Sextupole magnet

Sextupole magnets abide of groups of six magnets set out in an adjustment of alternating arctic and south alluring poles abiding about an axis.1 They are acclimated in atom axle ascendancy in atom accelerators.1

The architecture of sextupoles application electromagnets about involves six animate pole tips of alternating polarity. The animate is magnetised by a ample electric accepted that flows in the coils of wire captivated about the poles.

Sextupoles in particle accelerators

At the energies accomplished in top activity atom accelerators, alluring angle is added able than electrostatic, and use of the alluring appellation of the Lorentz force:

\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}),

is enabled with assorted magnets that accomplish up 'the lattice' appropriate to bend, beacon and focus a answerable atom beam.

The quadrupole magnets acclimated to focus and amalgamate the axle accept the adverse acreage that their absorption backbone (describable by a focal length) is abased on the activity of the atom getting focused—high activity particles accepting best focal lengths than those with lower energy. Since all astute beams accept some, non-negligible, activity spread, any absorption arrangement that relies absolutely on quadrupole magnets will aftereffect in the admeasurement of the axle "blowing up" with distance.

In beeline accelerators this is due to the under- or over-focusing of the particles, while in accumulator rings it is accompanying to the blush of the ring (the addiction for off-energy particles to accept altered ethics for the betatron appearance beforehand per orbit).

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

Sextupolar fields accept a focal breadth that is inversely proportional to the ambit from the centre of the allurement with which the atom passes. This is agnate to the activity of a quadrupole, whose aftereffect on the axle may be declared as a angle whose backbone depends on the ambit from the centre of the magnet.

If a sextupole is placed at a point at which the particles in the axle are abiding by their activity account (i.e. a arena of non-zero dispersion), again the sextupole can be set at a backbone that ensures that particles of all reasonable activity offsets are focused to the aforementioned point. This will abate the addiction of the quadrupole filigree to banish the beam.

Synchrocyclotron

The ambit of curvature for a atom affective relativistically in a changeless alluring acreage is

r = \frac{\gamma m_0 v}{q B}

where

\gamma=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}} is the Lorentz factor

m0 is the blow accumulation of the particle.

Note that in high-energy abstracts energy, E, and momentum, p, are acclimated rather than velocity, and both abstinent in units of energy. In that case one should use the substitution,

\frac{p}{E} = v

area this is in Natural units

The relativistic cyclotron abundance is

f=f_c\sqrt{1-\left(\frac{v}{c}\right)^2},

where

fc is the classical frequency, accustomed above, of a answerable atom with velocity

v ambit in a alluring field.

The blow accumulation of an electron is 511 keV/c2, so the abundance alteration is 1% for a alluring exhaustion tube with a 5.11 keV/c2 absolute accepted accelerating voltage. The proton accumulation is about two thousand times the electron mass, so the 1% alteration activity is about 9 MeV, which is acceptable to abet nuclear reactions.

edit Accessory cyclotron

An another to the synchrocyclotron is the accessory cyclotron, which has a alluring acreage that increases with radius, rather than with time. Recalling that

r = \frac{\gamma m_0 v}{q B},

one can accept B to be proportional to the Lorentz factor, B = γB0. This after-effects in the relation

r = \frac{m_0 v}{q B_0}

which afresh alone depends on the acceleration v, like in the non-relativistic case. The axle de-focusing aftereffect of this adorable acreage acclivity is compensated by ridges on the allurement faces which alter the acreage azimuthally as well. This allows particles to be accelerated continuously, on every aeon of the radio abundance (RF), rather than in bursts as in a lot of added accelerator types. This assumption that alternating acreage gradients accept a net absorption aftereffect is alleged able focusing. It was obscurely accepted apparently continued afore it was put into practice.

Related technologies

The ambagious of electrons in a annular exhaustion alcove aural a axle alluring acreage is aswell active in the magnetron, a accessory for bearing top abundance radio after-effects (microwaves).

The Synchrotron moves the particles through a aisle of connected radius, acceptance it to be fabricated as a aqueduct and so of abundant beyond ambit than is applied with the cyclotron and synchrocyclotron. The beyond ambit allows the use of abundant magnets, anniversary of which imparts angular drive and so allows particles of college acceleration (mass) to be kept aural the bound of the abandoned pipe. The alluring acreage backbone of anniversary of the bend magnets is added as the particles accretion activity in adjustment to accumulate the bend angle constant.

Problems

Sextupolar fields are non-linear (i.e. they depend on the artefact of the sizes of the axle displacements), and accept agreement which depend on both the accumbent and vertical offsets (i.e. they are coupled).

This leads to equations of motion that cannot be apparent for the accepted case, appropriately acute approximations to be acclimated if artful their furnishings on the beam.

In addition, the quadrature assurance of the sextupole bang on the axle account of the beam, can advance to top amplitude particles getting kicked far from the axle arbor and getting absent on the beam-pipe walls. Due to this mechanism, the accession of sextupole fields to an accelerator filigree will absolute the activating breach or accepting of the accelerator.