From Carr@SLAC.Stanford.edu Fri Jan 6 14:36:04 2006 Date: Tue, 3 Jan 2006 15:53:50 -0800 From: Roger Carr To: Achim W. Weidemann Cc: tanabe Subject: Re: Temperature rise of QM-001 /was: Everson Tesla Quad Achim, Here is a method of calculating the temperature of the hot part of a magnet coil that comes from Jack Tanabe. He says that you can use the following method (which I have interpreted conservatively) The true profile of temperature is parabolic, but if you assume that all the heat originates at the center, and get a triangular profile, the peak of the triangle will be at twice the temperature rise of the true, parabolic peak. Therefore, take the heat to arise all at the central plane of the coil. Then calculate: dQ/dt = -k A dT/dx, where dQ/dt is the energy dissipated per second, A is the area of the central plane (or the surface, in this approximation), dT/dx is the temperature gradient, where you already know the temperature at the surface, so dT/dx = (Thot -Tsurface)/half thickness of coil, and k is the heat conductivity of the coil. In a rough approximation, you can assume that the heat conductivity is just the heat conductivity of copper times the copper fill factor. Thus if the coil is 85% copper, k ~ 0.8* 0.391 Watts/m-K = 332 Watts/m-K, neglecting thte conductivity of epoxy. After doing this, divide Thot by two, according to Jack's rule, to get the actual high temperature. For a coil only a couple of cm thick, Thot should be only a few degrees above the surface temperature. Roger -- )'( )'( )'( )'( )'( )'( )'( )'( )'( )'( Roger Carr Linac Coherent Light Source Stanford Linear Accelerator Center MailStop 102, Building 280B, room 137 2575 Sand Hill Road Menlo Park, CA 94025 Tel: 650-926-3965 Fax: 650-926-4778 Email: Carr@SLAC )'( )'( )'( )'( )'( )'( )'( )'( )'( )'( Notre imagination vole. Nous sommes son ombre sur la terre - Vlad Nabokov Driving 100,000 miles at an average of 50 mph takes 2000 hours, or one work-year.