It has been studied the quantitative modification of the electron runaway flux due to a spectrum of kinetic Alfven waves (kAw), using the quasilinear (waves) and Fokker-Planck (collisions) equations. It is shown that these modes enhance the runaway production rate via their Cherenkov dissipation. The runaway flux for narrow and broad band spectrum for low and high phase velocities is calculated, and it is found as a general feature that its enhancement is the larger the weaker the background electric field, while for its absolute enhancement it is just the opposite. In some cases, the runaway production rate is found to be enhanced by many orders of magnitude over that without kinetic Alfven waves. It has also been discussed the consequences of this study for cosmic plasmas, namely: amplification of nonthermal emissions from stellar atmospheres, and planetary magnetospheres, (radio frequency waves, and X-ray), life extension of stellar radio bursts, enhancement of Langmuir turbulence, depletion of thermal population in extragalactic jets, and enhancement of auroral electrons precipitation.