Unit 8 - Magnetic design: short sample field of sector coils and sensitivities to parameters

<!--HTML--><p>This unit belongs to the fourth part of the course, which is focussed on magnet design.</p> <p>In this unit we derive analytical equations for the short sample current and field of a dipole as a function of the main parameters: coil width, filling factor of the cable, and critical surface of Nb-Ti, approximated with linear fit. For the Nb3Sn analytical equations can also be derived through a hyperbolic fit.</p> <p>We show that a fundamental parameter of the magnet design is the product between the slope of the critical surface and the slope of the loadline. This parameter separates "small" by "large" coils. Thanks to this parameter, one can derive the sensitivity of the short sample current/field on critical current, loadline slope, and copper fraction.</p> <p>The same computations are done for a quadrupole, both for Nb-Ti and Nb3Sn.&nbsp;&nbsp;</p>