Strong focusing
Encyclopedia
Accelerator physics
Accelerator physics deals with the problems of building and operating particle accelerators.The experiments conducted with particle accelerators are not regarded as part of accelerator physics. These belong to particle physics, nuclear physics, condensed matter physics, materials physics, etc...
strong focusing or alternating-gradient focusing is the principle that the net effect on a particle beam
Particle beam
A particle beam is a stream of charged or neutral particles which may be directed by magnets and focused by electrostatic lenses, although they may also be self-focusing ....
of charged particles passing through alternating field gradients is to make the beam converge. By contrast "Weak focusing
Weak focusing
In particle accelerators Weak focusing occurs when particles are kept in reasonably strong, uniform magnetic fields that causes them to move in circles under the influence of the Lorentz force....
" is the principle that nearby circles, described by charged particles moving in a uniform magnetic field, only intersect once per revolution.
Earnshaw's theorem
Earnshaw's theorem
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic...
shows that simultaneous focusing in two directions at once is impossible. However, ridged poles of a cyclotron
Cyclotron
In technology, a cyclotron is a type of particle accelerator. In physics, the cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicularly to the direction of a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction...
or two or more spaced quadrupole magnet
Quadrupole magnet
Quadrupole magnets consist of groups of four magnets laid out so that in the 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...
s (arranged in quadrature
Quadrature
Quadrature may refer to:In signal processing:*Quadrature amplitude modulation , a modulation method of using both an carrier wave and a 'quadrature' carrier wave that is 90° out of phase with the main, or in-phase, carrier...
) alternately focus horizontally and vertically.
Strong focusing was first conceived by Nicholas Christofilos
Nicholas Christofilos
Nicholas Constantine Christofilos was a Greek-American physicist.Christofilos was born in Boston, Massachusetts and raised in Greece...
in 1949 but not published (Christofilos opted instead to patent his idea), and was later independently invented in 1952 at Brookhaven National Laboratory
Brookhaven National Laboratory
Brookhaven National Laboratory , is a United States national laboratory located in Upton, New York on Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base...
. The advantages of strong focusing were then quickly realised, and deployed on the Alternating Gradient Synchrotron
Alternating Gradient Synchrotron
The Alternating Gradient Synchrotron is a particle accelerator located at the Brookhaven National Laboratory in Long Island, New York, USA....
. Courant, Livingston, Snyder and Blewett later acknowledged the priority of Christofilos' idea .
Courant and Snyder found that the net effect of alternating the field gradient was that both the vertical and horizontal focusing of protons could be made strong at the same time, allowing tight control of proton paths in the machine. This increased beam intensity while reducing the overall construction cost of a more powerful accelerator. The theory revolutionised cyclotron design, and permitted very high field strengths to be employed, while massively reducing the size of the magnets needed by minimising the size of the beam. Most particle accelerators today utilise the strong focusing principle.
Multipole magnets
Quadrupole magnet
Quadrupole magnets consist of groups of four magnets laid out so that in the 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...
and sextupole magnet
Sextupole magnet
Sextupole magnets consist of groups of six magnets set out in an arrangement of alternating north and south magnetic poles arranged around an axis. They are used in particle beam control in particle accelerators....
s, to focus the beam down, as magnet
Magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets.A permanent magnet is an object...
s give a more powerful deflection effect than earlier electrostatic systems at high beam kinetic energies. The multipole magnets refocus the beam after each deflection section, as deflection sections have a defocusing effect that can be countered with a convergent magnet 'lens'.
This can be shown schematically as a sequence of divergent and convergent lenses. The quadrupoles are often laid out in what are called FODO patterns (where F focusses vertically and defocusses horizontally, and D focusses horizontally and defocusses vertically and O is a space or deflection magnet). Following the beam particles in their trajectories through the focussing arrangement, an oscillating pattern would be seen.
Mathematical modelling
The action upon a set of charged particles by a set of linear magnets (i.e. only dipoles, quadrupoles and the field-free drift regions between them) can be expressed as matrices which can be multiplied together to give their net effect. Higher-order terms such as sextupoles, octupoles etc. may be treated by a variety of methods, depending on the phenomena of interest.See also
- Electron gunElectron gunAn electron gun is an electrical component that produces an electron beam that has a precise kinetic energy and is most often used in television sets and computer displays which use cathode ray tube technology, as well as in other instruments, such as electron microscopes and particle...
uses cylindrical symmetric fields such as provided by a Wehnelt cylinderWehnelt cylinderA Wehnelt cylinder is an electrode in the electron gun assembly of some thermionic devices, used for focusing and control of the electron beam. It is named after Arthur Rudolph Berthold Wehnelt, a German physicist, who invented it during the years 1902 and 1903. A Wehnelt cylinder is also known as...
to focus an electron beam - Maglev has also been a suggested use of strong focusing
- Quadrupole magnetQuadrupole magnetQuadrupole magnets consist of groups of four magnets laid out so that in the 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...
- Sextupole magnetSextupole magnetSextupole magnets consist of groups of six magnets set out in an arrangement of alternating north and south magnetic poles arranged around an axis. They are used in particle beam control in particle accelerators....
- Nicholas ChristofilosNicholas ChristofilosNicholas Constantine Christofilos was a Greek-American physicist.Christofilos was born in Boston, Massachusetts and raised in Greece...
the scientist that first conceived strong focusing