A new electron detector, 5.3 m downstream from the ZEUS interaction point, is under construction. A calorimeter has been designed in the frame work of the upgrade of the ZEUS luminosity system, and complements the two detectors measuring the flux of bremsstrahlung photons. It will measure the corresponding bremsstrahlung electrons in the 4-9 GeV range. The combined information of these three detectors will provide handles to determine both the calibrations and acceptances of the system components. The solution adopted, a tungsten/scintillator spaghetti calorimeter, is driven by the fact that the available space for such detector, located inside one of the HERA quadrapole magnets of the electron ring, is just ~30x100 mm^2, in the transversal plane, and ~100 mm, in the longitudinal direction. Using scintillating fibers, 0.5 mm Dia., with ~1 mm spacing the Moliere radius can be kept close to the half-width of the
detector avoiding significant energy leaks. Bench tests of different scintillating fibers concerning light yield, temperature stability (temperatures up to 80\060C are expected in the magnet), and radiation damage (also short-lived) have been performed. Results from test beam measurements at DESY, carried out with a prototype, are compared with Monte Carlo expectations.
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