An upgrade of the LHC injection chain, and especially the sequence of PS and SPS, up to an extraction energy of 1Â TeV, is one of the steps considered to improve the performance of the whole accelerator complex. The magnets for this upgrade require central magnetic field from 2 T (for a PS upgrade) to 4.5 T (for an SPS upgrade), for which superconducting magnets are a candidate. Due to the fast field sweep rate of the magnets (from about 1.5 T/s to 2.5Â T/s), internal heating from eddy and persistent current effects (AC loss) must be minimized. In this paper we discuss a rationale for the design and optimization of fast ramped superconducting accelerator magnets, specifically aimed at the LHC injectors. We introduce a design parameter, the product of bore field and field ramp-rate, providing a measure of the magnet performance, and we apply it to choose the design range for a technology demonstration magnet. We finally discuss the dependence of key design parameters on the bore field and the bore diameter, to provide an approximate scaling and guidelines for critical R&D
