This unit belongs to the second part of the course, which is focussed on the physics of electromagnets in the case of current-dominated layouts.
In this unit we see how to arrange current lines to generate a constant field inside a circular aperture. We will give the classical solutions (intersecting ellipse, the wall dipole and the cos theta distribution), and we will focus on a sector coil, showing that the field is proportional to the current density and to the width of the coil.
We will then prove how using a few wedges we can successively set to zero the high order multipoles, finding analytical solutions that allow to understand why the magnet designers selected some layouts for Tevatron, RHIC and LHC magnets. The same approach will be used to describe the case of the quadrupole.
Using this first approximation, that neglects iron contribution or grading, we will discuss the combination of current density, field and coil width used in superconducting magnets.