Cylindrically symmetric inertial confinement fusion systems based on a Z pinch compression of plasma in the presence of a megagauss axial magnetic field are analyzed. The ultra-high magnetic field provides stabilization of the pinch, thus making possible higher compression, confinement of the alpha -particles and initial preheating. The optimal parameters found for a break-even experiment are: current pulse amplitude 20 MA and FWHM 40 ns, initial radius of the compressed linear 3 mm, and a 30-fold radial compression. For the currents in the range 5-8 MA the axial magnetic field is shown to increase the DT neutron yield up to approximately 1015 cm-1.