The theory of whistler wave interaction with a modulated electron beam
of finite radius, injected parallel to the magnetic field in an unbou
nded space plasma is considered Tile study is done in the case of shea
red whistlers interacting with the thin beam, when the parallel wave n
umber is very small compared to the perpendicular one. The electromagn
etic fields inside and outside the beam are determined in the linear a
pproach; their asymptotic expressions in the beam vicinity are obtaine
d in a rather simple form. The energy balance between the thin modulat
ed beam and the sheared whistler is considered and dependence of emiss
ion power on the beam parameters is studied.