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.
\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.
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