The helical Cerenkov effect results from the helical electron motion in a medium caused by a magnetic field B. For B values of up to 100 T in strength helical Cerenkov radiation occurs in the visible spectrum for which an analytical expression for the number of emitted photons per unit path length is derived. In general, however, for a non-mono-energetic beam at a fixed radiation angle and a fixed arbitrary frequency, one may have simultaneous contributions from the helical Cerenkov effect and radiation occurring below and above the threshold of the helical Cerenkov effect with the fundamental frequencies and their harmonics. When B increases we come to the asymptotic regions where the number of harmonics on both sides of the threshold first decreases towards the respective fundamental frequencies and, eventually, disappears altogether. Also, a general asymptotic limit, in which there is no radiation below and above the threshold of the helical Cerenkov effect and only the helical Cerenkov effect remains at any angle of radiation and for any medium, we argue, should occur at about
T for the visible spectrum.