Sextupole magnet

Last updated
Sextupole electromagnet as used within the storage ring of the Australian Synchrotron to correct chromatic aberrations of the electron beam Aust.-Synchrotron,-Sextupole-Focusing-Magnet,-14.06.2007.jpg
Sextupole electromagnet as used within the storage ring of the Australian Synchrotron to correct chromatic aberrations of the electron beam
Field lines of an idealized sextupole magnet in the plane transverse to the beam direction Magnetic field of an idealized sextupole.svg
Field lines of an idealized sextupole magnet in the plane transverse to the beam direction

A sextupole magnet (also known as a hexapole magnet) consist of six magnetic poles set out in an arrangement of alternating north and south poles arranged around an axis. [1] They are used in particle accelerators [1] for the control of chromatic aberrations and for damping the head tail instability. Two sets of sextupole magnets are used in transmission electron microscopes to correct for spherical aberration.

Contents

The design of sextupoles using electromagnets generally involves six steel pole tips of alternating polarity. The steel is magnetised by a large electric current that flows in the coils of wire wrapped around the poles. The coils may be formed from hollow copper magnet wire that carry coolant, usually de-ionized water. The current density of such a conductor can be above 10 amps/mm2 (four times that of standard copper conductors).

In particle accelerators

At the energies reached in high energy particle accelerators, magnetic deflection is more powerful than electrostatic, and use of the magnetic term of the Lorentz force:

is enabled with various magnets that make up 'the lattice' required to bend, steer and focus a charged particle beam.

The quadrupole magnets used to focus and combine the beam have the unfortunate property that their focusing strength (describable by a focal length) is dependent on the energy of the particle being focused—high energy particles having longer focal lengths than those with lower energy. Since all realistic beams have some, non-negligible, energy spread, any focusing scheme that relies purely on quadrupole magnets will result in the size of the beam "blowing up" with distance.

In linear accelerators this is due to the under- or over-focusing of the particles, while in storage rings it is related to the chromaticity of the ring (the tendency for off-energy particles to have different values for the betatron phase advance per orbit).

Typically this is controlled with the addition of sextupolar fields to the lattice.

Sextupolar fields have a focal length that is inversely proportional to the distance from the center of the magnet with which the particle passes. This is similar to the action of a quadrupole, whose effect on the beam may be described as a bending whose strength depends on the distance from the center of the magnet.

If a sextupole is placed at a point at which the particles in the beam are arranged by their energy offset (i.e. a region of non-zero dispersion), then the sextupole can be set at a strength that ensures that particles of all reasonable energy offsets are focused to the same point. This will negate the tendency of the quadrupole lattice to disperse the beam.

Problems

Sextupolar fields are non-linear (i.e. they depend on the product of the sizes of the transverse displacements), and have terms which depend on both the horizontal and vertical offsets (i.e. they are coupled).

This leads to equations of motion that cannot be solved for the general case, thus requiring approximations to be used when calculating their effects on the beam.

In addition, the quadrature dependence of the sextupole kick on the transverse offset of the beam, can lead to high amplitude particles being kicked far from the beam axis and being lost on the beam-pipe walls. Due to this mechanism, the addition of sextupole fields to an accelerator lattice will limit the dynamic aperture or acceptance of the accelerator.

See also

Related Research Articles

<span class="mw-page-title-main">Magnetic field</span> Spatial distribution of vectors allowing the calculation of the magnetic force on a test particle

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field.

<span class="mw-page-title-main">Cyclotron</span> Type of particle accelerator

A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929–1930 at the University of California, Berkeley, and patented in 1932. A cyclotron accelerates charged particles 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 magnetic field and accelerated by a rapidly varying electric field. Lawrence was awarded the 1939 Nobel Prize in Physics for this invention.

<span class="mw-page-title-main">Linear particle accelerator</span> Type of particle accelerator

A linear particle accelerator 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 for particle physics.

<span class="mw-page-title-main">Insertion device</span>

An insertion device (ID) is a component in modern synchrotron light sources, so called because they are "inserted" into accelerator tracks. They are periodic magnetic structures that stimulate highly brilliant, forward-directed synchrotron radiation emission by forcing a stored charged particle beam to perform wiggles, or undulations, as they pass through the device. This motion is caused by the Lorentz force, and it is from this oscillatory motion that we get the names for the two classes of device, which are known as wigglers and undulators. As well as creating a brighter light, some insertion devices enable tuning of the light so that different frequencies can be generated for different applications.

<span class="mw-page-title-main">Magnetic moment</span> Magnetic strength and orientation of an object that produces a magnetic field

In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current, permanent magnets, elementary particles, various molecules, and many astronomical objects.

<span class="mw-page-title-main">Quadrupole magnet</span> Group of four magnets

Quadrupole magnets, abbreviated as Q-magnets, consist of groups of four magnets laid out so that in the planar multipole expansion of the field, the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. Quadrupole magnets are useful as they create a magnetic field whose magnitude grows rapidly with the radial distance from its longitudinal axis. This is used in particle beam focusing.

<span class="mw-page-title-main">Dipole magnet</span> Simplest type of magnet

A dipole magnet is the simplest type of magnet. It has two poles, one north and one south. Its magnetic field lines form simple closed loops which emerge from the north pole, re-enter at the south pole, then pass through the body of the magnet. The simplest example of a dipole magnet is a bar magnet.

<span class="mw-page-title-main">Synchrotron</span> Type of cyclic particle accelerator

A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The magnetic field which bends the particle beam into its closed path increases with time during the accelerating process, being synchronized to the increasing kinetic energy of the particles. The synchrotron is one of the first accelerator concepts to enable the construction of large-scale facilities, since bending, beam focusing and acceleration can be separated into different components. The most powerful modern particle accelerators use versions of the synchrotron design. The largest synchrotron-type accelerator, also the largest particle accelerator in the world, is the 27-kilometre-circumference (17 mi) Large Hadron Collider (LHC) near Geneva, Switzerland, built in 2008 by the European Organization for Nuclear Research (CERN). It can accelerate beams of protons to an energy of 6.5 tera electronvolts (TeV or 1012 eV).

An electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens assists in the transport of light in an optical instrument. Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or converge the electron trajectories. An electrostatic lens can also be used to focus an ion beam, for example to make a microbeam for irradiating individual cells.

<span class="mw-page-title-main">Betatron</span>

A betatron is a type of cyclic particle accelerator. It is essentially a transformer with a torus-shaped vacuum tube as its secondary coil. An alternating current in the primary coils accelerates electrons in the vacuum around a circular path. The betatron was the first machine capable of producing electron beams at energies higher than could be achieved with a simple electron gun, and the first circular accelerator in which particles orbited at a constant radius.

A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure reflecting various orders of complexity.

ANSTO's Australian Synchrotron is a 3 GeV national synchrotron radiation facility located in Clayton, in the south-eastern suburbs of Melbourne, Victoria, which opened in 2007.

<span class="mw-page-title-main">Swiss Light Source</span> Synchrotron radiation facility at Paul Scherrer Institute in Switzerland

The Swiss Light Source (SLS) is a synchrotron located at the Paul Scherrer Institute (PSI) in Switzerland for producing electromagnetic radiation of high brightness. Planning started in 1991, the project was approved in 1997, and first light from the storage ring was seen at December 15, 2000. The experimental program started in June 2001 and it is used for research in materials science, biology and chemistry.

<span class="mw-page-title-main">Strong focusing</span> Converging particle beams using alternating field gradients

In accelerator physics strong focusing or alternating-gradient focusing is the principle that the net effect on a particle beam of charged particles passing through alternating field gradients is to make the beam converge. By contrast, weak focusing is the principle that nearby circles, described by charged particles moving in a uniform magnetic field, only intersect once per revolution.

<span class="mw-page-title-main">Particle accelerator</span> Research apparatus for particle physics

A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.

<span class="mw-page-title-main">Magnetic lens</span>

A magnetic lens is a device for the focusing or deflection of moving charged particles, such as electrons or ions, by use of the magnetic Lorentz force. Its strength can often be varied by usage of electromagnets.

<span class="mw-page-title-main">Storage ring</span> Type of particle accelerator

A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating typically for many hours. Storage of a particular particle depends upon the mass, momentum and usually the charge of the particle to be stored. Storage rings most commonly store electrons, positrons, or protons.

Indus-2 is a synchrotron radiation source with a nominal electron energy of 2.5 GeV and a critical wavelength of about 1.98 angstroms. It is one of the most important projects in progress at the Raja Ramanna Centre for Advanced Technology. It is designed to cater to the needs of X-ray users, material scientists and researchers. Indus-1 has the distinction of being the first synchrotron generator of India with a 450 Mev storage ring. Indus-2 is an improvement over Indus-1.

In accelerator physics, a magnetic lattice is a composition of electromagnets at given longitudinal positions around the vacuum tube of a particle accelerator, and thus along the path of the enclosed charged particle beam. The lattice properties have a large influence on the properties of the particle beam, which is shaped by magnetic fields. Lattices can be closed, linear and are also used at interconnects between different accelerator structures.

Multipole magnets are magnets built from multiple individual magnets, typically used to control beams of charged particles. Each type of magnet serves a particular purpose.

References

  1. 1 2 "Sextupole magnet". The European X-Ray Laser Project (XFEL). n.d. Retrieved 2008-09-17.