At the speeds 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 quadrupoles in the filigree are of two types: 'F quadrupoles' (which are angular absorption but angular defocusing) and 'D quadrupoles' (which are angular absorption but angular defocusing). This bearings is due to the laws of electromagnetism (the Maxwell equations) which appearance that it is absurd for a quadrupole to focus in both planes at the aforementioned time.
If an F quadrupole and a D quadrupole are placed anon next to anniversary other, their fields absolutely abolish out (in accordance with Earnshaw's theorem). But if there is a amplitude amid them (and the breadth of this has been accurately chosen), the all-embracing aftereffect is absorption in both accumbent and vertical planes. A filigree can again be congenital up enabling the carriage of the axle over continued distances—for archetype annular an absolute ring. A accepted filigree is a FODO filigree consisting of a base of a absorption quadrupole, 'nothing' (often a angle magnet), a defocusing quadrupole and addition breadth of 'nothing'.
\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 quadrupoles in the filigree are of two types: 'F quadrupoles' (which are angular absorption but angular defocusing) and 'D quadrupoles' (which are angular absorption but angular defocusing). This bearings is due to the laws of electromagnetism (the Maxwell equations) which appearance that it is absurd for a quadrupole to focus in both planes at the aforementioned time.
If an F quadrupole and a D quadrupole are placed anon next to anniversary other, their fields absolutely abolish out (in accordance with Earnshaw's theorem). But if there is a amplitude amid them (and the breadth of this has been accurately chosen), the all-embracing aftereffect is absorption in both accumbent and vertical planes. A filigree can again be congenital up enabling the carriage of the axle over continued distances—for archetype annular an absolute ring. A accepted filigree is a FODO filigree consisting of a base of a absorption quadrupole, 'nothing' (often a angle magnet), a defocusing quadrupole and addition breadth of 'nothing'.
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