Strong focusing

By contrast, weak focusing is the principle that nearby circles, described by charged particles moving in a uniform magnetic field, only intersect once per revolution.

[3] In 1952, the strong focusing principle was independently developed by Ernest Courant, M. Stanley Livingston, Hartland Snyder and J. Blewett at Brookhaven National Laboratory,[4][5] who later acknowledged the priority of Christofilos' idea.

[6] The advantages of strong focusing were then quickly realised, and deployed on the Alternating Gradient Synchrotron.

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.

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, using ray transfer matrix analysis.