In the design of superconducting accelerator magnets the outline of the coil cross-section is in large part attributed by the minimization of the conductor volume, constrained by the central magnetic field and homogeneity. Such optimizations commonly assume either a Block or Cosine Theta coil type, which is then filled with (pre-determined) rectangular or key-stoned Rutherford cables. By optimizing the positions, angles and number of turns the field quality requirements and cost minimization are then achieved. However, this leaves to wonder what the idealized optimum looks like when such practical constraints are not present. Although in the past such an optimum has always been presented as two intersecting circles, this method results in a non-circular aperture and is thus not fully representative. This paper introduces a method in which organically shaped (non-graded) dipole coil layouts are optimized without any assumptions on the conductor. The resulting layouts are presented as function of overall current density, aperture size and required central magnetic field. The layouts should be viewed as an ultimate limit to what can be achieved to compare real coil layouts against and as an initial guide to find an overall outline for the coil.
Acknowledgment: FP7-EuCARD2 GA 312453