linear particle accelerator linear particle accelerator a linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high speed by subjecting them to a series of oscillating electric potentials along a linear beamline. the principles for such machines were proposed by gustav ising in 1924, while the first machine that worked was constructed by rolf widerøe in 1928 at the rwth aachen university. linacs have many applications: they generate x-rays and high energy electrons for medicinal purposes in radiation therapy, serve as particle injectors for higher-energy accelerators, and are used directly to achieve the highest kinetic energy for light particles (electrons and positrons) for particle physics. the linac within the australian synchrotron uses radio waves from a series of rf cavities at the start of the linac to accelerate the electron beam in bunches to energies of 100 mev. 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. history wideroe's linac concept. the voltage from an rf source is connected to a series of tubes which shield the particle between gaps. alvarez type linac in 1924, gustav ising published the first description of a linear particle accelerator using 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, built an 88-inch long, two gap version of 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 thousand 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 the utility of radio frequency 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 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 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 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 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 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 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 allowed for much more efficient acceleration, as 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. basic principles of operation animation showing how a linear accelerator works. in this example the particles accelerated (red dots) are assumed to have a positive charge. the graph v(x) shows the electrical potential along the axis of the accelerator at each point in time. the polarity of the rf voltage reverses as the particle passes through each electrode, so when the particle crosses each gap the electric field (e, arrows) has the correct direction to accelerate it. the animation shows a single particle being accelerated each cycle; in actual linacs a large number of particles are injected and accelerated each cycle. the action is shown slowed enormously. radiofrequency acceleration when a charged particle is placed in an electromagnetic field it experiences a force given by the lorentz force law: f → = q e → + q v → × b → =q+q\times (in si units) where q is the charge on the particle, e → is the electric field, v → is the particle velocity, and b → 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 radiofrequency (rf) acceleration. in rf acceleration, 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 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.: 9-12 focusing in order to ensure particles do not escape 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 is necessary to use groups of magnets to provide an overall focusing effect in both directions. phase stability 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 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 is accelerated.: 30–52 construction and operation quadrupole magnets surrounding the linac of the australian synchrotron are used to help focus the electron beam building covering the 2 mile (3.2 km) beam tube of the stanford linear accelerator (slac) at menlo park, california, the second most powerful linac in the world. it has about 80,000 accelerating electrodes and could accelerate electrons to 50 gev a linear particle accelerator consists of the following parts: a straight hollow pipe vacuum chamber which contains the other components. it is evacuated with a vacuum pump so that the accelerated particles will not collide with air molecules. the length will vary with the application. if the device is used for the production of x-rays for inspection or therapy the pipe may be only 0.5 to 1.5 meters long. if the device is to be an injector for a synchrotron it may be about ten meters long. if the device is used as the primary accelerator for nuclear particle investigations, it may be several thousand meters long. the particle source (s) at one end of the chamber which produces the charged particles which the machine accelerates. the design of the source depends on the particle that is being accelerated. electrons are generated by a cold cathode, a hot cathode, a photocathode, or radio frequency (rf) ion sources. protons are generated in an ion source, which can have many different designs. if heavier particles are to be accelerated, (e.g., uranium ions), a specialized ion source is needed. the source has its own high voltage supply to inject the particles into the beamline. extending along the pipe from the source is a series of open-ended cylindrical electrodes (c1, c2, c3, c4), whose length increases progressively with the distance from the source. the particles from the source pass through these electrodes. the length of each electrode is determined by the frequency and power of the driving power source and the particle to be accelerated, so that the particle passes through each electrode in exactly one-half cycle of the accelerating voltage. the mass of the particle has a large effect on the length of the cylindrical electrodes; for example an electron is considerably lighter than a proton and so will generally require a much smaller section of cylindrical electrodes as it accelerates very quickly. a target (not shown) with which the particles collide, located at the end of the accelerating electrodes. if electrons are accelerated to produce x-rays then a water cooled tungsten target is used. various target materials are used when protons or other nuclei are accelerated, depending upon the specific investigation. behind the target are various detectors to detect the particles resulting from the collision of the incoming particles with the atoms of the target. many linacs serve as the initial accelerator stage for larger particle accelerators such as synchrotrons and storage rings, and in this case after leaving the electrodes the accelerated particles enter the next stage of the accelerator. an electronic oscillator and amplifier (g) which generates a radio frequency ac voltage of high potential (usually thousands of volts) which is applied to the cylindrical electrodes. this is the accelerating voltage which produces the electric field which accelerates the particles. as shown, opposite phase voltage is applied to successive electrodes. a high power accelerator will have a separate amplifier