  We study the effect of umklapp scattering on the magnetic-field-induced
spin-density-wave (FISDW) phases which are experimentally observed in the
quasi-one-dimensional organic conductors of the Bechgaard salts family. Within
the framework of the quantized nesting model, we show that the transition
temperature is determined by a modified Stoner criterion which includes the
effect of umklapp scattering. We determine the SDW polarization (linear or
circular) by analyzing the Ginzburg-Landau expansion of the free energy. We
also study how umklapp processes modify the quantum Hall effect (QHE) and the
spectrum of the FISDW phases. We find that umklapp scattering stabilizes phases
which exhibit a sign reversal of the QHE, as experimentally observed in the
Bechgaard salts. These ``negative'' phases are characterized by the
simultaneous existence of two SDWs with comparable amplitudes. As the umklapp
scattering strength increases, they may become helicoidal (circularly polarized
SDWs). The QHE vanishes in the helicoidal phases, but a magnetoelectric effect
appears. These two characteristic properties may be utilized to detect the
magnetic-field-induced helicoidal SDW phases experimentally.
