Unit 3 - The multipolar expansion of magnetic field

<!--HTML--><p>This unit belongs to the second part of the course, which is focussed on the physics of electromagnets.&nbsp;</p> <p>In this unit we&nbsp;see how to express the magnetic field shape with a few coefficients, called the multipoles or field harmonics, thanks to the special form of the Maxwell equations. This formulations greatly simplifies the expression and the optimization of magnetic fields. It is based on the same principle of a Taylor expansion (power series), but applied to the complex domain.</p> <p>We will discuss which are the multipoles of the simplest case: the field generated by a current line. This interesting example will also allow to&nbsp;outline the validity limits of this approach (i.e., where and why the multipole expansion fails) and give few elements about divergent series. We then show that the decay of the field harmonics are a powerful analysis tool to find the location of assembly errors and&nbsp; to check the consistency of measurements, and the precision.</p> <p>Finally, we will summarize the beam dynamics requirements on the multipoles.&nbsp;</p> <p>&nbsp;</p>