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: :\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B}), 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 these effects are controlled with the addition of sextupolar fields. 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==