  We report the design and development of a compact electron and positron
spectrometer based on tapered Neodymium Iron Boron magnets. We show that the
tapered design forms a gradient magnetic field component allowing energy
dependent focusing of the dispersed charged particles along a chosen detector
plane using RADIA, a code developed by European Synchrotron Radiation Facility
for solving three-dimensional magnetostatics configuration, and a fourth order
Runge-Kutta Particle Tracking code. The mirror symmetric design allows for
simultaneous detection of pairs i.e. electrons and positrons with energies from
2 MeV to 500 MeV. We have developed a prototype matching the design
specifications. We investigate the effects of beam divergence on the energy
resolution and signal conversion efficiency for a photo-stimulated
luminescencebased Imaging Plates (IPs). The optimal entrance aperture of the
magnet is found to be elliptical and bigger than that of conventional pinhole
aperture-based spectrometer designs even for a divergent beam originating from
a point source at 20 cm away (i.e. solid angle of ~8 milli steradians). The
signal efficiency in BAS-IP of SR type ranges from 1% to 5% for a parallel beam
incident on a circular aperture of 20 mm diameter type at a chosen detection
plane whereas it drops by up to a factor of 3 in the presence of divergence of
~ 8 milli steradians. The proposed gradient magnet is suitable for the
detection of low flux and/or monoenergetic type electron/positron signals with
finite transverse sizes. It offers unparalleled advantages for gammaray
spectroscopy in the intermediate MeV range.
