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173-554: The design of a linac depends on the type of particle that is being accelerated: electrons , protons or ions. Linacs range in size from a cathode-ray tube (which is a type of linac) to the 3.2-kilometre-long (2.0 mi) linac at the SLAC National Accelerator Laboratory in Menlo Park, California . In 1924, Gustav Ising published the first description of a linear particle accelerator using

346-491: A Radio-frequency quadrupole (RFQ) stage from injection at 50kVdC to ~5MeV bunches, a Side Coupled Drift Tube Linac (SCDTL) to accelerate from 5Mev to ~ 40MeV and a Cell Coupled Linac (CCL) stage final, taking the output to 200-230MeV. Each stage is optimised to allow close coupling and synchronous operation during the beam energy build-up. The project aim is to make proton therapy a more accessible mainstream medicine as an alternative to existing radio therapy. The higher

519-404: A de Broglie wave in the manner of light . That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. The corpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment. The wave-like nature of light is displayed, for example, when a beam of light

692-550: A Little Linac model kit, containing 82 building blocks, was developed for children undergoing radiotherapy treatment for cancer. The hope is that building the model will alleviate some of the stress experienced by the child before undergoing treatment by helping them to understand what the treatment entails. The kit was developed by Professor David Brettle, Institute of Physics and Engineering in Medicine (IPEM) in collaboration with manufacturers Best-Lock Ltd. The model can be seen at

865-431: A beam line length reduction from some tens of metres to a few cm is quite possible. The LIGHT program (Linac for Image-Guided Hadron Therapy) hopes to create a design capable of accelerating protons to 200MeV or so for medical use over a distance of a few tens of metres, by optimising and nesting existing accelerator techniques The current design (2020) uses the highest practical bunch frequency (currently ~ 3 GHz) for

1038-426: A cavity due to wakefields can be complex and depends strongly on the specific accelerator mode of operation. For the straightforward case of a storage ring with repetitive particle bunches spaced by time interval T b and a bunch length much shorter than the wavelength of a given mode, the long term steady state wakefield voltage presented to the beam by the mode is given by where: As an example calculation, let

1211-648: A charged droplet of oil from falling as a result of gravity. This device could measure the electric charge from as few as 1–150 ions with an error margin of less than 0.3%. Comparable experiments had been done earlier by Thomson's team, using clouds of charged water droplets generated by electrolysis, and in 1911 by Abram Ioffe , who independently obtained the same result as Millikan using charged microparticles of metals, then published his results in 1913. However, oil drops were more stable than water drops because of their slower evaporation rate, and thus more suited to precise experimentation over longer periods of time. Around

1384-408: A computer program that solves for the fields. In the equation for V wake , the ratio R / Q o serves as a good comparative measure of wakefield amplitude for various cavity shapes, since the other terms are typically dictated by the application and are fixed. Mathematically, where relations defined above have been used. R / Q o is then a parameter that factors out cavity dissipation and

1557-457: A faster speed each time they pass between electrodes; there is little electric field inside the electrodes so the particles travel at a constant speed within each electrode. The particles are injected at the right time so that the oscillating voltage differential between electrodes is maximum as the particles cross each gap. If the peak voltage applied between the electrodes is V p {\displaystyle V_{p}} volts, and

1730-419: A few MeV. An advantageous alternative here, however, is a progressive wave, a traveling wave. The phase velocity the traveling wave must be roughly equal to the particle speed. Therefore, this technique is only suitable when the particles are almost at the speed of light, so that their speed only increases very little. The development of high-frequency oscillators and power amplifiers from the 1940s, especially

1903-407: A few lower-frequency dipole modes are excited by charged particle beam wakefields, all generally denoted higher order modes (HOMs). These modes serve no useful purpose for accelerator particle beam dynamics, only giving rise to beam instabilities, and are best heavily damped to have as low a Q L as possible. The damping is accomplished by preferentially allowing dipole and all HOMs to leak out of

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2076-465: A force given by the Lorentz force law: where q {\displaystyle q} is the charge on the particle, E → {\displaystyle {\vec {E}}} is the electric field, v → {\displaystyle {\vec {v}}} is the particle velocity, and B → {\displaystyle {\vec {B}}}

2249-410: A fourth state of matter in which the mean free path of the particles is so long that collisions may be ignored. In 1883, not yet well-known German physicist Heinrich Hertz tried to prove that cathode rays are electrically neutral and got what he interpreted as a confident absence of deflection in electrostatic, as opposed to magnetic, field. However, as J. J. Thomson explained in 1897, Hertz placed

2422-494: A friction that slows the electron. This force is caused by a back-reaction of the electron's own field upon itself. Photons mediate electromagnetic interactions between particles in quantum electrodynamics . An isolated electron at a constant velocity cannot emit or absorb a real photon; doing so would violate conservation of energy and momentum . Instead, virtual photons can transfer momentum between two charged particles. This exchange of virtual photons, for example, generates

2595-468: A given net power consumption when including refrigeration power for SRF. The R / Q o for the SRF cavity is 15 times less than the normal-conducting version, and thus less beam-instability susceptible. This one of the main reasons such SRF cavities are chosen for use in high-current storage rings. In addition to the fundamental accelerating TM 010 mode of an RF cavity, numerous higher frequency modes and

2768-469: A good electrical conductor – and operated near room temperature with exterior water cooling to remove the heat generated by the electrical loss in the cavity. In the past two decades, however, accelerator facilities have increasingly found superconducting cavities to be more suitable (or necessary) for their accelerators than normal-conducting copper versions. The motivation for using superconductors in RF cavities

2941-415: A group of particles into the first electrode once each cycle of the voltage, when the charge on the electrode is opposite to the charge on the particles. Each time the particle bunch passes through an electrode, the oscillating voltage changes polarity, so when the particles reach the gap between electrodes the electric field is in the correct direction to accelerate them. Therefore, the particles accelerate to

3114-560: A half-integer value, expressed in units of the reduced Planck constant , ħ . Being fermions , no two electrons can occupy the same quantum state , per the Pauli exclusion principle . Like all elementary particles, electrons exhibit properties of both particles and waves : They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have

3287-409: A horizontal waveguide loaded by a series of discs. The 1947 accelerator had an energy of 6 MeV. Over time, electron acceleration at the SLAC National Accelerator Laboratory would extend to a size of 2 miles (3.2 km) and an output energy of 50 GeV. As linear accelerators were developed with higher beam currents, using magnetic fields to focus proton and heavy ion beams presented difficulties for

3460-429: A lower mass and hence a longer de Broglie wavelength for a given energy. Electrons play an essential role in numerous physical phenomena, such as electricity , magnetism , chemistry , and thermal conductivity ; they also participate in gravitational , electromagnetic , and weak interactions . Since an electron has charge, it has a surrounding electric field ; if that electron is moving relative to an observer,

3633-448: A magnetic field of 0.5 Oe (40 A/m) and would produce a residual surface resistance in a superconductor that is orders of magnitude greater than the BCS resistance, rendering the superconductor too lossy for practical use. For this reason, superconducting cavities are surrounded by magnetic shielding to reduce the field permeating the cavity to typically <10 mOe (0.8 A/m). Using

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3806-464: A model of the electron – the Dirac equation , consistent with relativity theory, by applying relativistic and symmetry considerations to the hamiltonian formulation of the quantum mechanics of the electro-magnetic field. In order to resolve some problems within his relativistic equation, Dirac developed in 1930 a model of the vacuum as an infinite sea of particles with negative energy, later dubbed

3979-456: A particle with a positive charge, such as the proton, and a repulsive force on a particle with a negative charge. The strength of this force in nonrelativistic approximation is determined by Coulomb's inverse square law . When an electron is in motion, it generates a magnetic field . The Ampère–Maxwell law relates the magnetic field to the mass motion of electrons (the current ) with respect to an observer. This property of induction supplies

4152-439: A precise alignment of their components through the use of servo systems guided by a laser beam. Various new concepts are in development as of 2021. The primary goal is to make linear accelerators cheaper, with better focused beams, higher energy or higher beam current. Induction linear accelerators use the electric field induced by a time-varying magnetic field for acceleration—like the betatron . The particle beam passes through

4325-399: A resonant cavity to produce complex electric fields. These fields provide simultaneous acceleration and focusing to injected particle beams. Beginning in the 1960s, scientists at Stanford and elsewhere began to explore the use of superconducting radio frequency cavities for particle acceleration. Superconducting cavities made of niobium alloys allow for much more efficient acceleration, as

4498-468: A result. The development of the strong focusing principle in the early 1950s led to the installation of focusing quadrupole magnets inside the drift tubes, allowing for longer and thus more powerful linacs. Two of the earliest examples of Alvarez linacs with strong focusing magnets were built at CERN and Brookhaven National Laboratory . In 1947, at about the same time that Alvarez was developing his linac concept for protons, William Hansen constructed

4671-541: A series of accelerating gaps. Particles would proceed down a series of tubes. At a regular frequency, an accelerating voltage would be applied across each gap. As the particles gained speed while the frequency remained constant, the gaps would be spaced farther and farther apart, in order to ensure the particle would see a voltage applied as it reached each gap. Ising never successfully implemented this design. Rolf Wideroe discovered Ising's paper in 1927, and as part of his PhD thesis he built an 88-inch long, two gap version of

4844-408: A series of ring-shaped ferrite cores standing one behind the other, which are magnetized by high-current pulses, and in turn each generate an electrical field strength pulse along the axis of the beam direction. Induction linear accelerators are considered for short high current pulses from electrons but also from heavy ions. The concept goes back to the work of Nicholas Christofilos . Its realization

5017-553: A single electron. This prohibition against more than one electron occupying the same quantum energy state became known as the Pauli exclusion principle . The physical mechanism to explain the fourth parameter, which had two distinct possible values, was provided by the Dutch physicists Samuel Goudsmit and George Uhlenbeck . In 1925, they suggested that an electron, in addition to the angular momentum of its orbit, possesses an intrinsic angular momentum and magnetic dipole moment . This

5190-414: A small energy loss. The BCS resistance for niobium can be approximated when the temperature is less than half of niobium's superconducting critical temperature , T < T c /2, by where: Note that for superconductors, the BCS resistance increases quadratically with frequency, ~ f   , whereas for normal conductors the surface resistance increases as the root of frequency, ~√ f . For this reason,

5363-482: A solution that determined the location of an electron over time, this wave equation also could be used to predict the probability of finding an electron near a position, especially a position near where the electron was bound in space, for which the electron wave equations did not change in time. This approach led to a second formulation of quantum mechanics (the first by Heisenberg in 1925), and solutions of Schrödinger's equation, like Heisenberg's, provided derivations of

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5536-611: A substantially higher fraction of the input power could be applied to the beam rather than lost to heat. Some of the earliest superconducting linacs included the Superconducting Linear Accelerator (for electrons) at Stanford and the Argonne Tandem Linear Accelerator System (for protons and heavy ions) at Argonne National Laboratory . When a charged particle is placed in an electromagnetic field it experiences

5709-437: A surplus of the charge carrier, and which situation was a deficit. Between 1838 and 1851, British natural philosopher Richard Laming developed the idea that an atom is composed of a core of matter surrounded by subatomic particles that had unit electric charges . Beginning in 1846, German physicist Wilhelm Eduard Weber theorized that electricity was composed of positively and negatively charged fluids, and their interaction

5882-419: Is not to achieve a net power saving, but rather to increase the quality of the particle beam being accelerated. Though superconductors have little AC electrical resistance, the little power they do dissipate is radiated at very low temperatures, typically in a liquid helium bath at 1.6 K to 4.5 K, and maintaining such low temperatures takes a lot of energy. The refrigeration power required to maintain

6055-435: Is a subatomic particle with a negative one elementary electric charge . Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton . Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin ) of

6228-407: Is a challenging problem of modern theoretical physics. The admission of the hypothesis of a finite radius of the electron is incompatible to the premises of the theory of relativity. On the other hand, a point-like electron (zero radius) generates serious mathematical difficulties due to the self-energy of the electron tending to infinity. Observation of a single electron in a Penning trap suggests

6401-467: Is a combination of the words electr ic and i on . The suffix - on which is now used to designate other subatomic particles, such as a proton or neutron, is in turn derived from electron. While studying electrical conductivity in rarefied gases in 1859, the German physicist Julius Plücker observed the radiation emitted from the cathode caused phosphorescent light to appear on the tube wall near

6574-499: Is accelerated. A linear particle accelerator consists of the following parts: As shown in the animation, the oscillating voltage applied to alternate cylindrical electrodes has opposite polarity (180° out of phase ), so adjacent electrodes have opposite voltages. This creates an oscillating electric field (E) in the gap between each pair of electrodes, which exerts force on the particles when they pass through, imparting energy to them by accelerating them. The particle source injects

6747-496: Is actually smaller than its true value, and the charge decreases with increasing distance from the electron. This polarization was confirmed experimentally in 1997 using the Japanese TRISTAN particle accelerator. Virtual particles cause a comparable shielding effect for the mass of the electron. The interaction with virtual particles also explains the small (about 0.1%) deviation of the intrinsic magnetic moment of

6920-491: Is also independent of cavity size, it is constant as a cavity shape is scaled to change its frequency. As an example of the above parameters, a typical 9-cell SRF cavity for the International Linear Collider (a.k.a. a TESLA cavity) would have G =270 Ω and R s = 10 nΩ, giving Q o =2.7×10 . The critical parameter for SRF cavities in the above equations is the surface resistance R s , and

7093-592: Is analogous to the rotation of the Earth on its axis as it orbits the Sun. The intrinsic angular momentum became known as spin , and explained the previously mysterious splitting of spectral lines observed with a high-resolution spectrograph ; this phenomenon is known as fine structure splitting. In his 1924 dissertation Recherches sur la théorie des quanta (Research on Quantum Theory), French physicist Louis de Broglie hypothesized that all matter can be represented as

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7266-479: Is approximately 9.109 × 10  kg , or 5.489 × 10   Da . Due to mass–energy equivalence , this corresponds to a rest energy of 0.511 MeV (8.19 × 10  J) . The ratio between the mass of a proton and that of an electron is about 1836. Astronomical measurements show that the proton-to-electron mass ratio has held the same value, as is predicted by the Standard Model, for at least half

7439-411: Is commonplace for a 1.3 GHz niobium SRF resonant cavity at 1.8  kelvins to obtain a quality factor of Q =5×10 . Such a very high Q resonator stores energy with very low loss and narrow bandwidth . These properties can be exploited for a variety of applications, including the construction of high-performance particle accelerator structures. The amount of loss in an SRF resonant cavity

7612-402: Is converted into heat. In an energy recovery linac (ERL), the accelerated in resonators and, for example, in undulators . The electrons used are fed back through the accelerator, out of phase by 180 degrees. They therefore pass through the resonators in the decelerating phase and thus return their remaining energy to the field. The concept is comparable to the hybrid drive of motor vehicles, where

7785-401: Is highly dependent on progress in the development of more suitable ferrite materials. With electrons, pulse currents of up to 5 kiloamps at energies up to 5 MeV and pulse durations in the range of 20 to 300 nanoseconds were achieved. In previous electron linear accelerators, the accelerated particles are used only once and then fed into an absorber (beam dump) , in which their residual energy

7958-426: Is in particle accelerators . Accelerators typically use resonant RF cavities formed from or coated with superconducting materials. Electromagnetic fields are excited in the cavity by coupling in an RF source with an antenna. When the RF fed by the antenna is the same as that of a cavity mode, the resonant fields build to high amplitudes. Charged particles passing through apertures in the cavity are then accelerated by

8131-455: Is in existence, the Coulomb force from the ambient electric field surrounding an electron causes a created positron to be attracted to the original electron, while a created electron experiences a repulsion. This causes what is called vacuum polarization . In effect, the vacuum behaves like a medium having a dielectric permittivity more than unity . Thus the effective charge of an electron

8304-424: Is necessary to use groups of magnets to provide an overall focusing effect in both directions. Focusing along the direction of travel, also known as phase stability , is an inherent property of RF acceleration. If the particles in a bunch all reach the accelerating region during the rising phase of the oscillating field, then particles which arrive early will see slightly less voltage than the "reference" particle at

8477-468: Is not followed, the Q  vs  E curve often shows an excessive degradation of Q o with increasing field, as shown by the " Q  slope" curve in the plot below. Finding the root causes of Q  slope phenomena is the subject of ongoing fundamental SRF research. The insight gained could lead to simpler cavity fabrication processes as well as benefit future material development efforts to find higher T c alternatives to niobium. In 2012,

8650-570: Is one of humanity's earliest recorded experiences with electricity . In his 1600 treatise De Magnete , the English scientist William Gilbert coined the Neo-Latin term electrica , to refer to those substances with property similar to that of amber which attract small objects after being rubbed. Both electric and electricity are derived from the Latin ēlectrum (also the root of

8823-407: Is passed through parallel slits thereby creating interference patterns. In 1927, George Paget Thomson and Alexander Reid discovered the interference effect was produced when a beam of electrons was passed through thin celluloid foils and later metal films, and by American physicists Clinton Davisson and Lester Germer by the reflection of electrons from a crystal of nickel . Alexander Reid, who

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8996-516: Is so minute that it is often explained with the following comparison: Galileo Galilei (1564–1642) was one of the first investigators of pendulous motion, a simple form of mechanical resonance . Had Galileo experimented with a 1 Hz resonator with a quality factor Q typical of today's SRF cavities and left it swinging in an entombed lab since the early 17th century, that pendulum would still be swinging today with about half of its original amplitude. The most common application of superconducting RF

9169-426: Is the as-yet elusive ability to consistently produce high Q cavities in high volume production, which would be required for a large linear collider . Nevertheless, for many applications the capabilities of SRF cavities provide the only solution for a host of demanding performance requirements. Several extensive treatments of SRF physics and technology are available, many of them free of charge and online. There are

9342-426: Is the magnetic field. The cross product in the magnetic field term means that static magnetic fields cannot be used for particle acceleration, as the magnetic force acts perpendicularly to the direction of particle motion. As electrostatic breakdown limits the maximum constant voltage which can be applied across a gap to produce an electric field, most accelerators use some form of RF acceleration. In RF acceleration,

9515-479: Is used to drive a series of gaps, those gaps must be placed increasingly far apart as the speed of the particle increases. This is to ensure that the particle "sees" the same phase of the oscillator's cycle as it reaches each gap. As particles asymptotically approach the speed of light, the gap separation becomes constant: additional applied force increases the energy of the particles but does not significantly alter their speed. In order to ensure particles do not escape

9688-453: Is viewed as measure of the cavity geometry's effectiveness of producing accelerating voltage per stored energy in its volume. The wakefield being proportional to R / Q o can be seen intuitively since a cavity with small beam apertures concentrates the electric field on axis and has high R / Q o , but also clips off more of the particle bunch's radiation field as deleterious wakefields. The calculation of electromagnetic field buildup in

9861-399: Is where the complex physics comes into play. For normal-conducting copper cavities operating near room temperature, R s is simply determined by the empirically measured bulk electrical conductivity σ by For copper at 300 K, σ =5.8×10  (Ω·m) and at 1.3 GHz, R s copper = 9.4 mΩ. For Type II superconductors in RF fields, R s can be viewed as

10034-583: The Chalk River Laboratories in Ontario, Canada, which still now produce most Mo-99 from highly enriched uranium could be replaced by this new process. In this way, the sub-critical loading of soluble uranium salts in heavy water with subsequent photo neutron bombardment and extraction of the target product, Mo-99, will be achieved. Electron The electron ( e , or β in nuclear reactions)

10207-461: The Dirac sea . This led him to predict the existence of a positron, the antimatter counterpart of the electron. This particle was discovered in 1932 by Carl Anderson , who proposed calling standard electrons negatrons and using electron as a generic term to describe both the positively and negatively charged variants. In 1947, Willis Lamb , working in collaboration with graduate student Robert Retherford , found that certain quantum states of

10380-703: The Jefferson Lab (US), in the Budker Institute of Nuclear Physics (Russia) and at JAEA (Japan). At the University of Mainz , an ERL called MESA is expected to begin operation in 2024. The concept of the Compact Linear Collider (CLIC) (original name CERN Linear Collider, with the same abbreviation) for electrons and positrons provides a traveling wave accelerator for energies of the order of 1 tera-electron volt (TeV). Instead of

10553-458: The Lamb shift observed in spectral lines . The Compton Wavelength shows that near elementary particles such as the electron, the uncertainty of the energy allows for the creation of virtual particles near the electron. This wavelength explains the "static" of virtual particles around elementary particles at a close distance. An electron generates an electric field that exerts an attractive force on

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10726-464: The Science Museum, London . The expected shortages of Mo-99 , and the technetium-99m medical isotope obtained from it, have also shed light onto linear accelerator technology to produce Mo-99 from non-enriched Uranium through neutron bombardment. This would enable the medical isotope industry to manufacture this crucial isotope by a sub-critical process. The aging facilities, for example

10899-476: The Standard Model of particle physics. Individual electrons can now be easily confined in ultra small ( L = 20 nm , W = 20 nm ) CMOS transistors operated at cryogenic temperature over a range of −269 °C (4  K ) to about −258 °C (15  K ). The electron wavefunction spreads in a semiconductor lattice and negligibly interacts with the valence band electrons, so it can be treated in

11072-603: The V ss wake wakefields is thus addressed differently for the fundamental accelerating mode TM 01 and all other RF modes, as described next. The complex calculations treating wakefield-related beam stability for the TM 010 mode in accelerators show that there are specific regions of phase between the beam bunches and the driven RF mode that allow stable operation at the highest possible beam currents. At some point of increasing beam current, though, just about any accelerator configuration will become unstable. As pointed out above,

11245-416: The absolute value of this function is squared , it gives the probability that a particle will be observed near a location—a probability density . Electrons are identical particles because they cannot be distinguished from each other by their intrinsic physical properties. In quantum mechanics, this means that a pair of interacting electrons must be able to swap positions without an observable change to

11418-414: The age of the universe . Electrons have an electric charge of −1.602 176 634 × 10 coulombs , which is used as a standard unit of charge for subatomic particles, and is also called the elementary charge . Within the limits of experimental accuracy, the electron charge is identical to the charge of a proton, but with the opposite sign. The electron is commonly symbolized by e , and

11591-726: The alloy of the same name ), which came from the Greek word for amber, ἤλεκτρον ( ēlektron ). In the early 1700s, French chemist Charles François du Fay found that if a charged gold-leaf is repulsed by glass rubbed with silk, then the same charged gold-leaf is attracted by amber rubbed with wool. From this and other results of similar types of experiments, du Fay concluded that electricity consists of two electrical fluids , vitreous fluid from glass rubbed with silk and resinous fluid from amber rubbed with wool. These two fluids can neutralize each other when combined. American scientist Ebenezer Kinnersley later also independently reached

11764-405: The double-slit experiment . The wave-like nature of the electron allows it to pass through two parallel slits simultaneously, rather than just one slit as would be the case for a classical particle. In quantum mechanics, the wave-like property of one particle can be described mathematically as a complex -valued function, the wave function , commonly denoted by the Greek letter psi ( ψ ). When

11937-462: The e / m ratio but did not take the step of interpreting their results as showing a new particle, while J. J. Thomson would subsequently in 1899 give estimates for the electron charge and mass as well: e  ~  6.8 × 10   esu and m  ~  3 × 10  g The name "electron" was adopted for these particles by the scientific community, mainly due to the advocation by G. F. FitzGerald , J. Larmor , and H. A. Lorentz . The term

12110-414: The muon and the tau , which are identical to the electron in charge, spin and interactions , but are more massive. Leptons differ from the other basic constituent of matter, the quarks , by their lack of strong interaction . All members of the lepton group are fermions because they all have half-odd integer spin; the electron has spin ⁠ 1 / 2 ⁠ . The invariant mass of an electron

12283-459: The spectral lines of the hydrogen atom. However, Bohr's model failed to account for the relative intensities of the spectral lines and it was unsuccessful in explaining the spectra of more complex atoms. Chemical bonds between atoms were explained by Gilbert Newton Lewis , who in 1916 proposed that a covalent bond between two atoms is maintained by a pair of electrons shared between them. Later, in 1927, Walter Heitler and Fritz London gave

12456-399: The spinon , the orbiton and the holon (or chargon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can behave as independent quasiparticles . The issue of the radius of the electron

12629-438: The "high T c " superconducting materials are suitable for RF applications. Shortcomings of these materials arise due to their underlying physics as well as their bulk mechanical properties not being amenable to fabricating accelerator cavities. However, depositing films of promising materials onto other mechanically amenable cavity materials may provide a viable option for exotic materials serving SRF applications. At present,

12802-599: The 1870s, the English chemist and physicist Sir William Crookes developed the first cathode-ray tube to have a high vacuum inside. He then showed in 1874 that the cathode rays can turn a small paddle wheel when placed in their path. Therefore, he concluded that the rays carried momentum. Furthermore, by applying a magnetic field, he was able to deflect the rays, thereby demonstrating that the beam behaved as though it were negatively charged. In 1879, he proposed that these properties could be explained by regarding cathode rays as composed of negatively charged gaseous molecules in

12975-477: The Coulomb force. Energy emission can occur when a moving electron is deflected by a charged particle, such as a proton. The deceleration of the electron results in the emission of Bremsstrahlung radiation. An inelastic collision between a photon (light) and a solitary (free) electron is called Compton scattering . This collision results in a transfer of momentum and energy between the particles, which modifies

13148-561: The Q(E) dependence on SRF cavities discovered for the first time in such a way that the Q-rise phenomenon was observed in Ti doped SRF cavity. The quality factor increases with increase in accelerating field and was explained by the presence of sharper peaks in the electronic density of states at the gap edges in doped cavities and such peaks being broadened by the rf current. Later the similar phenomenon

13321-408: The RF power creates a standing wave . Some linacs have short, vertically mounted waveguides, while higher energy machines tend to have a horizontal, longer waveguide and a bending magnet to turn the beam vertically towards the patient. Medical linacs use monoenergetic electron beams between 4 and 25 MeV, giving an X-ray output with a spectrum of energies up to and including the electron energy when

13494-465: The RF to outside of the cryostat to standard RF loads. Another approach is to place the HOM loads directly on the beampipe as hollow cylinders with RF lossy material attached to the interior surface, as shown in the adjacent image. This "beamline load" approach can be more technically challenging, since the load must absorb high RF power while preserving a high-vacuum beamline environment in close proximity to

13667-438: The SRF cavity, and then coupling them to resistive RF loads. The leaking out of undesired RF modes occurs along the beampipe, and results from a careful design of the cavity aperture shapes. The aperture shapes are tailored to keep the TM 01 mode "trapped" with high Q o inside of the cavity and allow HOMs to propagate away. The propagation of HOMs is sometimes facilitated by having a larger diameter beampipe on one side of

13840-438: The above approximations for a niobium a SRF cavity at 1.8 K, 1.3 GHz, and assuming a magnetic field of 10 mOe (0.8 A/m), the surface resistance components would be The Q o just described can be further improved by up to a factor of 2 by performing a mild vacuum bake of the cavity. Empirically, the bake seems to reduce the BCS resistance by 50%, but increases the residual resistance by 30%. The plot below shows

14013-447: The accelerating field is increased all the way up to the point of a magnetic quench field, as indicated by the "ideal" dashed line in the plot below. In reality, though, even a well prepared niobium cavity will have a Q  vs  E curve that lies beneath the ideal, as shown by the "good" curve in the plot. There are many phenomena that can occur in an SRF cavity to degrade its Q  vs  E performance, such as impurities in

14186-411: The accelerator, it is necessary to provide some form of focusing to redirect particles moving away from the central trajectory back towards the intended path. With the discovery of strong focusing , quadrupole magnets are used to actively redirect particles moving away from the reference path. As quadrupole magnets are focusing in one transverse direction and defocusing in the perpendicular direction, it

14359-420: The atmosphere. The antiparticle of the electron is called the positron ; it is identical to the electron, except that it carries electrical charge of the opposite sign. When an electron collides with a positron , both particles can be annihilated , producing gamma ray photons . The ancient Greeks noticed that amber attracted small objects when rubbed with fur. Along with lightning , this phenomenon

14532-577: The average output current is still limited.) The high density of the output makes the linac particularly attractive for use in loading storage ring facilities with particles in preparation for particle to particle collisions. The high mass output also makes the device practical for the production of antimatter particles, which are generally difficult to obtain, being only a small fraction of a target's collision products. These may then be stored and further used to study matter-antimatter annihilation. Linac-based radiation therapy for cancer treatment began with

14705-401: The beam wakefield amplitude is proportional to the cavity parameter R / Q o , so this is typically used as a comparative measure of the likelihood of TM 01 related beam instabilities. A comparison of R / Q o and R for a 500 MHz superconducting cavity and a 500 MHz normal-conducting cavity is shown below. The accelerating voltage provided by both cavities is comparable for

14878-480: The beginning of the twentieth century, it was found that under certain conditions a fast-moving charged particle caused a condensation of supersaturated water vapor along its path. In 1911, Charles Wilson used this principle to devise his cloud chamber so he could photograph the tracks of charged particles, such as fast-moving electrons. By 1914, experiments by physicists Ernest Rutherford , Henry Moseley , James Franck and Gustav Hertz had largely established

15051-455: The buildup of wakefields would be V ss wake =637× V wake . A pitfall for any accelerator cavity would be the presence of what is termed a "trapped mode". This is an HOM that does not leak out of the cavity and consequently has a Q L that can be orders of magnitude larger than used in this example. In this case, the buildup of wakefields of the trapped mode would likely cause a beam instability. The beam instability implications due to

15224-402: The cathode; and the region of the phosphorescent light could be moved by application of a magnetic field. In 1869, Plücker's student Johann Wilhelm Hittorf found that a solid body placed in between the cathode and the phosphorescence would cast a shadow upon the phosphorescent region of the tube. Hittorf inferred that there are straight rays emitted from the cathode and that the phosphorescence

15397-517: The cavity's effectiveness of providing accelerating electric field due to the influence of its shape alone, which excludes specific material wall loss. The Geometry Factor is given by and then The geometry factor is quoted for cavity designs to allow comparison to other designs independent of wall loss, since wall loss for SRF cavities can vary substantially depending on material preparation, cryogenic bath temperature, electromagnetic field level, and other highly variable parameters. The Geometry Factor

15570-454: The cavity, beyond the smaller diameter cavity iris, as seen in the SRF cavity CAD cross-section at the top of this wiki page. The larger beampipe diameter allows the HOMs to easily propagate away from the cavity to an HOM antenna or beamline absorber. The resistive load for HOMs can be implemented by having loop antennas located at apertures on the side of the beampipe, with coaxial lines routing

15743-427: The center of the bunch. Those particles will therefore receive slightly less acceleration and eventually fall behind the reference particle. Correspondingly, particles which arrive after the reference particle will receive slightly more acceleration, and will catch up to the reference as a result. This automatic correction occurs at each accelerating gap, so the bunch is refocused along the direction of travel each time it

15916-553: The charge carriers were much heavier hydrogen or nitrogen atoms. Schuster's estimates would subsequently turn out to be largely correct. In 1892 Hendrik Lorentz suggested that the mass of these particles (electrons) could be a consequence of their electric charge. While studying naturally fluorescing minerals in 1896, the French physicist Henri Becquerel discovered that they emitted radiation without any exposure to an external energy source. These radioactive materials became

16089-427: The charge on each particle is q {\displaystyle q} elementary charges , the particle gains an equal increment of energy of q V p {\displaystyle qV_{p}} electron volts when passing through each gap. Thus the output energy of the particles is electron volts, where N {\displaystyle N} is the number of accelerating electrodes in

16262-588: The concept of an indivisible quantity of electric charge to explain the chemical properties of atoms. Irish physicist George Johnstone Stoney named this charge "electron" in 1891, and J. J. Thomson and his team of British physicists identified it as a particle in 1897 during the cathode-ray tube experiment . Electrons participate in nuclear reactions , such as nucleosynthesis in stars , where they are known as beta particles . Electrons can be created through beta decay of radioactive isotopes and in high-energy collisions, for instance, when cosmic rays enter

16435-537: The cryogenic bath at low temperature in the presence of heat from small RF power dissipation is dictated by the Carnot efficiency , and can easily be comparable to the normal-conductor power dissipation of a room-temperature copper cavity. The principle motivations for using superconducting RF cavities, are: When future advances in superconducting material science allow higher superconducting critical temperatures T c and consequently higher SRF bath temperatures, then

16608-401: The de facto choice for SRF material is still pure niobium, which has a critical temperature of 9.3 K and functions as a superconductor nicely in a liquid helium bath of 4.2 K or lower, and has excellent mechanical properties. The physics of Superconducting RF can be complex and lengthy. A few simple approximations derived from the complex theories, though, can serve to provide some of

16781-430: The deflecting electrodes in a highly-conductive area of the tube, resulting in a strong screening effect close to their surface. The German-born British physicist Arthur Schuster expanded upon Crookes's experiments by placing metal plates parallel to the cathode rays and applying an electric potential between the plates. The field deflected the rays toward the positively charged plate, providing further evidence that

16954-433: The device. Where Ising had proposed a spark gap as the voltage source, Wideroe used a 25kV vacuum tube oscillator. He successfully demonstrated that he had accelerated sodium and potassium ions to an energy of 50,000 electron volts (50 keV), twice the energy they would have received if accelerated only once by the tube. By successfully accelerating a particle multiple times using the same voltage source, Wideroe demonstrated

17127-603: The dielectric strength limits the maximum acceleration that can be achieved within a certain distance. This limit can be circumvented using accelerated waves in plasma to generate the accelerating field in Kielfeld accelerators : A laser or particle beam excites an oscillation in a plasma , which is associated with very strong electric field strengths. This means that significantly (factors of 100s to 1000s ) more compact linear accelerators can possibly be built. Experiments involving high power lasers in metal vapour plasmas suggest that

17300-427: The effects of quantum mechanics ; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron. There are elementary particles that spontaneously decay into less massive particles. An example is the muon , with a mean lifetime of 2.2 × 10  seconds, which decays into an electron, a muon neutrino and an electron antineutrino . The electron, on

17473-465: The electric fields and deflected by the magnetic fields. The resonant frequency driven in SRF cavities typically ranges from 200 MHz to 3 GHz, depending on the particle species to be accelerated. The most common fabrication technology for such SRF cavities is to form thin walled (1–3 mm) shell components from high purity niobium sheets by stamping . These shell components are then welded together to form cavities. A simplified diagram of

17646-486: The electromagnetic field in the above expressions are generally not solved analytically, since the cavity boundaries rarely lie along axes of common coordinate systems. Instead, the calculations are performed by any of a variety of computer programs that solve for the fields for non-simple cavity shapes, and then numerically integrate the above expressions. An RF cavity parameter known as the Geometry Factor ranks

17819-454: The electron from the Bohr magneton (the anomalous magnetic moment ). The extraordinarily precise agreement of this predicted difference with the experimentally determined value is viewed as one of the great achievements of quantum electrodynamics . The apparent paradox in classical physics of a point particle electron having intrinsic angular momentum and magnetic moment can be explained by

17992-560: The electron has an intrinsic magnetic moment along its spin axis. It is approximately equal to one Bohr magneton , which is a physical constant that is equal to 9.274 010 0657 (29) × 10  J⋅T . The orientation of the spin with respect to the momentum of the electron defines the property of elementary particles known as helicity . The electron has no known substructure . Nevertheless, in condensed matter physics , spin–charge separation can occur in some materials. In such cases, electrons 'split' into three independent particles,

18165-438: The electrons are directed at a high-density (such as tungsten ) target. The electrons or X-rays can be used to treat both benign and malignant disease. The LINAC produces a reliable, flexible and accurate radiation beam. The versatility of LINAC is a potential advantage over cobalt therapy as a treatment tool. In addition, the device can simply be powered off when not in use; there is no source requiring heavy shielding – although

18338-456: The energy states of an electron in a hydrogen atom that were equivalent to those that had been derived first by Bohr in 1913, and that were known to reproduce the hydrogen spectrum. Once spin and the interaction between multiple electrons were describable, quantum mechanics made it possible to predict the configuration of electrons in atoms with atomic numbers greater than hydrogen. In 1928, building on Wolfgang Pauli's work, Paul Dirac produced

18511-477: The field level in the cavity should generally be as high as possible to most efficiently accelerate the beam passing through it. The Q o values described by the above calculations tend to degrade as the fields increase, which is plotted for a given cavity as a " Q  vs  E " curve, where " E " refers to the accelerating electric field of the TM 01 mode. Ideally, the cavity Q o would remain constant as

18684-448: The first high-energy particle collider was ADONE , which began operations in 1968. This device accelerated electrons and positrons in opposite directions, effectively doubling the energy of their collision when compared to striking a static target with an electron. The Large Electron–Positron Collider (LEP) at CERN , which was operational from 1989 to 2000, achieved collision energies of 209 GeV and made important measurements for

18857-583: The first patient treated in 1953 in London, UK, at the Hammersmith Hospital , with an 8 MV machine built by Metropolitan-Vickers and installed in 1952, as the first dedicated medical linac. A short while later in 1954, a 6 MV linac was installed in Stanford, USA, which began treatments in 1956. Medical linear accelerators accelerate electrons using a tuned-cavity waveguide, in which

19030-420: The first travelling-wave electron accelerator at Stanford University. Electrons are sufficiently lighter than protons that they achieve speeds close to the speed of light early in the acceleration process. As a result, "accelerating" electrons increase in energy but can be treated as having a constant velocity from an accelerator design standpoint. This allowed Hansen to use an accelerating structure consisting of

19203-406: The formation of virtual photons in the electric field generated by the electron. These photons can heuristically be thought of as causing the electron to shift about in a jittery fashion (known as zitterbewegung ), which results in a net circular motion with precession . This motion produces both the spin and the magnetic moment of the electron. In atoms, this creation of virtual photons explains

19376-445: The formation of bubbles on the surface of the cavity, which would cause mechanical perturbations. An antenna is needed in the setup to couple RF power to the cavity fields and, in turn, any passing particle beam. The cold portions of the setup need to be extremely well insulated, which is best accomplished by a vacuum vessel surrounding the helium vessel and all ancillary cold components. The full SRF cavity containment system, including

19549-489: The frequency of the acceleration voltage selected, the more individual acceleration thrusts per path length a particle of a given speed experiences, and the shorter the accelerator can therefore be overall. That is why accelerator technology developed in the pursuit of higher particle energies, especially towards higher frequencies. The linear accelerator concepts (often called accelerator structures in technical terms) that have been used since around 1950 work with frequencies in

19722-568: The full explanation of the electron-pair formation and chemical bonding in terms of quantum mechanics . In 1919, the American chemist Irving Langmuir elaborated on the Lewis's static model of the atom and suggested that all electrons were distributed in successive "concentric (nearly) spherical shells, all of equal thickness". In turn, he divided the shells into a number of cells each of which contained one pair of electrons. With this model Langmuir

19895-421: The hydrogen atom, which should have the same energy, were shifted in relation to each other; the difference came to be called the Lamb shift . About the same time, Polykarp Kusch , working with Henry M. Foley , discovered the magnetic moment of the electron is slightly larger than predicted by Dirac's theory. This small difference was later called anomalous magnetic dipole moment of the electron. This difference

20068-436: The ideal Q o not only for low field amplitudes, but up to cavity fields that are typically 75% of the magnetic field quench limit. Few cavities make it to the magnetic field quench limit since residual losses and vanishingly small defects heat up localized spots, which eventually exceed the superconducting critical temperature and lead to a thermal quench . When using superconducting RF cavities in particle accelerators,

20241-469: The ideal Q o values for a range of residual magnetic field for a baked and unbaked cavity. In general, much care and attention to detail must be exercised in the experimental setup of SRF cavities so that there is not Q o degradation due to RF losses in ancillary components, such as stainless steel vacuum flanges that are too close to the cavity's evanescent fields. However, careful SRF cavity preparation and experimental configuration have achieved

20414-419: The important parameters of SRF cavities. By way of background, some of the pertinent parameters of RF cavities are itemized as follows. A resonator's quality factor is defined by where: The energy stored in the cavity is given by the integral of field energy density over its volume, where: The power dissipated is given by the integral of resistive wall losses over its surface, where: The integrals of

20587-436: The initial stages of the accelerator. Because the magnetic force is dependent on the particle velocity, it was desirable to create a type of accelerator which could simultaneously accelerate and focus low-to-mid energy hadrons . In 1970, Soviet physicists I. M. Kapchinsky and Vladimir Teplyakov proposed the radio-frequency quadrupole (RFQ) type of accelerating structure. RFQs use vanes or rods with precisely designed shapes in

20760-491: The key elements of an SRF cavity setup is shown below. The cavity is immersed in a saturated liquid helium bath. Pumping removes helium vapor boil-off and controls the bath temperature. The helium vessel is often pumped to a pressure below helium's superfluid lambda point to take advantage of the superfluid's thermal properties. Because superfluid has very high thermal conductivity, it makes an excellent coolant. In addition, superfluids boil only at free surfaces, preventing

20933-500: The kinetic energy released during braking is made available for the next acceleration by charging a battery. The Brookhaven National Laboratory and the Helmholtz-Zentrum Berlin with the project "bERLinPro" reported on corresponding development work. The Berlin experimental accelerator uses superconducting niobium cavity resonators. In 2014, three free-electron lasers based on ERLs were in operation worldwide: in

21106-552: The klystron, was essential for these two acceleration techniques . The first larger linear accelerator with standing waves - for protons - was built in 1945/46 in the Lawrence Berkeley National Laboratory under the direction of Luis W. Alvarez . The frequency used was 200 MHz .  The first electron accelerator with traveling waves of around 2 GHz was developed a little later at Stanford University by W.W. Hansen and colleagues. In

21279-447: The light and free electrons is called Thomson scattering or linear Thomson scattering. Superconducting radio frequency Superconducting radio frequency (SRF) science and technology involves the application of electrical superconductors to radio frequency devices. The ultra-low electrical resistivity of a superconducting material allows an RF resonator to obtain an extremely high quality factor , Q . For example, it

21452-455: The machine. At speeds near the speed of light, the incremental velocity increase will be small, with the energy appearing as an increase in the mass of the particles. In portions of the accelerator where this occurs, the tubular electrode lengths will be almost constant. Additional magnetic or electrostatic lens elements may be included to ensure that the beam remains in the center of the pipe and its electrodes. Very long accelerators may maintain

21625-489: The magnetic field and the electron velocity. This centripetal force causes the electron to follow a helical trajectory through the field at a radius called the gyroradius . The acceleration from this curving motion induces the electron to radiate energy in the form of synchrotron radiation. The energy emission in turn causes a recoil of the electron, known as the Abraham–Lorentz–Dirac Force , which creates

21798-462: The magnetic field that drives an electric motor . The electromagnetic field of an arbitrary moving charged particle is expressed by the Liénard–Wiechert potentials , which are valid even when the particle's speed is close to that of light ( relativistic ). When an electron is moving through a magnetic field, it is subject to the Lorentz force that acts perpendicularly to the plane defined by

21971-469: The majority of superconducting cavity applications favor lower frequencies, <3 GHz, and normal-conducting cavity applications favor higher frequencies, >0.5 GHz, there being some overlap depending on the application. The superconductor's residual resistance arises from several sources, such as random material defects, hydrides that can form on the surface due to hot chemistry and slow cool-down, and others that are yet to be identified. One of

22144-409: The maximum power that can be imparted to electrons in a synchrotron of given size. Linacs are also capable of prodigious output, producing a nearly continuous stream of particles, whereas a synchrotron will only periodically raise the particles to sufficient energy to merit a "shot" at the target. (The burst can be held or stored in the ring at energy to give the experimental electronics time to work, but

22317-426: The negatively charged particles produced by radioactive materials, by heated materials and by illuminated materials were universal. Thomson measured m / e for cathode ray "corpuscles", and made good estimates of the charge e , leading to value for the mass m , finding a value 1400 times less massive than the least massive ion known: hydrogen. In the same year Emil Wiechert and Walter Kaufmann also calculated

22490-406: The niobium, hydrogen contamination due to excessive heat during chemistry, and a rough surface finish. After a couple decades of development, a necessary prescription for successful SRF cavity production is emerging. This includes: There remains some uncertainty as to the root cause of why some of these steps lead to success, such as the electropolish and vacuum bake. However, if this prescription

22663-1001: The observer will observe it to generate a magnetic field . Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz force law . Electrons radiate or absorb energy in the form of photons when they are accelerated. Laboratory instruments are capable of trapping individual electrons as well as electron plasma by the use of electromagnetic fields. Special telescopes can detect electron plasma in outer space. Electrons are involved in many applications, such as tribology or frictional charging, electrolysis, electrochemistry, battery technologies, electronics , welding , cathode-ray tubes , photoelectricity, photovoltaic solar panels, electron microscopes , radiation therapy , lasers , gaseous ionization detectors , and particle accelerators . Interactions involving electrons with other subatomic particles are of interest in fields such as chemistry and nuclear physics . The Coulomb force interaction between

22836-430: The other hand, is thought to be stable on theoretical grounds: the electron is the least massive particle with non-zero electric charge, so its decay would violate charge conservation . The experimental lower bound for the electron's mean lifetime is 6.6 × 10 years, at a 90% confidence level . As with all particles, electrons can act as waves. This is called the wave–particle duality and can be demonstrated using

23009-485: The other hand, with ions of this energy range, the speed also increases significantly due to further acceleration. The acceleration concepts used today for ions are always based on electromagnetic standing waves that are formed in suitable resonators . Depending on the type of particle, energy range and other parameters, very different types of resonators are used; the following sections only cover some of them. Electrons can also be accelerated with standing waves above

23182-461: The otherwise necessary numerous klystron amplifiers to generate the acceleration power, a second parallel electron linear accelerator of lower energy is to be used, which works with superconducting cavities in which standing waves are formed. High-frequency power is extracted from it at regular intervals and transmitted to the main accelerator. In this way, the very high acceleration field strength of 80 MV / m should be achieved. In cavity resonators,

23355-446: The particle travels, and the central tubes are only used to shield the particles during the decelerating portion of the oscillator's phase. Using this approach to acceleration meant that Alvarez's first linac was able to achieve proton energies of 31.5 MeV in 1947, the highest that had ever been reached at the time. The initial Alvarez type linacs had no strong mechanism for keeping the beam focused and were limited in length and energy as

23528-425: The particle traverses a series of accelerating regions, driven by a source of voltage in such a way that the particle sees an accelerating field as it crosses each region. In this type of acceleration, particles must necessarily travel in "bunches" corresponding to the portion of the oscillator's cycle where the electric field is pointing in the intended direction of acceleration. If a single oscillating voltage source

23701-409: The passing beam is analogous to a drumstick striking a drumhead and exciting many resonant mechanical modes. The beam wakefields in an RF cavity excite a subset of the spectrum of the many electromagnetic modes , including the externally driven TM 01 mode. There are then a host of beam instabilities that can occur as the repetitive particle beam passes through the RF cavity, each time adding to

23874-518: The phase shift δ=0 , which would be close to the case for the TM 01 mode by design and unfortunately likely to occur for a few HOM's. Having δ=0 (or an integer multiple of an RF mode's period, δ=n2π ) gives the worse-case wakefield build-up, where successive bunches are maximally decelerated by previous bunches' wakefields and give up even more energy than with only their "self wake". Then, taking ω o  = 2 π  500 MHz, T b =1 μs, and Q L =10 ,

24047-551: The photon, have symmetric wave functions instead. In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the same location or state. This is responsible for the Pauli exclusion principle , which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in

24220-456: The positive protons within atomic nuclei and the negative electrons without allows the composition of the two known as atoms . Ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system. The exchange or sharing of the electrons between two or more atoms is the main cause of chemical bonding . In 1838, British natural philosopher Richard Laming first hypothesized

24393-452: The positron is symbolized by e . The electron has an intrinsic angular momentum or spin of ⁠ ħ / 2 ⁠ . This property is usually stated by referring to the electron as a spin-1/2 particle. For such particles the spin magnitude is ⁠ ħ / 2 ⁠ , while the result of the measurement of a projection of the spin on any axis can only be ± ⁠ ħ / 2 ⁠ . In addition to spin,

24566-547: The proceedings of CERN accelerator schools, a scientific paper giving a thorough presentation of the many aspects of an SRF cavity to be used in the International Linear Collider , bi-annual International Conferences on RF Superconductivity held at varying global locations in odd numbered years, and tutorials presented at the conferences. A large variety of RF cavities are used in particle accelerators. Historically most have been made of copper –

24739-445: The quantifiable residual resistance contributions is due to an external magnetic field pinning magnetic fluxons in a Type II superconductor. The pinned fluxon cores create small normal-conducting regions in the niobium that can be summed to estimate their net resistance. For niobium, the magnetic field contribution to R s can be approximated by where: The Earth's nominal magnetic flux of 0.5  gauss (50 μT ) translates to

24912-523: The range from around 100 MHz to a few gigahertz (GHz) and use the electric field component of electromagnetic waves. When it comes to energies of more than a few MeV, accelerators for ions are different from those for electrons. The reason for this is the large mass difference between the particles. Electrons are already close to the speed of light , the absolute speed limit, at a few MeV; with further acceleration, as described by relativistic mechanics , almost only their energy and momentum increase. On

25085-403: The rays carried negative charge. By measuring the amount of deflection for a given electric and magnetic field , in 1890 Schuster was able to estimate the charge-to-mass ratio of the ray components. However, this produced a value that was more than a thousand times greater than what was expected, so little credence was given to his calculations at the time. This is because it was assumed that

25258-426: The reduced thermocline between the cavity and the surrounding environment could yield a significant net power savings by SRF over the normal conducting approach to RF cavities. Other issues will need to be considered with a higher bath temperature, though, such as the fact that superfluidity (which is presently exploited with liquid helium) would not be present with (for example) liquid nitrogen. At present, none of

25431-455: The same conclusion. A decade later Benjamin Franklin proposed that electricity was not from different types of electrical fluid, but a single electrical fluid showing an excess (+) or deficit (−). He gave them the modern charge nomenclature of positive and negative respectively. Franklin thought of the charge carrier as being positive, but he did not correctly identify which situation was

25604-423: The same orbit. In a simplified picture, which often tends to give the wrong idea but may serve to illustrate some aspects, every photon spends some time as a combination of a virtual electron plus its antiparticle, the virtual positron, which rapidly annihilate each other shortly thereafter. The combination of the energy variation needed to create these particles, and the time during which they exist, fall under

25777-489: The single particle formalism, by replacing its mass with the effective mass tensor . In the Standard Model of particle physics, electrons belong to the group of subatomic particles called leptons , which are believed to be fundamental or elementary particles . Electrons have the lowest mass of any charged lepton (or electrically charged particle of any type) and belong to the first generation of fundamental particles. The second and third generation contain charged leptons,

25950-435: The state of the system. The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, ψ ( r 1 , r 2 ) = − ψ ( r 2 , r 1 ) , where the variables r 1 and r 2 correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal probabilities. Bosons , such as

26123-484: The structure of an atom as a dense nucleus of positive charge surrounded by lower-mass electrons. In 1913, Danish physicist Niels Bohr postulated that electrons resided in quantized energy states, with their energies determined by the angular momentum of the electron's orbit about the nucleus. The electrons could move between those states, or orbits, by the emission or absorption of photons of specific frequencies. By means of these quantized orbits, he accurately explained

26296-504: The subject of much interest by scientists, including the New Zealand physicist Ernest Rutherford who discovered they emitted particles. He designated these particles alpha and beta , on the basis of their ability to penetrate matter. In 1900, Becquerel showed that the beta rays emitted by radium could be deflected by an electric field, and that their mass-to-charge ratio was the same as for cathode rays. This evidence strengthened

26469-447: The sudden increase of the conducting wall diameter in the transition from the small-diameter beampipe to the large hollow RF cavity. A portion of the particle's radiation field is then "clipped off" upon re-entrance into the beampipe and left behind as wakefields in the cavity. The wakefields are simply superimposed upon the externally driven accelerating fields in the cavity. The spawning of electromagnetic cavity modes as wakefields from

26642-508: The sum of the superconducting BCS resistance and temperature-independent "residual resistances", The BCS resistance derives from BCS theory . One way to view the nature of the BCS RF resistance is that the superconducting Cooper pairs , which have zero resistance for DC current, have finite mass and momentum which has to alternate sinusoidally for the AC currents of RF fields, thus giving rise to

26815-423: The term electrolion in 1881. Ten years later, he switched to electron to describe these elementary charges, writing in 1894: "... an estimate was made of the actual amount of this most remarkable fundamental unit of electricity, for which I have since ventured to suggest the name electron ". A 1906 proposal to change to electrion failed because Hendrik Lorentz preferred to keep electron . The word electron

26988-522: The threshold of detectability expressed by the Heisenberg uncertainty relation , Δ E  · Δ t  ≥  ħ . In effect, the energy needed to create these virtual particles, Δ E , can be "borrowed" from the vacuum for a period of time, Δ t , so that their product is no more than the reduced Planck constant , ħ ≈ 6.6 × 10  eV·s . Thus, for a virtual electron, Δ t is at most 1.3 × 10  s . While an electron–positron virtual pair

27161-423: The treatment room itself requires considerable shielding of the walls, doors, ceiling etc. to prevent escape of scattered radiation. Prolonged use of high powered (>18 MeV) machines can induce a significant amount of radiation within the metal parts of the head of the machine after power to the machine has been removed (i.e. they become an active source and the necessary precautions must be observed). In 2019

27334-576: The two diagrams, the curve and arrows indicate the force acting on the particles. Only at the points with the correct direction of the electric field vector, i.e. the correct direction of force, can particles absorb energy from the wave. (An increase in speed cannot be seen in the scale of these images.) The linear accelerator could produce higher particle energies than the previous electrostatic particle accelerators (the Cockcroft–Walton accelerator and Van de Graaff generator ) that were in use when it

27507-426: The upper limit of the particle's radius to be 10  meters. The upper bound of the electron radius of 10  meters can be derived using the uncertainty relation in energy. There is also a physical constant called the " classical electron radius ", with the much larger value of 2.8179 × 10  m , greater than the radius of the proton. However, the terminology comes from a simplistic calculation that ignores

27680-496: The utility of radio frequency (RF) acceleration. This type of linac was limited by the voltage sources that were available at the time, and it was not until after World War II that Luis Alvarez was able to use newly developed high frequency oscillators to design the first resonant cavity drift tube linac. An Alvarez linac differs from the Wideroe type in that the RF power is applied to the entire resonant chamber through which

27853-449: The vacuum vessel and many details not discussed here, is a cryomodule . Entry into superconducting RF technology can incur more complexity, expense, and time than normal-conducting RF cavity strategies. SRF requires chemical facilities for harsh cavity treatments, a low-particulate cleanroom for high-pressure water rinsing and assembly of components, and complex engineering for the cryomodule vessel and cryogenics. A vexing aspect of SRF

28026-487: The view that electrons existed as components of atoms. In 1897, the British physicist J. J. Thomson , with his colleagues John S. Townsend and H. A. Wilson , performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier. By 1899 he showed that their charge-to-mass ratio, e / m , was independent of cathode material. He further showed that

28199-415: The wakefield energy in a collection of modes. For a particle bunch with charge q , a length much shorter than the wavelength of a given cavity mode, and traversing the cavity at time t =0, the amplitude of the wakefield voltage left behind in the cavity in a given mode is given by where: The shunt impedance R can be calculated from the solution of the electromagnetic fields of a mode, typically by

28372-473: The wavelength of the photon by an amount called the Compton shift . The maximum magnitude of this wavelength shift is h / m e c , which is known as the Compton wavelength . For an electron, it has a value of 2.43 × 10  m . When the wavelength of the light is long (for instance, the wavelength of the visible light is 0.4–0.7 μm) the wavelength shift becomes negligible. Such interaction between

28545-563: Was Thomson's graduate student, performed the first experiments but he died soon after in a motorcycle accident and is rarely mentioned. De Broglie's prediction of a wave nature for electrons led Erwin Schrödinger to postulate a wave equation for electrons moving under the influence of the nucleus in the atom. In 1926, this equation, the Schrödinger equation , successfully described how electron waves propagated. Rather than yielding

28718-416: Was able to qualitatively explain the chemical properties of all elements in the periodic table, which were known to largely repeat themselves according to the periodic law . In 1924, Austrian physicist Wolfgang Pauli observed that the shell-like structure of the atom could be explained by a set of four parameters that defined every quantum energy state, as long as each state was occupied by no more than

28891-734: Was caused by the rays striking the tube walls. Furthermore, he also discovered that these rays are deflected by magnets just like lines of current. In 1876, the German physicist Eugen Goldstein showed that the rays were emitted perpendicular to the cathode surface, which distinguished between the rays that were emitted from the cathode and the incandescent light. Goldstein dubbed the rays cathode rays . Decades of experimental and theoretical research involving cathode rays were important in J. J. Thomson 's eventual discovery of electrons. Goldstein also experimented with double cathodes and hypothesized that one ray may repulse another, although he didn't believe that any particles might be involved. During

29064-672: Was governed by the inverse square law . After studying the phenomenon of electrolysis in 1874, Irish physicist George Johnstone Stoney suggested that there existed a "single definite quantity of electricity", the charge of a monovalent ion . He was able to estimate the value of this elementary charge e by means of Faraday's laws of electrolysis . However, Stoney believed these charges were permanently attached to atoms and could not be removed. In 1881, German physicist Hermann von Helmholtz argued that both positive and negative charges were divided into elementary parts, each of which "behaves like atoms of electricity". Stoney initially coined

29237-620: Was invented. In these machines, the particles were only accelerated once by the applied voltage, so the particle energy in electron volts was equal to the accelerating voltage on the machine, which was limited to a few million volts by insulation breakdown. In the linac, the particles are accelerated multiple times by the applied voltage, so the particle energy is not limited by the accelerating voltage. High power linacs are also being developed for production of electrons at relativistic speeds, required since fast electrons traveling in an arc will lose energy through synchrotron radiation ; this limits

29410-426: Was later explained by the theory of quantum electrodynamics , developed by Sin-Itiro Tomonaga , Julian Schwinger and Richard Feynman in the late 1940s. With the development of the particle accelerator during the first half of the twentieth century, physicists began to delve deeper into the properties of subatomic particles . The first successful attempt to accelerate electrons using electromagnetic induction

29583-415: Was made in 1942 by Donald Kerst . His initial betatron reached energies of 2.3 MeV, while subsequent betatrons achieved 300 MeV. In 1947, synchrotron radiation was discovered with a 70 MeV electron synchrotron at General Electric . This radiation was caused by the acceleration of electrons through a magnetic field as they moved near the speed of light. With a beam energy of 1.5 GeV,

29756-414: Was observed with nitrogen doping and which has been the current state-of-art cavity preparation for high performance. One of the main reasons for using SRF cavities in particle accelerators is that their large apertures result in low beam impedance and higher thresholds of deleterious beam instabilities. As a charged particle beam passes through a cavity, its electromagnetic radiation field is perturbed by

29929-413: Was originally coined by George Johnstone Stoney in 1891 as a tentative name for the basic unit of electrical charge (which had then yet to be discovered). The electron's charge was more carefully measured by the American physicists Robert Millikan and Harvey Fletcher in their oil-drop experiment of 1909, the results of which were published in 1911. This experiment used an electric field to prevent

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