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying electric field. Lawrence was awarded the 1939 Nobel Prize in Physics for this invention.[6][7]

Lawrence's 60-inch (152 cm) cyclotron, c. 1939, showing the beam of accelerated ions (likely protons or deuterons) exiting the machine and ionizing the surrounding air causing a blue glow

The cyclotron was the first "cyclical" accelerator.[8] The primary accelerators before the development of the cyclotron were electrostatic accelerators, such as the Cockcroft–Walton generator and the Van de Graaff generator. In these accelerators, particles would cross an accelerating electric field only once. Thus, the energy gained by the particles was limited by the maximum electrical potential that could be achieved across the accelerating region. This potential was in turn limited by electrostatic breakdown to a few million volts. In a cyclotron, by contrast, the particles encounter the accelerating region many times by following a spiral path, so the output energy can be many times the energy gained in a single accelerating step.[4]

Cyclotrons were the most powerful particle accelerator technology until the 1950s, when they were surpassed by the synchrotron.[9] Nonetheless, they are still widely used to produce particle beams for nuclear medicine and basic research. As of 2020, close to 1,500 cyclotrons were in use worldwide for the production of radionuclides for nuclear medicine.[10] In addition, cyclotrons can be used for particle therapy, where particle beams are directly applied to patients.[10]

Contents

History

edit
Lawrence's original 4.5-inch (11 cm) cyclotronLawrence's 60-inch (150 cm) cyclotron at Lawrence Radiation LaboratoryUniversity of California, Berkeley, California, constructed in 1939. The magnet is on the left, with the vacuum chamber between its pole pieces, and the beamline which analyzed the particles is on the right.

In 1927, while a student at Kiel, German physicist Max Steenbeck was the first to formulate the concept of the cyclotron, but he was discouraged from pursuing the idea further.[11] In late 1928 and early 1929, Hungarian physicist Leo Szilárd filed patent applications in Germany for the linear accelerator, cyclotron, and betatron.[12] In these applications, Szilárd became the first person to discuss the resonance condition (what is now called the cyclotron frequency) for a circular accelerating apparatus. However, neither Steenbeck's ideas nor Szilard's patent applications were ever published and therefore did not contribute to the development of the cyclotron.[13] Several months later, in the early summer of 1929, Ernest Lawrence independently conceived the cyclotron concept after reading a paper by Rolf Widerøe describing a drift tube accelerator.[14][15][16] He published a paper in Science in 1930 (the first published description of the cyclotron concept), after a student of his built a crude model in April of that year. [17] He patented the device in 1932.[4][18]

To construct the first such device, Lawrence used large electromagnets recycled from obsolete arc converters provided by the Federal Telegraph Company.[19] He was assisted by a graduate student, M. Stanley Livingston. Their first working cyclotron became operational in January 1931. This machine had a diameter of 4.5 inches (11 cm), and accelerated protons to an energy up to 80 keV.[20]

At the Radiation Laboratory on the campus of the University of California, Berkeley (now the Lawrence Berkeley National Laboratory), Lawrence and his collaborators went on to construct a series of cyclotrons which were the most powerful accelerators in the world at the time; a 27 in (69 cm) 4.8 MeV machine (1932), a 37 in (94 cm) 8 MeV machine (1937), and a 60 in (152 cm) 16 MeV machine (1939). Lawrence received the 1939 Nobel Prize in Physics for the invention and development of the cyclotron and for results obtained with it.[21]

The first European cyclotron was constructed in the Soviet Union in the physics department of the V.G. Khlopin Radium Institute in Leningrad, headed by Vitaly Khlopin [ru]. This Leningrad instrument was first proposed in 1932 by George Gamow and Lev Mysovskii [ru] and was installed and became operative by 1937.[22][23][24]

Two cyclotrons were built in Nazi Germany.[25] The first was constructed in 1937, in Otto Hahn's laboratory at the Kaiser Wilhelm Institute in Berlin, and was also used by Rudolf Fleischmann. It was the first cyclotron with a Greinacher multiplier to increase the voltage to 2.8 MV and 3 mA current. A second cyclotron was built in Heidelberg under the supervision of Walther Bothe and Wolfgang Gentner, with support from the Heereswaffenamt, and became operative in 1943.[26]

By the late 1930s it had become clear that there was a practical limit on the beam energy that could be achieved with the traditional cyclotron design, due to the effects of special relativity.[27] As particles reach relativistic speeds, their effective mass increases, which causes the resonant frequency for a given magnetic field to change. To address this issue and reach higher beam energies using cyclotrons, two primary approaches were taken, synchrocyclotrons (which hold the magnetic field constant, but decrease the accelerating frequency) and isochronous cyclotrons (which hold the accelerating frequency constant, but alter the magnetic field).[28]

Lawrence's team built one of the first synchrocyclotrons in 1946. This 184 in (4.7 m) machine eventually achieved a maximum beam energy of 350 MeV for protons. However, synchrocyclotrons suffer from low beam intensities (< 1 μA), and must be operated in a "pulsed" mode, further decreasing the available total beam. As such, they were quickly overtaken in popularity by isochronous cyclotrons.[28]

The first isochronous cyclotron (other than classified prototypes) was built by F. Heyn and K.T. Khoe in Delft, the Netherlands, in 1956.[29] Early isochronous cyclotrons were limited to energies of ~50 MeV per nucleon, but as manufacturing and design techniques gradually improved, the construction of "spiral-sector" cyclotrons allowed the acceleration and control of more powerful beams. Later developments included the use of more powerful superconducting magnets and the separation of the magnets into discrete sectors, as opposed to a single large magnet.[28]

Principle of operation

edit
Diagram of a cyclotron. The magnet's pole pieces are shown smaller than in reality; they must actually be at least as wide as the accelerating electrodes ("dees") to create a uniform field.
 

Approaches to relativistic cyclotrons


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De: BARILOCHENSE6999 Enviado: 09/08/2024 17:17

Cyclotron principle

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Diagram of cyclotron operation from Lawrence's 1934 patent. The hollow, open-faced D-shaped electrodes (left), known as dees, are enclosed in a flat vacuum chamber which is installed in a narrow gap between the two poles of a large magnet (right).Vacuum chamber of Lawrence 69 cm (27 in) 1932 cyclotron with cover removed, showing the dees. The 13,000 V RF accelerating potential at about 27 MHz is applied to the dees by the two feedlines visible at top right. The beam emerges from the dees and strikes the target in the chamber at bottom.

In a particle accelerator, charged particles are accelerated by applying an electric field across a gap. The force on a particle crossing this gap is given by the Lorentz force law:

�=�[�+(��)]{displaystyle mathbf {F} =q[mathbf {E} +(mathbf {v} 	imes mathbf {B} )]}

where q is the charge on the particle, E is the electric fieldv is the particle velocity, and B is the magnetic flux density. It is not possible to accelerate particles using only a static magnetic field, as the magnetic force always acts perpendicularly to the direction of motion, and therefore can only change the direction of the particle, not the speed.[30]

In practice, the magnitude of an unchanging electric field which can be applied across a gap is limited by the need to avoid electrostatic breakdown.[31]: 21  As such, modern particle accelerators use alternating (radio frequency) electric fields for acceleration. Since an alternating field across a gap only provides an acceleration in the forward direction for a portion of its cycle, particles in RF accelerators travel in bunches, rather than a continuous stream. In a linear particle accelerator, in order for a bunch to "see" a forward voltage every time it crosses a gap, the gaps must be placed further and further apart, in order to compensate for the increasing speed of the particle.[32]

A cyclotron, by contrast, uses a magnetic field to bend the particle trajectories into a spiral, thus allowing the same gap to be used many times to accelerate a single bunch. As the bunch spirals outward, the increasing distance between transits of the gap is exactly balanced by the increase in speed, so a bunch will reach the gap at the same point in the RF cycle every time.[32]

The frequency at which a particle will orbit in a perpendicular magnetic field is known as the cyclotron frequency, and depends, in the non-relativistic case, solely on the charge and mass of the particle, and the strength of the magnetic field:

�=��2��{displaystyle f={frac {qB}{2pi m}}}

where f is the (linear) frequency, q is the charge of the particle, B is the magnitude of the magnetic field that is perpendicular to the plane in which the particle is travelling, and m is the particle mass. The property that the frequency is independent of particle velocity is what allows a single, fixed gap to be used to accelerate a particle travelling in a spiral.[32]

Particle energy

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Each time a particle crosses the accelerating gap in a cyclotron, it is given an accelerating force by the electric field across the gap, and the total particle energy gain can be calculated by multiplying the increase per crossing by the number of times the particle crosses the gap.[33]

However, given the typically high number of revolutions, it is usually simpler to estimate the energy by combining the equation for frequency in circular motion:

�=�2��{displaystyle f={frac {v}{2pi r}}}

with the cyclotron frequency equation to yield:

�=����{displaystyle v={frac {qBr}{m}}}

The kinetic energy for particles with speed v is therefore given by:

�=12��2=�2�2�22�{displaystyle E={frac {1}{2}}mv^{2}={frac {q^{2}B^{2}r^{2}}{2m}}}

where r is the radius at which the energy is to be determined. The limit on the beam energy which can be produced by a given cyclotron thus depends on the maximum radius which can be reached by the magnetic field and the accelerating structures, and on the maximum strength of the magnetic field which can be achieved.[8]

K-factor

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In the nonrelativistic approximation, the maximum kinetic energy per atomic mass for a given cyclotron is given by:

��=(���max)22��(��)2=�(��)2{displaystyle {frac {T}{A}}={frac {(eBr_{max })^{2}}{2m_{a}}}left({frac {Q}{A}}
ight)^{2}=Kleft({frac {Q}{A}}
ight)^{2}}

where {displaystyle e} is the elementary charge, {displaystyle B} is the strength of the magnet, �max{displaystyle r_{max }} is the maximum radius of the beam, ��{displaystyle m_{a}} is an atomic mass unit{displaystyle Q} is the charge of the beam particles, and {displaystyle A} is the atomic mass of the beam particles. The value of K

�=(���max)22��{displaystyle K={frac {(eBr_{max })^{2}}{2m_{a}}}}

is known as the "K-factor", and is used to characterize the maximum kinetic beam energy of protons (quoted in MeV). It represents the theoretical maximum energy of protons (with Q and A equal to 1) accelerated in a given machine.[34]

Particle trajectory

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The trajectory followed by a particle in the cyclotron approximated with a Fermat's spiral

While the trajectory followed by a particle in the cyclotron is conventionally referred to as a "spiral", it is more accurately described as a series of arcs of constant radius. The particle speed, and therefore orbital radius, only increases at the accelerating gaps. Away from those regions, the particle will orbit (to a first approximation) at a fixed radius.[35]

Assuming a uniform energy gain per orbit (which is only valid in the non-relativistic case), the average orbit may be approximated by a simple spiral. If the energy gain per turn is given by ΔE, the particle energy after n turns will be:�(�)=�Δ�{displaystyle E(n)=nDelta E}Combining this with the non-relativistic equation for the kinetic energy of a particle in a cyclotron gives:�(�)=2�Δ����{displaystyle r(n)={{sqrt {2mDelta E}} over qB}{sqrt {n}}}This is the equation of a Fermat spiral.

Stability and focusing

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As a particle bunch travels around a cyclotron, two effects tend to make its particles spread out. The first is simply the particles injected from the ion source having some initial spread of positions and velocities. This spread tends to get amplified over time, making the particles move away from the bunch center. The second is the mutual repulsion of the beam particles due to their electrostatic charges.[36] Keeping the particles focused for acceleration requires confining the particles to the plane of acceleration (in-plane or "vertical"[a] focusing), preventing them from moving inward or outward from their correct orbit ("horizontal"[a] focusing), and keeping them synchronized with the accelerating RF field cycle (longitudinal focusing).[35]

Transverse stability and focusing

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The in-plane or "vertical"[a] focusing is typically achieved by varying the magnetic field around the orbit, i.e. with azimuth. A cyclotron using this focusing method is thus called an azimuthally-varying field (AVF) cyclotron.[37] The variation in field strength is provided by shaping the steel poles of the magnet into sectors[35] which can have a shape reminiscent of a spiral and also have a larger area towards the outer edge of the cyclotron to improve the vertical focus of the particle beam.[38] This solution for focusing the particle beam was proposed by L. H. Thomas in 1938[37] and almost all modern cyclotrons use azimuthally-varying fields.[39]

The "horizontal"[a] focusing happens as a natural result of cyclotron motion. Since for identical particles travelling perpendicularly to a constant magnetic field the trajectory curvature radius is only a function of their speed, all particles with the same speed will travel in circular orbits of the same radius, and a particle with a slightly incorrect trajectory will simply travel in a circle with a slightly offset center. Relative to a particle with a centered orbit, such a particle will appear to undergo a horizontal oscillation relative to the centered particle. This oscillation is stable for particles with a small deviation from the reference energy.[35]

Longitudinal stability

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The instantaneous level of synchronization between a particle and the RF field is expressed by phase difference between the RF field and the particle. In the first harmonic mode (i.e. particles make one revolution per RF cycle) it is the difference between the instantaneous phase of the RF field and the instantaneous azimuth of the particle. Fastest acceleration is achieved when the phase difference equals 90° (modulo360°).[35]: ch.2.1.3  Poor synchronization, i.e. phase difference far from this value, leads to the particle being accelerated slowly or even decelerated (outside of the 0–180° range).

As the time taken by a particle to complete an orbit depends only on particle's type, magnetic field (which may vary with the radius), and Lorentz factor (see § Relativistic considerations), cyclotrons have no longitudinal focusing mechanism which would keep the particles synchronized to the RF field. The phase difference, that the particle had at the moment of its injection into the cyclotron, is preserved throughout the acceleration process, but errors from imperfect match between the RF field frequency and the cyclotron frequency at a given radius accumulate on top of it.[35]: ch.2.1.3  Failure of the particle to be injected with phase difference within about ±20° from the optimum may make its acceleration too slow and its stay in the cyclotron too long. As a consequence, half-way through the process the phase difference escapes the 0–180° range, the acceleration turns into deceleration, and the particle fails to reach the target energy. Grouping of the particles into correctly synchronized bunches before their injection into the cyclotron thus greatly increases the injection efficiency.[35]: ch.7

Relativistic considerations

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In the non-relativistic approximation, the cyclotron frequency does not depend upon the particle's speed or the radius of the particle's orbit. As the beam spirals outward, the rotation frequency stays constant, and the beam continues to accelerate as it travels a greater distance in the same time period. In contrast to this approximation, as particles approach the speed of light, the cyclotron frequency decreases due to the change in relativistic mass. This change is proportional to the particle's Lorentz factor.[30]: 6–9

The relativistic mass can be written as:

�=�01−(��)2=�01−�2=��0,{displaystyle m={frac {m_{0}}{sqrt {1-left({frac {v}{c}}
ight)^{2}}}}={frac {m_{0}}{sqrt {1-eta ^{2}}}}=gamma {m_{0}},}

where:

  • �0{displaystyle m_{0}} is the particle rest mass,
  • �=��{displaystyle eta ={frac {v}{c}}} is the relative velocity, and
  • �=11−�2=11−(��)2{displaystyle gamma ={frac {1}{sqrt {1-eta ^{2}}}}={frac {1}{sqrt {1-left({frac {v}{c}}
ight)^{2}}}}} is the Lorentz factor.[30]: 6–9

Substituting this into the equations for cyclotron frequency and angular frequency gives:

�=��2���0�=����0{displaystyle {egin{aligned}f&={frac {qB}{2pi gamma m_{0}}}[6pt]omega &={frac {qB}{gamma m_{0}}}end{aligned}}}

The gyroradius for a particle moving in a static magnetic field is then given by:[30]: 6–9 �=���0���=��0���=�0���−2−�−2{displaystyle r={frac {gamma eta m_{0}c}{qB}}={frac {gamma m_{0}v}{qB}}={frac {m_{0}}{qB{sqrt {v^{-2}-c^{-2}}}}}}

Expressing the speed in this equation in terms of frequency and radius�=2���{displaystyle v=2pi fr}yields the connection between the magnetic field strength, frequency, and radius:(12��)2=(�0��)2+(��)2{displaystyle left({frac {1}{2pi f}}
ight)^{2}=left({frac {m_{0}}{qB}}
ight)^{2}+left({frac {r}{c}}
ight)^{2}}


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De: BARILOCHENSE6999 Enviado: 09/08/2024 17:51
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