Generalized design formulas for low energy electromagnetic quads

This technical note is the result of the quadrupole magnet design efforts that went into the development of proposals for large high-powered linear accelerators such as the Accelerator for Production of Tritium (APT), Accelerator for Base Conversion (of Plutonium) (ABC), and Accelerator for Treatment of (radioactive) Waste (ATW). In all these applications it was necessary to develop designs for numerous (hundreds) of electromagnetic quadrupoles (EMQs). EMQs are required since long-term reliability, radiation damage potential, and large aperture dictate against the use of permanent magnet quadrupoles (PMQs) for these powerful machines. One object of the magnet design effort was to provide a quick, reliable, and easy means of converting raw physics requirements (magnetic impulse, focal length, and boretube aperture) into realistic electrical, cooling, facility interface, and mechanical specifications and configurations--in other words, to easily convert physics requirements to a reliable design that could be drawn on paper, shown to vendors, and presented to peer review committees as a well-developed and believable concept. The empirical formulas that were derived have been gathered together in this technical note. They will be useful for other designers interested in an easy way of coming up with a rather complete mechanical as well as electrical and magnetic design for EMQs. Included are lab tests of designs derived from these formulas and comparisons with other real EMQ designs. These demonstrate the good accuracy of the empirical formulas