Unit 4 - How to generate dipole and quadrupole fields with current lines

<!--HTML--><p>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.</p> <p>In this unit we&nbsp;see how to arrange current lines&nbsp;to generate a constant field inside a circular&nbsp;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.</p> <p>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&nbsp;layouts for Tevatron, RHIC and LHC magnets. The same approach will be used to describe the case of the quadrupole.</p> <p>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.</p>