Magnets and Magnetic Field Effects

The magnets of the circular accelerators that comprise the Fermilab complex have contributed to, responded to, and solved a string of accelerator physics issues. Most importantly, the magnets are supposed to generate high quality magnetic fields needed for stable long-term dynamics of the particles circulating in the rings. The quality of the transverse magnetic field B is given by the multipole coefficients in the expansion: $$ {B}_x+i\cdot {B}_y={B}_0{\displaystyle \sum_{n=0}\left({b}_n+i{a}_n\right){\left[\frac{x+ iy}{R_0}\right]}^n}, $$ (3.1) where R 0 is the reference radius (1 in. in the Fermilab accelerators), the pole number is 2(n + 1) and b n (a n ) are the normal (skew) multipole coefficients, and b 0 is unity. For example, the multipoles allowed by dipole symmetry, b 2, b 4, b 6, … are designed to be small and would be 0 for a pure cos θ coil winding. The precise coil placement, and hence good magnetic field uniformity at the relative level of the multipole coefficients of few 10−4, had the biggest effect on the accelerator performance.