Cyclotron - Knowledge

2996: 1382:), 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. 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. 3488: 3257: 2862: 382: 3295: 3333: 3219: 3181: 3132: 3097: 40: 162: 193:. 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. Several months later, in the early summer of 1929, Ernest Lawrence independently conceived the cyclotron concept after reading a paper by 2697: 1338:

the bunch center. The second is the mutual repulsion of the beam particles due to their electrostatic charges. Keeping the particles focused for acceleration requires confining the particles to the plane of acceleration (in-plane or "vertical" focusing), preventing them from moving inward or outward from their correct orbit ("horizontal" focusing), and keeping them synchronized with the accelerating RF field cycle (longitudinal focusing).

1192: 2518: 362: 154: 1350:. A cyclotron using this focusing method is thus called an azimuthally-varying field (AVF) cyclotron. The variation in field strength is provided by shaping the steel poles of the magnet into sectors 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. This solution for focusing the particle beam was proposed by 3371: 349: 2684:) is the fixed-field alternating gradient accelerator (FFA). In an isochronous cyclotron, the magnetic field is shaped by using precisely machined steel magnet poles. This variation provides a focusing effect as the particles cross the edges of the poles. In an FFA, separate magnets with alternating directions are used to focus the beam using the principle of 1358:

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.

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shielding, and the enclosing building. Cyclotrons have a single electrical driver, which saves both equipment and power costs. Furthermore, cyclotrons are able to produce a continuous beam of particles at the target, so the average power passed from a particle beam into a target is relatively high compared to the pulsed beam of a synchrotron.

233:), 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 2780:"Superconducting" in the cyclotron context refers to the type of magnet used to bend the particle orbits into a spiral. Superconducting magnets can produce substantially higher fields in the same area than normal conducting magnets, allowing for more compact, powerful machines. The first superconducting cyclotron was the K500 at the 2760:

create a nonuniform magnetic field stronger in peripheral regions. Most modern cyclotrons are of this type. The pole pieces can also be shaped to cause the beam to keep the particles focused in the acceleration plane as they orbit. This is known as "sector focusing" or "azimuthally-varying field focusing", and uses the principle of

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research where the primary consideration is not achieving the maximum possible energy. Cyclotron based nuclear physics experiments are used to measure basic properties of isotopes (particularly short lived radioactive isotopes) including half life, mass, interaction cross sections, and decay schemes.

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increases as the particle reaches relativistic velocities, acceleration of relativistic particles requires modification of the cyclotron to ensure the particle crosses the gap at the same point in each RF cycle. If the frequency of the accelerating electric field is varied while the magnetic field is

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is another type of particle accelerator that uses magnets to bend particles into a circular trajectory. Unlike in a cyclotron, the particle path in a synchrotron has a fixed radius. Particles in a synchrotron pass accelerating stations at increasing frequency as they get faster. To compensate for

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effects become important, the beam becomes out of phase with the oscillating electric field, and cannot receive any additional acceleration. The classical cyclotron (constant field and frequency) is therefore only capable of accelerating particles up to a few percent of the speed of light. Synchro-,

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The synchrocyclotron extended the energy of the cyclotron into the relativistic regime by decreasing the frequency of the accelerating field as the orbit of the particles increased to keep it synchronized with the particle revolution frequency. Because this requires pulsed operation, the integrated

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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

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The "horizontal" 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

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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

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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

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The first isochronous cyclotron (other than classified prototypes) was built by F. Heyn and K.T. Khoe in Delft, the Netherlands, in 1956. Early isochronous cyclotrons were limited to energies of ~50 MeV per nucleon, but as manufacturing and design techniques gradually improved, the construction

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experiments. With the advent of strong focusing synchrotrons, cyclotrons were supplanted as the accelerators capable of producing the highest energies. However, due to their compactness, and therefore lower expense compared to high energy synchrotrons, cyclotrons are still used to create beams for

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Only accelerators with time-independent frequency and bending field strength can operate in continuous mode, i.e. output a bunch of particles in each cycle of the accelerating field. If any of these quantities sweeps during the acceleration, the operation mode must be pulsed, i.e. the machine will

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Beams of particles heavier than hydrogen are referred to as heavy ion beams, and can range from deuterium nuclei (one proton and one neutron) up to uranium nuclei. The increase in energy required to accelerate heavier particles is balanced by stripping more electrons from the atom to increase the

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Accelerating negative hydrogen ions simplifies extracting the beam from the machine. At the radius corresponding to the desired beam energy, a metal foil is used to strip the electrons from the H ions, transforming them into positively charged H ions. The change in polarity causes the beam to be

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These cyclotrons extend output energy into the relativistic regime by altering the magnetic field to compensate for the change in cyclotron frequency as the particles reached relativistic speed. They use specially shaped magnet pole pieces that are wider near the outer diameter of the cyclotron to

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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

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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,

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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

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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

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in front of Lawrence's 69 cm (27 in) cyclotron at the Lawrence Radiation Laboratory. The curving metal frame is the magnet's core, the large cylindrical boxes contain the coils of wire that generate the magnetic field. The vacuum chamber containing the "dee" electrodes is in the center

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is that because the same accelerating gap is used many times, it is both more space efficient and more cost efficient; particles can be brought to higher energies in less space, and with less equipment. The compactness of the cyclotron reduces other costs as well, such as foundations, radiation

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The simplest way to strike a target with a cyclotron beam is to insert it directly into the path of the beam in the cyclotron. Internal targets have the disadvantage that they must be compact enough to fit within the cyclotron beam chamber, making them impractical for many medical and research

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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

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Keeping the frequency constant allows isochronous cyclotrons to operate in a continuous mode, which makes them capable of producing much greater beam current than synchrocyclotrons. On the other hand, as precise matching of the orbital frequency to the accelerating field frequency is the

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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.

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As of 2020, there were approximately 80 facilities worldwide for radiotherapy using beams of protons and heavy ions, consisting of a mixture of cyclotrons and synchrotrons. Cyclotrons are primarily used for proton beams, while synchrotrons are used to produce heavier ions.

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While extracting a beam from a cyclotron to impinge on an external target is more complicated than using an internal target, it allows for greater control of the placement and focus of the beam, and much more flexibility in the types of targets to which the beam can be

1815: 1968: 2123: 2661: 2505: 324:. 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, 1696: 508:) 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 3429:

in the magnetic field to accelerate electrons in a circular path. While static magnetic fields cannot provide acceleration, as the force always acts perpendicularly to the direction of particle motion, changing fields can be used to induce an

497:. 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. 3875: 2688:. The field of the focusing and bending magnets in an FFA is not varied over time, so the beam chamber must still be wide enough to accommodate a changing beam radius within the field of the focusing magnets as the beam accelerates. 273: 258: 3546:

The terms "horizontal" and "vertical" do not refer to the physical orientation of the cyclotron, but are relative to the plane of acceleration. Vertical is perpendicular to the plane of acceleration, and horizontal is parallel to

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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.

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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

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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.

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this frequency increase, both the frequency of the applied accelerating electric field and the magnetic field must be increased in tandem, leading to the "synchro" portion of the name.

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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.

173:, 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. 1610: 573: 1603: 654: 2747:

total beam current was low compared to the classical cyclotron. In terms of beam energy, these were the most powerful accelerators during the 1950s, before the development of the

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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

699: 218:. 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 80 320:

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

1256: 455: 512:, 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 1371:

360°). 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).

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imaging. While cyclotron produced radioisotopes are widely used for diagnostic purposes, therapeutic uses are still largely in development. Proposed isotopes include

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in 1930 (the first published description of the cyclotron concept), after a student of his built a crude model in April of that year. He patented the device in 1932.

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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

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was the first to formulate the concept of the cyclotron, but he was discouraged from pursuing the idea further. In late 1928 and early 1929, Hungarian physicist

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built a 30 cm (12 in) 1 MeV cyclotron as an undergraduate project, which is now used for a senior-level undergraduate and a graduate lab course.

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Moderate variation of the field strength with radius does not matter in synchrocyclotrons, because the frequency variation compensates for it automatically.

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effects – the mutual repulsion of the particles in the beam. As the amount of particles (beam current) in a cyclotron beam is increased, the effects of

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The earliest and simplest cyclotron. Classical cyclotrons have uniform magnetic fields and a constant accelerating frequency. They are limited to

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However, as discussed above, a constant frequency acceleration method is only possible when the accelerated particles are approximately obeying

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of "spiral-sector" cyclotrons allowed the acceleration and control of more powerful beams. Later developments included the use of more powerful

5480: 5425: 4843: 4047: 3516:– an accelerator concept similar to the cyclotron which uses a linear accelerator type accelerating structure with a constant magnetic field. 86:

outwards from the center of a flat cylindrical vacuum chamber along a spiral path. The particles are held to a spiral trajectory by a static

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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

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If instead the magnetic field is varied with radius while the frequency of the accelerating field is held constant, this leads to the

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

527:, and depends, in the non-relativistic case, solely on the charge and mass of the particle, and the strength of the magnetic field: 5745:

An experiment done by Fred M. Niell, III his senior year of high school (1994–95) with which he won the overall grand prize in the

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grow stronger until they disrupt the orbits of neighboring particles. This puts a functional limit on the beam intensity, or the

1527:{\displaystyle m={\frac {m_{0}}{\sqrt {1-\left({\frac {v}{c}}\right)^{2}}}}={\frac {m_{0}}{\sqrt {1-\beta ^{2}}}}=\gamma {m_{0}},} 948:{\displaystyle {\frac {T}{A}}={\frac {(eBr_{\max })^{2}}{2m_{a}}}\left({\frac {Q}{A}}\right)^{2}=K\left({\frac {Q}{A}}\right)^{2}} 4379: 5813: 5768: 5230: 5156: 4950: 4767: 4354: 4155: 3771: 3210: 3028:

isochronous, and other types of cyclotrons can overcome this limitation, with the tradeoff of increased complexity and cost.

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Cyclotron beams can be used to bombard other atoms to produce short-lived isotopes with a variety of medical uses, including

1810:{\displaystyle {\begin{aligned}f&={\frac {qB}{2\pi \gamma m_{0}}}\\\omega &={\frac {qB}{\gamma m_{0}}}\end{aligned}}} 500:

In practice, the magnitude of an unchanging electric field which can be applied across a gap is limited by the need to avoid

230: 5101: 5042:. 13th International Conference on Cyclotrons and their Applications. Vancouver, Canada: World Scientific. pp. 115–118. 532: 618: 332:

further decreasing the available total beam. As such, they were quickly overtaken in popularity by isochronous cyclotrons.

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An approach which combines static magnetic fields (as in the synchrocyclotron) and alternating gradient focusing (as in a

1963:{\displaystyle r={\frac {\gamma \beta m_{0}c}{qB}}={\frac {\gamma m_{0}v}{qB}}={\frac {m_{0}}{qB{\sqrt {v^{-2}-c^{-2}}}}}} 101:

The cyclotron was the first "cyclical" accelerator. The primary accelerators before the development of the cyclotron were

4314: 2118:{\displaystyle \left({\frac {1}{2\pi f}}\right)^{2}=\left({\frac {m_{0}}{qB}}\right)^{2}+\left({\frac {r}{c}}\right)^{2}} 4288: 663: 5796: 226: 79: 3406:

The spiraling of electrons in a cylindrical vacuum chamber within a transverse magnetic field is also employed in the

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Separated sector cyclotrons are machines in which the magnet is in separate sections, separated by gaps without field.

5643: 5259: 4922: 4826: 4592: 4554: 4529: 4250: 3825: 3787: 3414:). In the magnetron, electrons are bent into a circular path by a magnetic field, and their motion is used to excite 2656:{\displaystyle B(r)={\frac {m_{0}}{q{\sqrt {\left({\frac {1}{2\pi f}}\right)^{2}-\left({\frac {r}{c}}\right)^{2}}}}}} 2500:{\displaystyle f(r)={\frac {1}{2\pi {\sqrt {\left({\frac {m_{0}}{qB}}\right)^{2}+\left({\frac {r}{c}}\right)^{2}}}}}} 1346:

The in-plane or "vertical" focusing is typically achieved by varying the magnetic field around the orbit, i.e. with

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

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In this type of cyclotron, the accelerating frequency is varied as a function of particle orbit radius such that:

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is the magnitude of the magnetic field that is perpendicular to the plane in which the particle is travelling, and

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Cyclotrons were the most powerful particle accelerator technology until the 1950s, when they were surpassed by the

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deflected in the opposite direction by the magnetic field, allowing the beam to be transported out of the machine.

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the instantaneous azimuth of the particle. Fastest acceleration is achieved when the phase difference equals 90° (

3455: 1691:{\displaystyle \gamma ={\frac {1}{\sqrt {1-\beta ^{2}}}}={\frac {1}{\sqrt {1-\left({\frac {v}{c}}\right)^{2}}}}} 5858: 4729:

Proceedings of the 52nd ICFA Advanced Beam Dynamics Workshop on High-Intensity and High-Brightness Hadron Beams

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The decrease in accelerating frequency is tuned to match the increase in gamma for a constant magnetic field.

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Combining this with the non-relativistic equation for the kinetic energy of a particle in a cyclotron gives:

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comic strip to be pulled in April 1945 for having Superman bombarded with the radiation from a cyclotron.

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Mann, F. J. (December 1946). "Federal Telephone and Radio Corporation, A Historical Review: 1909–1946".

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magnets and the separation of the magnets into discrete sectors, as opposed to a single large magnet.

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and basic research. As of 2020, close to 1,500 cyclotrons were in use worldwide for the production of

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at the RIKEN Nishina Center for Accelerator Based Science – the highest energy cyclotron in the world

3324: 2781: 211: 102: 4978:. 9th International Conference on Cyclotrons and their Applications. Caen, France. pp. 231–240. 5065:. 15th International Conference on Cyclotrons and their Applications. Caen, France. pp. 90–93. 4784: 4446: 3519: 2666:

responsibility of the magnetic field variation with radius, the variation must be precisely tuned.

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Heyn, F.; Khoe, Kong Tat (1958). "Operation of a Radial Sector Fixed-Frequency Proton Cyclotron".

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Bethe, H. A.; Rose, M. E. (15 December 1937). "The Maximum Energy Obtainable from the Cyclotron".

4059: 3727: 3438:. The betatron was developed in 1940, although the idea had been proposed substantially earlier. 5809: 5451: 4612: 3248: 2917: 2806:

The simplest type of cyclotron beam, proton beams are typically created by ionizing hydrogen gas.

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Regulatory control of the safety of ion radiotherapy facilities : a guide for best practice

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Cyclotrons and their applications 2004. Proceedings of the seventeenth international conference

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The first suggestion that energetic protons could be an effective treatment method was made by

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The frequency at which a particle will orbit in a perpendicular magnetic field is known as the

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to increase the voltage to 2.8 MV and 3 mA current. A second cyclotron was built in

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To construct the first such device, Lawrence used large electromagnets recycled from obsolete

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that could be achieved across the accelerating region. This potential was in turn limited by

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Diagram of cyclotron operation from Lawrence's 1934 patent. The hollow, open-faced D-shaped

5678: 5343: 5002: 4877: 4487: 4406: 4259: 3975: 3929: 3857:. CAS-CERN Accelerator School: 5th general accelerator physics course. Jyvaskyla, Finland: 3759: 3698: 3507: 1542: 1027: 501: 122: 118: 71: 4721: 4641: 1706:

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

8: 3501: 3431: 2980: 2189: 524: 5709: 5682: 5347: 5006: 4881: 4491: 4410: 4263: 3979: 3933: 3763: 3702: 5790: 5696: 5565: 5311: 5286: 5133: 5129:"In a breakthrough, Canadian researchers develop a new way to produce medical isotopes" 4276:

State Institute of Radium, founded in 1922, now known as V. G. Khlopin Radium Institute

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Lawrence and His Laboratory: A History of the Lawrence Berkeley Laboratory', Volume I.

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Proceedings of the 19th International Conference on Cyclotrons and their Applications

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Reiser, Martin (1966). "Space Charge Effects and Current Limitations in Cyclotrons".

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for the invention and development of the cyclotron and for results obtained with it.

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Proceedings of the 7th International Conference on Cyclotrons and their Applications

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speed, so a bunch will reach the gap at the same point in the RF cycle every time.

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E. O. Lawrence; N. E. Edlefsen (1930). "On the Production of High Speed Protons".

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of particles which can be accelerated at one time, as distinct from their energy.

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yields the connection between the magnetic field strength, frequency, and radius:

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Widerøe, R. (1928). "Ueber Ein Neues Prinzip Zur Herstellung Hoher Spannungen".

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only once. Thus, the energy gained by the particles was limited by the maximum

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For several decades, cyclotrons were the best source of high-energy beams for

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A history of cyclotron development at the Berkeley Radiation Laboratory, now

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The trajectory followed by a particle in the cyclotron approximated with a

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electric charge of the particles, thus increasing acceleration efficiency.

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in 1938 and almost all modern cyclotrons use azimuthally-varying fields.

62:) exiting the machine and ionizing the surrounding air causing a blue glow 4943:

Up from nothing : the Michigan State University Cyclotron Laboratory

4855:. CERN Accelerator School – Introductory Course. High Tatras. p. 36. 4340: 4055: 3473: 3442: 3435: 3256: 3180: 2925: 2913: 2748: 2735: 2681: 2290: 130: 5733: 2960:

in a paper published in 1946 while he was involved in the design of the

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particle velocities (the output energy small compared to the particle's

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Characteristic properties of cyclotrons and other circular accelerators

133:. Nonetheless, they are still widely used to produce particle beams for 4025: 3411: 2794: 1972:

Expressing the speed in this equation in terms of frequency and radius

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SciPost Physics Proceedings issue 5, Review of Particle Physics at PSI

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period. In contrast to this approximation, as particles approach the

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Serving the Reich: the Struggle for the Soul of Physics Under Hitler

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To make use of the cyclotron beam, it must be directed to a target.

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The Operation of Cyclotrons Used for Radiopharmaceutical Production

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for a particle moving in a static magnetic field is then given by:

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particle will orbit (to a first approximation) at a fixed radius.

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Close, F. E.; Close, Frank; Marten, Michael; et al. (2004).

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Superheroes!:Capes cowls and the creation of comic book culture

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Cyclotron produced radionuclides : principles and practice

4524:(2nd ed.). Hackensack, N.J.: World Scientific. p. 1. 3294: 3286: 2983:, while minimizing damage to healthy tissue along their path. 2972: 1318:{\displaystyle r(n)={{\sqrt {2m\Delta E}} \over qB}{\sqrt {n}}} 55: 4821:(Third ed.). Newark: John WIley & Sons. p. 178. 3685:

Lawrence, Earnest O.; Livingston, M. Stanley (April 1, 1932).

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Not applicable, because the particle orbit radius is constant.

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for nuclear medicine. In addition, cyclotrons can be used for

3370: 3362: 513: 197:

describing a drift tube accelerator. He published a paper in

5369: 4991:"A review of ion sources for medical accelerators (invited)" 4094: 3522:– a braking force on beams that are bent in a magnetic field 5746: 4851: 4619: 3858: 5764: 4722:"Space Charge Effects in Isochronous FFAGs and Cyclotrons" 4720:

Planche, T.; Rao, Y-N; Baartman, R. (September 17, 2012).

4547:

An introduction to the physics of high energy accelerators

3730:. Dept. of Physics and Astronomy, Georgia State University 3560:

output a bunch of particles only at the end of each sweep.

3241:

Oldest continuously operated large cyclotron in existence

263:. This Leningrad instrument was first proposed in 1932 by 5615: 1395:, the cyclotron frequency decreases due to the change in 504:. As such, modern particle accelerators use alternating ( 145:, where particle beams are directly applied to patients. 51: 5818: 5102:"Cyclotrons – What are They and Where Can you Find Them" 2127: 1095:

is the atomic mass of the beam particles. The value of

4522:

An introduction to the physics of particle accelerators

2753: 2521:

In isochronous cyclotrons, the magnetic field strength

3755:

The Particle Odyssey: A Journey to the Heart of Matter

5634:

Aykroyd, Dan; Ramis, Harold (1985). Shay, Don (ed.).

5108:. International Atomic Energy Agency. 27 January 2021 4866:

Daniel Clery (4 January 2010). "The Next Big Beam?".

3670:, filed: January 26, 1932, granted: February 20, 1934 3410:, a device for producing high frequency radio waves ( 3317:

Largest normal conducting cyclotron ever constructed

3165:

and largest single-magnet cyclotron ever constructed

2553: 2397: 2367: 2013: 1978: 1829: 1714: 1613: 1578: 1545: 1414: 1264: 1223: 1166:{\displaystyle K={\frac {(eBr_{\max })^{2}}{2m_{a}}}} 1106: 1081: 1061: 1030: 1003: 983: 963: 825: 715: 666: 621: 535: 402: 5254:. Vienna: International Atomic Energy Agency. 2020. 5222:

A Brief History of the Harvard University Cyclotrons

5151:. Vienna: International Atomic Energy Agency. 2008. 3817:

Principles of Physics: A Calculus-Based Text, Vol. 2

3483: 1341: 240:

The first European cyclotron was constructed in the

5799:– the largest single-magnet cyclotron in the world. 4819:

Practical radiotherapy : physics and equipment

373:which is installed in a narrow gap between the two 177:In 1927, while a student at Kiel, German physicist 157:

Lawrence's original 4.5-inch (11 cm) cyclotron

5776:– the highest beam current cyclotron in the world. 5452:"30 Years of Superconducting Cyclotron Technology" 5037: 4719: 4139: 3684: 2793:The particles for cyclotron beams are produced in 2670:Fixed-field alternating gradient accelerator (FFA) 2655: 2499: 2373: 2117: 1999: 1962: 1809: 1690: 1597: 1558: 1526: 1317: 1250: 1165: 1087: 1067: 1043: 1016: 989: 969: 947: 794: 693: 648: 567: 449: 4988: 4587:. Oxford: Oxford University Press. pp. 6–9. 3903:(Berkeley: University of California Press, 2000) 3668:Method and apparatus for the acceleration of ions 3031:An additional limitation of cyclotrons is due to 3011:The most obvious advantage of a cyclotron over a 225:At the Radiation Laboratory on the campus of the 5830: 5389:"The High Intensity Proton Accelerator Facility" 5284: 5055: 4731:. HB2012. Beijing, China: CERN. pp. 231–234 3751: 2721:There are a number of basic types of cyclotron: 1399:. This change is proportional to the particle's 1379: 1130: 1009: 856: 658:with the cyclotron frequency equation to yield: 278:and was installed and became operative by 1937. 82:, and patented in 1932. A cyclotron accelerates 5285:Peach, K; Wilson, P; Jones, B (December 2011). 4914:Handbook of Accelerator Physics and Engineering 4785:"Cyclotrons: Magnetic Design and Beam Dynamics" 4377: 4291:. V.G. Khlopin Radium Institute. Archived from 3899:81-82 in Heilbron, J. L., and Robert W. Seidel 3232:Protons, Alpha Particles, Neutrons, Heavy Ions 2975:. Ion beams from cyclotrons can be used, as in 5038:Grey-Morgan, T.; Hubbard, RE (November 1992). 4783:Zaremba, Simon; Kleeven, Wiel (22 June 2017). 4782: 4544: 1385: 369:(left), known as dees, are enclosed in a flat 165:Lawrence's 60-inch (150 cm) cyclotron at 5819:National Superconducting Cyclotron Laboratory 5386: 5056:Gelbart, W.Z.; Stevenson, N. R. (June 1998). 4989:Muramatsu, M.; Kitagawa, A. (February 2012). 4816: 4188: 4186: 4013:Archiv für Elektronik und Übertragungstechnik 3820:(5 ed.). Cengage Learning. p. 753. 2990: 2766: 185:filed patent applications in Germany for the 5633: 4865: 4073:Livingston, M. Stanley (19–22 August 1975). 3964:"Szilard as Inventor: Accelerators and More" 3870: 3868: 3848:"A Brief History and Review of Accelerators" 3814:Serway, Raymond A.; Jewett, John W. (2012). 3813: 3655: 3542: 3540: 3538: 3536: 3054: 2774: 2676:Fixed-field alternating gradient accelerator 1183:equal to 1) accelerated in a given machine. 703:The kinetic energy for particles with speed 43:Lawrence's 60-inch (152 cm) cyclotron, 4841: 4817:Cherry, Pam; Duxbury, Angela, eds. (2020). 4747: 4745: 4678: 4676: 4674: 4672: 4670: 4668: 4666: 4519: 4440: 4438: 4436: 4434: 4432: 4430: 4428: 3758:. Oxford University Press. pp. 84–87. 3023:. If the particles become fast enough that 2979:, to penetrate the body and kill tumors by 5051: 5049: 4183: 4137: 4072: 3680: 3678: 3676: 3555: 3553: 2891: 2145: 2142: 5690: 5636:Making Ghostbusters : the screenplay 5503: 5310: 5014: 4936: 4934: 4606: 4604: 4578: 4576: 4574: 4572: 4570: 4568: 4566: 4396: 4243: 3987: 3865: 3710: 3533: 3393:K-value of 2600 is highest ever achieved 2529:has the same shape as the Lorentz factor 1406:The relativistic mass can be written as: 1361: 1332: 1075:is the charge of the beam particles, and 343: 214:. He was assisted by a graduate student, 5287:"Accelerator science in medical physics" 5280: 5278: 4964: 4962: 4742: 4682: 4663: 4585:An introduction to particle accelerators 4515: 4513: 4511: 4509: 4477: 4444: 4425: 4349:. London: The Bodley Head. p. 190. 4084:. Zurich, Switzerland. pp. 635–638. 3841: 3839: 3837: 3809: 3807: 3472:a miniature cyclotron forms part of the 2994: 2860: 2695: 2516: 2512: 1190: 380: 360: 347: 285:. The first was constructed in 1937, in 160: 152: 38: 5449: 5387:Grillenberger, J.; et al. (2021). 5225:. Harvard University Press. p. 9. 5059:Solid Targetry Systems: A Brief History 5046: 4789:CERN Yellow Reports: School Proceedings 4651:. Fermi National Accelerator Laboratory 4538: 4473: 4471: 4131: 4009: 3961: 3747: 3745: 3697:(1). American Physical Society: 19–35. 3673: 3550: 3418:, producing electromagnetic radiation. 3401: 14: 5831: 5803: 5707: 5665:"Building a Cyclotron on a Shoestring" 5333: 5218: 5171: 4940: 4931: 4610: 4601: 4582: 4563: 4545:Edwards, D. A.; Syphers, M.J. (1993). 4520:Conte, Mario; MacKay, William (2008). 3962:Telegdi, Valentine L. (October 2000). 3918:"Szilard's Inventions Patently Halted" 3915: 3845: 3065: 2724: 1186: 568:{\displaystyle f={\frac {qB}{2\pi m}}} 356: 5814:Lawrence Berkeley National Laboratory 5769:Lawrence Berkeley National Laboratory 5758: 5730:"Resonance Mapping and the Cyclotron" 5727: 5662: 5275: 4968: 4959: 4506: 4445:Craddock, M.K. (September 10, 2010). 3911: 3909: 3834: 3804: 3589: 3587: 3577: 3575: 3211:Lawrence Berkeley National Laboratory 2967:Beams from cyclotrons can be used in 2150: 2139: 2128:Approaches to relativistic cyclotrons 1598:{\displaystyle \beta ={\frac {v}{c}}} 649:{\displaystyle f={\frac {v}{2\pi r}}} 231:Lawrence Berkeley National Laboratory 90:and accelerated by a rapidly varying 5485:MSUToday | Michigan State University 5430:MSUToday | Michigan State University 5336:IEEE Transactions on Nuclear Science 5126: 4917:. World Scientific. pp. 13–15. 4910: 4904: 4639: 4468: 4339: 4246:"Nuclear Energy in the Soviet Union" 4225:from the original on 24 October 2008 4170: 3742: 3725: 3279:Highest beam power of any cyclotron 2755:Isochronous cyclotron (isocyclotron) 297:. It was the first cyclotron with a 5638:. New York, NY: New York Zoetrope. 5506:"Status of RIBF accelerators RIKEN" 5504:Kamigaito, O.; et al. (2010). 4751: 4613:Cyclotrons for high-intensity beams 3719: 3046: 2845: 2836: 2740: 2350: 1024:is the maximum radius of the beam, 24: 5720:About a neighborhood cyclotron in 5710:"The Cyclotron Comes to the 'Hood" 5656: 5174:"Radiological Use of Fast Protons" 3906: 3584: 3572: 3458:famously asked for dailies of the 2817: 2716: 2691: 1380:§ Relativistic considerations 1290: 1242: 694:{\displaystyle v={\frac {qBr}{m}}} 596: 227:University of California, Berkeley 80:University of California, Berkeley 50:, showing the beam of accelerated 25: 5870: 5753: 4251:Bulletin of the Atomic Scientists 4219:"The Nobel Prize in Physics 1939" 4058:. 8 December 2008. Archived from 3607: 3084: 3070: 2873: 2708:has been removed from the magnet 2382:held constant, this leads to the 1342:Transverse stability and focusing 244:in the physics department of the 5461:. Tokyo, Japan. pp. 531–534 5423: 5291:The British Journal of Radiology 4995:Review of Scientific Instruments 4692:CERN Particle Accelerator School 4649:U.S. Particle Accelerator School 4480:Review of Scientific Instruments 3639:"Ernest Lawrence – Biographical" 3486: 3369: 3355:First superconducting cyclotron 3331: 3293: 3255: 3217: 3179: 3130: 3095: 2700:A French cyclotron, produced in 437: 429: 418: 404: 317:, and became operative in 1943. 293:in Berlin, and was also used by 94:. Lawrence was awarded the 1939 5627: 5609: 5584: 5558: 5533: 5497: 5473: 5443: 5417: 5399: 5380: 5362: 5327: 5239: 5212: 5165: 5141: 5120: 5094: 5069: 5031: 4982: 4969:Clark, David (September 1981). 4945:. : Michigan State University. 4859: 4835: 4810: 4776: 4713: 4642:"Cyclotrons: Old but Still New" 4633: 4390: 4371: 4333: 4307: 4281: 4237: 4211: 4164: 4088: 4066: 4040: 4003: 3955: 3886: 3846:Bryant, P.J. (September 1992). 3563: 3456:United States Department of War 3365:Superconducting Ring Cyclotron 2951: 2886: 2869:. The magnet is painted yellow. 2828: 2800: 997:is the strength of the magnet, 585:is the charge of the particle, 5781:Superconducting Ring Cyclotron 4685:"Beam dynamics for cyclotrons" 4454:Proceedings of Cyclotrons 2010 4272:10.1080/00963402.1971.11455411 4075:"The History of the Cyclotron" 3780: 3631: 2563: 2557: 2407: 2401: 1274: 1268: 1251:{\displaystyle E(n)=n\Delta E} 1233: 1227: 1136: 1116: 862: 842: 450:{\displaystyle \mathbf {F} =q} 444: 441: 425: 414: 13: 1: 5545:hyperphysics.phy-astr.gsu.edu 5127:Hume, M. (21 February 2012). 4198:American Institute of Physics 4138:Alonso, M.; Finn, E. (1992). 3615:"Ernest Lawrence's Cyclotron" 3600: 3449: 2788: 2762:alternating-gradient focusing 1605:is the relative velocity, and 281:Two cyclotrons were built in 246:V.G. Khlopin Radium Institute 167:Lawrence Radiation Laboratory 44: 4890:10.1126/science.327.5962.142 4447:"Eighty Years of Cyclotrons" 4380:"Wolfgang Gentner 1906–1980" 3897:II — A Million Volts or Bust 3203:First isochronous cyclotron 3126:Lawrence 184-inch Cyclotron 3091:Lawrence 4.5-inch Cyclotron 2962:Harvard Cyclotron Laboratory 2865:A modern cyclotron used for 2784:, which came online in 1981. 2525:as a function of the radius 1213:, the particle energy after 27:Type of particle accelerator 7: 5810:Ernest Lawrence's Cyclotron 5297:(special_issue_1): S4–S10. 4844:"Cyclotrons – II & FFA" 4797:10.23730/CYRSP-2017-001.177 4382:(in German). Archived from 4109:10.1126/science.72.1867.372 3916:Dannen, Gene (March 2001). 3893:Lawrence and His Laboratory 3880:ITN Imaging Technology News 3479: 3434:in the same manner as in a 3007:between the magnet's poles. 2912:emitting isotopes, such as 2808: 2533:as a function of the speed 2259:Other circular accelerators 1386:Relativistic considerations 812: 581:is the (linear) frequency, 510:linear particle accelerator 10: 5875: 5708:Jardin, X. (12 Jan 2005). 5172:Wilson, Robert R. (1946). 4972:Ion Sources for Cyclotrons 4842:Mike Seidel (2019-09-19). 3476:used for catching ghosts. 2999:M. Stanley Livingston and 2991:Advantages and limitations 2768:Separated sector cyclotron 2673: 2354: 1325:This is the equation of a 977:is the elementary charge, 377:of a large magnet (right). 148: 107:Cockcroft–Walton generator 103:electrostatic accelerators 32:Cyclotron (disambiguation) 29: 5823:Michigan State University 4700:10.5170/CERN-2006-012.209 4583:Wilson, E. J. N. (2001). 4419:10.1103/PhysRev.52.1254.2 4244:Emelyanov, V. S. (1971). 3788:"Ernest Lawrence – Facts" 3361: 3325:Michigan State University 3323: 3285: 3247: 3209: 3171: 3125: 3113:4.5 inches (0.11 m) 3090: 3083: 3080: 3077: 3074: 3069: 3064: 3061: 3058: 3053: 2782:Michigan State University 2776:Superconducting cyclotron 2319: 2289: 2264: 2257: 2232: 2207: 2182: 2175: 2170: 2167: 2162: 2159: 2137: 2000:{\displaystyle v=2\pi fr} 1017:{\displaystyle r_{\max }} 305:under the supervision of 212:Federal Telegraph Company 5411:guinnessworldrecords.com 5356:10.1109/TNS.1966.4324198 5219:Wilson, Richard (2004). 4173:Electrical Communication 3526: 3520:Radiation reaction force 3155:184 inches (4.7 m) 3119:First working cyclotron 2856: 313:, with support from the 291:Kaiser Wilhelm Institute 171:University of California 4941:Austin, Sam M. (2015). 3349:52 inches (1.3 m) 3235:88 inches (2.2 m) 3037:electrostatic repulsion 3021:Newton's laws of motion 2892:Radioisotope production 2374:{\displaystyle \gamma } 707:is therefore given by: 502:electrostatic breakdown 123:electrostatic breakdown 111:Van de Graaff generator 5774:PSI Proton Accelerator 4315:"History / Chronology" 4194:"The First Cyclotrons" 3175:Isochronous Cyclotron 3008: 2870: 2713: 2657: 2538: 2501: 2375: 2119: 2001: 1964: 1811: 1692: 1599: 1560: 1528: 1362:Longitudinal stability 1333:Stability and focusing 1319: 1252: 1199: 1167: 1089: 1069: 1045: 1018: 991: 971: 949: 796: 695: 650: 569: 451: 387: 378: 353: 344:Principle of operation 235:Nobel Prize in Physics 174: 158: 96:Nobel Prize in Physics 63: 5859:Particle accelerators 5765:The 88-Inch Cyclotron 5728:Niell, F. M. (2005). 5541:"Magnetron Operation" 4611:Seidel, Mike (2013). 4378:Ulrich Schmidt-Rohr. 3712:10.1103/PhysRev.40.19 3663:U.S. patent 1,948,384 2998: 2864: 2699: 2658: 2543:isochronous cyclotron 2520: 2513:Isochronous cyclotron 2502: 2376: 2120: 2002: 1965: 1812: 1693: 1600: 1561: 1559:{\displaystyle m_{0}} 1529: 1320: 1253: 1194: 1168: 1090: 1070: 1046: 1044:{\displaystyle m_{a}} 1019: 992: 972: 950: 797: 696: 651: 570: 495:magnetic flux density 452: 384: 364: 351: 299:Greinacher multiplier 289:'s laboratory at the 216:M. Stanley Livingston 164: 156: 42: 5570:physics.illinois.edu 5450:Blosser, H. (2004). 5303:10.1259/bjr/16022594 4683:Chautard, F (2006). 4289:"History / Memorial" 4221:. Nobel Foundation. 3726:Nave, C. R. (2012). 3666:Lawrence, Ernest O. 3508:Fast neutron therapy 3402:Related technologies 3311:56 feet (17 m) 2551: 2395: 2365: 2183:Classical cyclotron 2011: 1976: 1827: 1712: 1611: 1576: 1543: 1412: 1262: 1221: 1104: 1079: 1059: 1028: 1001: 981: 961: 823: 713: 664: 619: 533: 400: 119:electrical potential 98:for this invention. 78:in 1929–1930 at the 72:particle accelerator 30:For other uses, see 5849:American inventions 5844:Accelerator physics 5804:Historic cyclotrons 5683:2004PhT....57k..30F 5407:"Largest cyclotron" 5348:1966ITNS...13..171R 5007:2012RScI...83bB909M 4911:Chao, Alex (1999). 4882:2010Sci...327..142C 4755:Accelerator physics 4752:Lee, S.-Y. (1999). 4640:Barletta, William. 4549:. New York: Wiley. 4492:1958RScI...29..662H 4411:1937PhRv...52.1254B 4264:1971BuAtS..27i..38E 3980:2000PhT....53j..25T 3934:2001PhT....54c.102D 3855:Proceedings, Vol. 2 3764:2002pojh.book.....C 3703:1932PhRv...40...19L 3502:Cyclotron radiation 3432:electromotive force 2948:-77, among others. 2726:Classical cyclotron 2143:Accelerating field 2134: 1187:Particle trajectory 525:cyclotron frequency 357:Cyclotron principle 5839:1932 introductions 5791:Rutgers University 5759:Current facilities 5663:Feder, T. (2004). 5619:; Michael Kantor. 5134:The Globe and Mail 4026:10.1007/BF01656341 3213:88-inch Cyclotron 3013:linear accelerator 3009: 3001:Ernest O. Lawrence 2871: 2797:of various types. 2714: 2653: 2539: 2497: 2371: 2132: 2115: 1997: 1960: 1807: 1805: 1688: 1595: 1556: 1524: 1315: 1248: 1200: 1163: 1085: 1065: 1041: 1014: 987: 967: 945: 792: 691: 646: 565: 447: 388: 386:chamber at bottom. 379: 354: 322:special relativity 295:Rudolf Fleischmann 187:linear accelerator 175: 159: 64: 5787:Rutgers Cyclotron 5722:Anchorage, Alaska 5692:10.1063/1.1839371 5596:Britannica Online 5374:cyclotron.lbl.gov 5232:978-0-674-01460-2 5158:978-92-0-100208-2 5016:10.1063/1.3671744 4952:978-0-99672-521-7 4876:(5962): 142–143. 4769:978-981-02-3709-7 4500:10.1063/1.1716293 4405:(12): 1254–1255. 4356:978-1-84792-248-9 4157:978-0-201-56518-8 4103:(1867): 376–377. 3989:10.1063/1.1325189 3942:10.1063/1.1366083 3882:. March 10, 2020. 3773:978-0-19-860943-8 3465:In the 1984 film 3416:resonant cavities 3399: 3398: 2867:radiation therapy 2651: 2648: 2636: 2608: 2495: 2492: 2480: 2452: 2348: 2347: 2103: 2075: 2035: 1958: 1955: 1900: 1867: 1801: 1760: 1686: 1685: 1673: 1643: 1642: 1593: 1501: 1500: 1466: 1465: 1453: 1397:relativistic mass 1313: 1306: 1296: 1161: 1088:{\displaystyle A} 1068:{\displaystyle Q} 990:{\displaystyle B} 970:{\displaystyle e} 933: 902: 887: 834: 790: 730: 689: 644: 563: 516:of the particle. 467:on the particle, 392:Lorentz force law 326:synchrocyclotrons 189:, cyclotron, and 84:charged particles 16:(Redirected from 5866: 5854:Nuclear medicine 5744: 5742: 5741: 5732:. Archived from 5719: 5704: 5694: 5650: 5649: 5631: 5625: 5624: 5613: 5607: 5606: 5604: 5602: 5588: 5582: 5581: 5579: 5577: 5562: 5556: 5555: 5553: 5551: 5537: 5531: 5530: 5528: 5527: 5521: 5515:. Archived from 5510: 5501: 5495: 5494: 5492: 5491: 5477: 5471: 5470: 5468: 5466: 5456: 5447: 5441: 5440: 5438: 5436: 5421: 5415: 5414: 5403: 5397: 5396: 5384: 5378: 5377: 5366: 5360: 5359: 5331: 5325: 5324: 5314: 5282: 5273: 5272: 5270: 5268: 5253: 5243: 5237: 5236: 5216: 5210: 5209: 5190:10.1148/47.5.487 5169: 5163: 5162: 5145: 5139: 5138: 5124: 5118: 5117: 5115: 5113: 5098: 5092: 5091: 5089: 5087: 5073: 5067: 5066: 5064: 5053: 5044: 5043: 5035: 5029: 5028: 5018: 4986: 4980: 4979: 4977: 4966: 4957: 4956: 4938: 4929: 4928: 4908: 4902: 4901: 4863: 4857: 4856: 4848: 4839: 4833: 4832: 4814: 4808: 4807: 4805: 4803: 4780: 4774: 4773: 4760:World Scientific 4749: 4740: 4739: 4737: 4736: 4726: 4717: 4711: 4710: 4708: 4706: 4689: 4680: 4661: 4660: 4658: 4656: 4646: 4637: 4631: 4630: 4628: 4626: 4617: 4608: 4599: 4598: 4580: 4561: 4560: 4542: 4536: 4535: 4517: 4504: 4503: 4475: 4466: 4465: 4463: 4461: 4456:. Lanzhou, China 4451: 4442: 4423: 4422: 4394: 4388: 4387: 4375: 4369: 4368: 4337: 4331: 4330: 4328: 4326: 4317:. Archived from 4311: 4305: 4304: 4302: 4300: 4285: 4279: 4278: 4241: 4235: 4234: 4232: 4230: 4215: 4209: 4208: 4206: 4204: 4190: 4181: 4180: 4168: 4162: 4161: 4145: 4135: 4129: 4128: 4092: 4086: 4085: 4079: 4070: 4064: 4063: 4052:Bancroft Library 4044: 4038: 4037: 4007: 4001: 4000: 3998: 3996: 3991: 3959: 3953: 3952: 3950: 3948: 3913: 3904: 3890: 3884: 3883: 3872: 3863: 3862: 3852: 3843: 3832: 3831: 3811: 3802: 3801: 3799: 3798: 3784: 3778: 3777: 3749: 3740: 3739: 3737: 3735: 3723: 3717: 3716: 3714: 3682: 3671: 3665: 3659: 3653: 3652: 3650: 3649: 3635: 3629: 3628: 3626: 3625: 3611: 3594: 3591: 3582: 3581:Design-dependent 3579: 3570: 3567: 3561: 3557: 3548: 3544: 3496: 3491: 3490: 3374: 3373: 3336: 3335: 3298: 3297: 3260: 3259: 3222: 3221: 3184: 3183: 3163:synchrocyclotron 3135: 3134: 3100: 3099: 3086: 3072: 3067: 3056: 3051: 3050: 3047:Notable examples 2981:radiation damage 2969:particle therapy 2958:Robert R. Wilson 2847:External targets 2838:Internal targets 2742:Synchrocyclotron 2662: 2660: 2659: 2654: 2652: 2650: 2649: 2647: 2646: 2641: 2637: 2629: 2619: 2618: 2613: 2609: 2607: 2593: 2586: 2580: 2579: 2570: 2536: 2532: 2528: 2524: 2506: 2504: 2503: 2498: 2496: 2494: 2493: 2491: 2490: 2485: 2481: 2473: 2463: 2462: 2457: 2453: 2451: 2443: 2442: 2433: 2426: 2414: 2384:synchrocyclotron 2380: 2378: 2377: 2372: 2357:Synchrocyclotron 2351:Synchrocyclotron 2260: 2234:Synchrocyclotron 2178: 2146:Bending magnetic 2135: 2131: 2124: 2122: 2121: 2116: 2114: 2113: 2108: 2104: 2096: 2086: 2085: 2080: 2076: 2074: 2066: 2065: 2056: 2046: 2045: 2040: 2036: 2034: 2020: 2006: 2004: 2003: 1998: 1969: 1967: 1966: 1961: 1959: 1957: 1956: 1954: 1953: 1938: 1937: 1925: 1916: 1915: 1906: 1901: 1899: 1891: 1887: 1886: 1873: 1868: 1866: 1858: 1854: 1853: 1837: 1816: 1814: 1813: 1808: 1806: 1802: 1800: 1799: 1798: 1785: 1777: 1761: 1759: 1758: 1757: 1738: 1730: 1697: 1695: 1694: 1689: 1687: 1684: 1683: 1678: 1674: 1666: 1653: 1649: 1644: 1641: 1640: 1625: 1621: 1604: 1602: 1601: 1596: 1594: 1586: 1566:is the particle 1565: 1563: 1562: 1557: 1555: 1554: 1533: 1531: 1530: 1525: 1520: 1519: 1518: 1502: 1499: 1498: 1483: 1482: 1481: 1472: 1467: 1464: 1463: 1458: 1454: 1446: 1433: 1432: 1431: 1422: 1324: 1322: 1321: 1316: 1314: 1309: 1307: 1305: 1297: 1283: 1281: 1257: 1255: 1254: 1249: 1216: 1212: 1172: 1170: 1169: 1164: 1162: 1160: 1159: 1158: 1145: 1144: 1143: 1134: 1133: 1114: 1094: 1092: 1091: 1086: 1074: 1072: 1071: 1066: 1053:atomic mass unit 1050: 1048: 1047: 1042: 1040: 1039: 1023: 1021: 1020: 1015: 1013: 1012: 996: 994: 993: 988: 976: 974: 973: 968: 954: 952: 951: 946: 944: 943: 938: 934: 926: 913: 912: 907: 903: 895: 888: 886: 885: 884: 871: 870: 869: 860: 859: 840: 835: 827: 807: 801: 799: 798: 793: 791: 789: 781: 780: 779: 770: 769: 760: 759: 749: 744: 743: 731: 723: 706: 700: 698: 697: 692: 690: 685: 674: 655: 653: 652: 647: 645: 643: 629: 592: 588: 584: 580: 574: 572: 571: 566: 564: 562: 551: 543: 492: 483:is the particle 482: 472: 462: 456: 454: 453: 448: 440: 432: 421: 407: 311:Wolfgang Gentner 277: 262: 210:provided by the 143:particle therapy 135:nuclear medicine 49: 46: 21: 5874: 5873: 5869: 5868: 5867: 5865: 5864: 5863: 5829: 5828: 5806: 5761: 5756: 5739: 5737: 5659: 5657:Further reading 5654: 5653: 5646: 5632: 5628: 5617:Laurence Maslon 5614: 5610: 5600: 5598: 5590: 5589: 5585: 5575: 5573: 5564: 5563: 5559: 5549: 5547: 5539: 5538: 5534: 5525: 5523: 5519: 5508: 5502: 5498: 5489: 5487: 5479: 5478: 5474: 5464: 5462: 5454: 5448: 5444: 5434: 5432: 5422: 5418: 5405: 5404: 5400: 5385: 5381: 5368: 5367: 5363: 5332: 5328: 5283: 5276: 5266: 5264: 5262: 5251: 5245: 5244: 5240: 5233: 5217: 5213: 5170: 5166: 5159: 5147: 5146: 5142: 5125: 5121: 5111: 5109: 5100: 5099: 5095: 5085: 5083: 5075: 5074: 5070: 5062: 5054: 5047: 5036: 5032: 4987: 4983: 4975: 4967: 4960: 4953: 4939: 4932: 4925: 4909: 4905: 4864: 4860: 4846: 4840: 4836: 4829: 4815: 4811: 4801: 4799: 4781: 4777: 4770: 4750: 4743: 4734: 4732: 4724: 4718: 4714: 4704: 4702: 4687: 4681: 4664: 4654: 4652: 4644: 4638: 4634: 4624: 4622: 4615: 4609: 4602: 4595: 4581: 4564: 4557: 4543: 4539: 4532: 4518: 4507: 4476: 4469: 4459: 4457: 4449: 4443: 4426: 4399:Physical Review 4395: 4391: 4386:on 6 July 2007. 4376: 4372: 4357: 4338: 4334: 4324: 4322: 4313: 4312: 4308: 4298: 4296: 4287: 4286: 4282: 4242: 4238: 4228: 4226: 4217: 4216: 4212: 4202: 4200: 4192: 4191: 4184: 4169: 4165: 4158: 4136: 4132: 4093: 4089: 4077: 4071: 4067: 4046: 4045: 4041: 4008: 4004: 3994: 3992: 3960: 3956: 3946: 3944: 3914: 3907: 3891: 3887: 3874: 3873: 3866: 3850: 3844: 3835: 3828: 3812: 3805: 3796: 3794: 3786: 3785: 3781: 3774: 3750: 3743: 3733: 3731: 3724: 3720: 3691:Physical Review 3683: 3674: 3661: 3660: 3656: 3647: 3645: 3637: 3636: 3632: 3623: 3621: 3613: 3612: 3608: 3603: 3598: 3597: 3592: 3585: 3580: 3573: 3568: 3564: 3558: 3551: 3545: 3534: 3529: 3492: 3485: 3482: 3452: 3404: 3368: 3330: 3292: 3254: 3251:Ring Cyclotron 3216: 3178: 3146:Alpha particles 3129: 3094: 3049: 2993: 2954: 2898:medical imaging 2894: 2889: 2880:nuclear physics 2876: 2859: 2848: 2839: 2831: 2820: 2819:Heavy ion beams 2811: 2803: 2791: 2777: 2769: 2756: 2743: 2732:nonrelativistic 2727: 2719: 2717:Cyclotron types 2710:(red, at right) 2694: 2692:Classifications 2686:strong focusing 2678: 2672: 2642: 2628: 2624: 2623: 2614: 2597: 2592: 2588: 2587: 2585: 2581: 2575: 2571: 2569: 2552: 2549: 2548: 2534: 2530: 2526: 2522: 2515: 2486: 2472: 2468: 2467: 2458: 2444: 2438: 2434: 2432: 2428: 2427: 2425: 2418: 2413: 2396: 2393: 2392: 2366: 2363: 2362: 2359: 2353: 2334: 2302: 2258: 2209: 2176: 2164: 2154: 2152: 2148:field strength 2147: 2130: 2109: 2095: 2091: 2090: 2081: 2067: 2061: 2057: 2055: 2051: 2050: 2041: 2024: 2019: 2015: 2014: 2012: 2009: 2008: 1977: 1974: 1973: 1946: 1942: 1930: 1926: 1924: 1917: 1911: 1907: 1905: 1892: 1882: 1878: 1874: 1872: 1859: 1849: 1845: 1838: 1836: 1828: 1825: 1824: 1804: 1803: 1794: 1790: 1786: 1778: 1776: 1769: 1763: 1762: 1753: 1749: 1739: 1731: 1729: 1722: 1715: 1713: 1710: 1709: 1679: 1665: 1661: 1660: 1648: 1636: 1632: 1620: 1612: 1609: 1608: 1585: 1577: 1574: 1573: 1550: 1546: 1544: 1541: 1540: 1514: 1510: 1509: 1494: 1490: 1477: 1473: 1471: 1459: 1445: 1441: 1440: 1427: 1423: 1421: 1413: 1410: 1409: 1388: 1364: 1344: 1335: 1308: 1298: 1282: 1280: 1263: 1260: 1259: 1222: 1219: 1218: 1217:turns will be: 1214: 1211: 1207: 1197:Fermat's spiral 1189: 1154: 1150: 1146: 1139: 1135: 1129: 1125: 1115: 1113: 1105: 1102: 1101: 1080: 1077: 1076: 1060: 1057: 1056: 1035: 1031: 1029: 1026: 1025: 1008: 1004: 1002: 999: 998: 982: 979: 978: 962: 959: 958: 939: 925: 921: 920: 908: 894: 890: 889: 880: 876: 872: 865: 861: 855: 851: 841: 839: 826: 824: 821: 820: 815: 805: 782: 775: 771: 765: 761: 755: 751: 750: 748: 739: 735: 722: 714: 711: 710: 704: 675: 673: 665: 662: 661: 633: 628: 620: 617: 616: 611:circular motion 599: 597:Particle energy 590: 586: 582: 578: 552: 544: 542: 534: 531: 530: 506:radio frequency 488: 478: 468: 460: 436: 428: 417: 403: 401: 398: 397: 359: 346: 338:superconducting 315:Heereswaffenamt 271: 256: 151: 76:Ernest Lawrence 47: 35: 28: 23: 22: 15: 12: 11: 5: 5872: 5862: 5861: 5856: 5851: 5846: 5841: 5827: 5826: 5816: 5805: 5802: 5801: 5800: 5794: 5789:– Students at 5784: 5777: 5771: 5760: 5757: 5755: 5754:External links 5752: 5751: 5750: 5725: 5705: 5658: 5655: 5652: 5651: 5644: 5626: 5608: 5583: 5557: 5532: 5496: 5472: 5442: 5416: 5398: 5379: 5361: 5342:(4): 171–177. 5326: 5274: 5260: 5238: 5231: 5211: 5184:(5): 487–491. 5164: 5157: 5140: 5119: 5093: 5068: 5045: 5030: 4981: 4958: 4951: 4930: 4923: 4903: 4858: 4834: 4827: 4809: 4775: 4768: 4762:. p. 14. 4741: 4712: 4662: 4632: 4600: 4593: 4562: 4555: 4537: 4530: 4505: 4467: 4424: 4389: 4370: 4355: 4332: 4306: 4280: 4236: 4210: 4182: 4163: 4156: 4148:Addison Wesley 4130: 4087: 4065: 4062:on 2012-05-27. 4039: 4020:(4): 387–406. 4002: 3954: 3928:(3): 102–104. 3905: 3885: 3864: 3833: 3826: 3803: 3792:nobelprize.org 3779: 3772: 3741: 3718: 3672: 3654: 3643:nobelprize.org 3630: 3605: 3604: 3602: 3599: 3596: 3595: 3583: 3571: 3562: 3549: 3531: 3530: 3528: 3525: 3524: 3523: 3517: 3511: 3505: 3498: 3497: 3494:Physics portal 3481: 3478: 3451: 3448: 3403: 3400: 3397: 3396: 3394: 3391: 3388: 3385: 3382: 3379: 3376: 3366: 3359: 3358: 3356: 3353: 3350: 3347: 3344: 3341: 3338: 3337:United States 3328: 3321: 3320: 3318: 3315: 3312: 3309: 3306: 3303: 3300: 3290: 3283: 3282: 3280: 3277: 3274: 3271: 3268: 3265: 3262: 3252: 3245: 3244: 3242: 3239: 3236: 3233: 3230: 3227: 3224: 3223:United States 3214: 3207: 3206: 3204: 3201: 3198: 3195: 3192: 3189: 3186: 3176: 3169: 3168: 3166: 3159: 3156: 3153: 3143: 3140: 3137: 3136:United States 3127: 3123: 3122: 3120: 3117: 3114: 3111: 3108: 3105: 3102: 3101:United States 3092: 3088: 3087: 3082: 3079: 3076: 3073: 3068: 3063: 3060: 3057: 3048: 3045: 2992: 2989: 2977:proton therapy 2953: 2950: 2922:technetium-99m 2893: 2890: 2888: 2885: 2875: 2874:Basic research 2872: 2858: 2855: 2854: 2853: 2849: 2846: 2844: 2840: 2837: 2830: 2827: 2826: 2825: 2821: 2818: 2816: 2812: 2809: 2807: 2804: 2801: 2790: 2787: 2786: 2785: 2778: 2775: 2773: 2770: 2767: 2765: 2757: 2754: 2752: 2744: 2741: 2739: 2728: 2725: 2718: 2715: 2693: 2690: 2674:Main article: 2671: 2668: 2645: 2640: 2635: 2632: 2627: 2622: 2617: 2612: 2606: 2603: 2600: 2596: 2591: 2584: 2578: 2574: 2568: 2565: 2562: 2559: 2556: 2514: 2511: 2489: 2484: 2479: 2476: 2471: 2466: 2461: 2456: 2450: 2447: 2441: 2437: 2431: 2424: 2421: 2417: 2412: 2409: 2406: 2403: 2400: 2370: 2355:Main article: 2352: 2349: 2346: 2345: 2342: 2339: 2336: 2331: 2326: 2323: 2317: 2316: 2313: 2310: 2307: 2299: 2298:Electrostatic 2296: 2293: 2287: 2286: 2283: 2280: 2277: 2274: 2273:Electrostatic 2271: 2268: 2262: 2261: 2255: 2254: 2251: 2248: 2245: 2242: 2241:Electrostatic 2239: 2236: 2230: 2229: 2226: 2223: 2220: 2217: 2216:Electrostatic 2214: 2211: 2205: 2204: 2201: 2198: 2195: 2192: 2187: 2184: 2180: 2179: 2173: 2172: 2169: 2166: 2161: 2157: 2156: 2149: 2144: 2141: 2138: 2129: 2126: 2112: 2107: 2102: 2099: 2094: 2089: 2084: 2079: 2073: 2070: 2064: 2060: 2054: 2049: 2044: 2039: 2033: 2030: 2027: 2023: 2018: 1996: 1993: 1990: 1987: 1984: 1981: 1952: 1949: 1945: 1941: 1936: 1933: 1929: 1923: 1920: 1914: 1910: 1904: 1898: 1895: 1890: 1885: 1881: 1877: 1871: 1865: 1862: 1857: 1852: 1848: 1844: 1841: 1835: 1832: 1797: 1793: 1789: 1784: 1781: 1775: 1772: 1770: 1768: 1765: 1764: 1756: 1752: 1748: 1745: 1742: 1737: 1734: 1728: 1725: 1723: 1721: 1718: 1717: 1704: 1703: 1700:Lorentz factor 1682: 1677: 1672: 1669: 1664: 1659: 1656: 1652: 1647: 1639: 1635: 1631: 1628: 1624: 1619: 1616: 1606: 1592: 1589: 1584: 1581: 1571: 1553: 1549: 1523: 1517: 1513: 1508: 1505: 1497: 1493: 1489: 1486: 1480: 1476: 1470: 1462: 1457: 1452: 1449: 1444: 1439: 1436: 1430: 1426: 1420: 1417: 1401:Lorentz factor 1393:speed of light 1387: 1384: 1376:Lorentz factor 1363: 1360: 1343: 1340: 1334: 1331: 1312: 1304: 1301: 1295: 1292: 1289: 1286: 1279: 1276: 1273: 1270: 1267: 1247: 1244: 1241: 1238: 1235: 1232: 1229: 1226: 1209: 1188: 1185: 1157: 1153: 1149: 1142: 1138: 1132: 1128: 1124: 1121: 1118: 1112: 1109: 1084: 1064: 1038: 1034: 1011: 1007: 986: 966: 942: 937: 932: 929: 924: 919: 916: 911: 906: 901: 898: 893: 883: 879: 875: 868: 864: 858: 854: 850: 847: 844: 838: 833: 830: 814: 811: 788: 785: 778: 774: 768: 764: 758: 754: 747: 742: 738: 734: 729: 726: 721: 718: 688: 684: 681: 678: 672: 669: 642: 639: 636: 632: 627: 624: 598: 595: 561: 558: 555: 550: 547: 541: 538: 475:electric field 446: 443: 439: 435: 431: 427: 424: 420: 416: 413: 410: 406: 371:vacuum chamber 358: 355: 345: 342: 254:Vitaly Khlopin 208:arc converters 150: 147: 115:electric field 105:, such as the 92:electric field 88:magnetic field 26: 9: 6: 4: 3: 2: 5871: 5860: 5857: 5855: 5852: 5850: 5847: 5845: 5842: 5840: 5837: 5836: 5834: 5824: 5820: 5817: 5815: 5811: 5808: 5807: 5798: 5795: 5792: 5788: 5785: 5782: 5778: 5775: 5772: 5770: 5766: 5763: 5762: 5748: 5736:on 2009-05-05 5735: 5731: 5726: 5723: 5717: 5716: 5711: 5706: 5702: 5698: 5693: 5688: 5684: 5680: 5677:(11): 30–31. 5676: 5672: 5671: 5670:Physics Today 5666: 5661: 5660: 5647: 5645:0-918432-68-5 5641: 5637: 5630: 5623:. p. 91. 5622: 5618: 5612: 5597: 5593: 5592:"Synchrotron" 5587: 5571: 5567: 5561: 5546: 5542: 5536: 5522:on 2012-07-10 5518: 5514: 5507: 5500: 5486: 5482: 5476: 5460: 5453: 5446: 5431: 5427: 5424:Koch, Geoff. 5420: 5412: 5408: 5402: 5394: 5390: 5383: 5375: 5371: 5365: 5357: 5353: 5349: 5345: 5341: 5337: 5330: 5322: 5318: 5313: 5308: 5304: 5300: 5296: 5292: 5288: 5281: 5279: 5263: 5261:9789201631190 5257: 5250: 5249: 5242: 5234: 5228: 5224: 5223: 5215: 5207: 5203: 5199: 5195: 5191: 5187: 5183: 5179: 5175: 5168: 5160: 5154: 5150: 5144: 5136: 5135: 5130: 5123: 5107: 5103: 5097: 5082: 5081:www.triumf.ca 5078: 5072: 5061: 5060: 5052: 5050: 5041: 5034: 5026: 5022: 5017: 5012: 5008: 5004: 5001:(2): 02B909. 5000: 4996: 4992: 4985: 4974: 4973: 4965: 4963: 4954: 4948: 4944: 4937: 4935: 4926: 4924:9789810235000 4920: 4916: 4915: 4907: 4899: 4895: 4891: 4887: 4883: 4879: 4875: 4871: 4870: 4862: 4854: 4853: 4845: 4838: 4830: 4828:9781119512721 4824: 4820: 4813: 4798: 4794: 4791:: 177 Pages. 4790: 4786: 4779: 4771: 4765: 4761: 4757: 4756: 4748: 4746: 4730: 4723: 4716: 4701: 4697: 4693: 4686: 4679: 4677: 4675: 4673: 4671: 4669: 4667: 4650: 4643: 4636: 4621: 4614: 4607: 4605: 4596: 4594:9780198508298 4590: 4586: 4579: 4577: 4575: 4573: 4571: 4569: 4567: 4558: 4556:9780471551638 4552: 4548: 4541: 4533: 4531:9789812779601 4527: 4523: 4516: 4514: 4512: 4510: 4501: 4497: 4493: 4489: 4485: 4481: 4474: 4472: 4455: 4448: 4441: 4439: 4437: 4435: 4433: 4431: 4429: 4420: 4416: 4412: 4408: 4404: 4400: 4393: 4385: 4381: 4374: 4366: 4362: 4358: 4352: 4348: 4347: 4342: 4336: 4321:on 2011-04-26 4320: 4316: 4310: 4295:on 2011-04-26 4294: 4290: 4284: 4277: 4273: 4269: 4265: 4261: 4257: 4253: 4252: 4247: 4240: 4224: 4220: 4214: 4199: 4195: 4189: 4187: 4179:(4): 397–398. 4178: 4174: 4167: 4159: 4153: 4149: 4144: 4143: 4134: 4126: 4122: 4118: 4114: 4110: 4106: 4102: 4098: 4091: 4083: 4076: 4069: 4061: 4057: 4053: 4049: 4043: 4035: 4031: 4027: 4023: 4019: 4016:(in German). 4015: 4014: 4006: 3990: 3985: 3981: 3977: 3974:(10): 25–28. 3973: 3969: 3968:Physics Today 3965: 3958: 3943: 3939: 3935: 3931: 3927: 3923: 3922:Physics Today 3919: 3912: 3910: 3902: 3898: 3894: 3889: 3881: 3877: 3871: 3869: 3861:. p. 12. 3860: 3856: 3849: 3842: 3840: 3838: 3829: 3827:9781133712749 3823: 3819: 3818: 3810: 3808: 3793: 3789: 3783: 3775: 3769: 3765: 3761: 3757: 3756: 3748: 3746: 3729: 3722: 3713: 3708: 3704: 3700: 3696: 3692: 3688: 3681: 3679: 3677: 3669: 3664: 3658: 3644: 3640: 3634: 3620: 3616: 3610: 3606: 3590: 3588: 3578: 3576: 3566: 3556: 3554: 3543: 3541: 3539: 3537: 3532: 3521: 3518: 3515: 3512: 3509: 3506: 3503: 3500: 3499: 3495: 3489: 3484: 3477: 3475: 3471: 3469: 3463: 3461: 3457: 3447: 3444: 3439: 3437: 3433: 3428: 3424: 3419: 3417: 3413: 3409: 3395: 3392: 3389: 3386: 3383: 3380: 3377: 3372: 3367: 3364: 3360: 3357: 3354: 3351: 3348: 3345: 3342: 3339: 3334: 3329: 3326: 3322: 3319: 3316: 3313: 3310: 3307: 3304: 3301: 3296: 3291: 3288: 3284: 3281: 3278: 3275: 3272: 3269: 3266: 3263: 3258: 3253: 3250: 3246: 3243: 3240: 3237: 3234: 3231: 3228: 3225: 3220: 3215: 3212: 3208: 3205: 3202: 3199: 3196: 3193: 3190: 3187: 3182: 3177: 3174: 3170: 3167: 3164: 3160: 3157: 3154: 3151: 3147: 3144: 3141: 3138: 3133: 3128: 3124: 3121: 3118: 3115: 3112: 3109: 3106: 3103: 3098: 3093: 3089: 3052: 3044: 3042: 3038: 3034: 3029: 3026: 3022: 3017: 3014: 3005: 3002: 2997: 2988: 2984: 2982: 2978: 2974: 2970: 2965: 2963: 2959: 2949: 2947: 2943: 2939: 2935: 2931: 2927: 2924:are used for 2923: 2919: 2915: 2911: 2907: 2903: 2899: 2884: 2881: 2868: 2863: 2850: 2841: 2835: 2834: 2822: 2813: 2805: 2799: 2798: 2796: 2783: 2779: 2771: 2763: 2758: 2750: 2745: 2737: 2733: 2729: 2723: 2722: 2711: 2707: 2703: 2698: 2689: 2687: 2683: 2677: 2667: 2663: 2643: 2638: 2633: 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