The impedance of layered vacuum chambers

USING AN ALGORITHM FOR THE CALCULATION OF ELECTRO-MAGNETIC FIELDS OF OSCILLATING CIRCULAR CYLINDRICAL BEAMS SURROUNDED BY ANY NUMBER OF ANNULAR LAYERS OF ARBITRARY MATERIAL PROPERTIES, WE CALCULATE THE TRANSVERSE RESISTIVE WALL IMPEDANCE OF THE BEAM SCREENS FOR THE LHC and FLHC, A LARGER HADRON COLLIDER. THESE CONSIST OF TUBES OF STAINLESS STEEL WITH THIN INSIDE LAYERS OF COPPER. THE RESULTS ARE COMPARED WITH THOSE OF AN APPROXIMATE ANALYTIC CALCULATION WHICH GIVES INCORRECT RESULTS WHEN THE SKIN DEPTH BECOMES SO LARGE THAT IT APPROACHES THE WALL RADIUS.