Theoretical analysis shows that a small-amplitude laser wake (an electrostatic Langmuir wave), driven in a periodically stratified, cylindrical plasma column, generates a superluminal, azimuthally polarized rotational current at a Langmuir frequency. The current radiates a radially polarized (i.e. transverse magnetic) Cherenkov signal into the plasma-free space. The opening angle of the Cherenkov emission cone is defined by the spatial period of stratification. Lifetime of the laser wake, limited by wave breaking in the inhomogeneous plasma, defines the THz signal length. This length ranges from a few picoseconds to hundreds of picoseconds, depending on the wake amplitude, amplitude of background density modulation, and stratification period. Monochromaticity and coherence distinguishes this THz signal from the ultrashort, uncollimated, broadband signals generated by photoionization currents in plasma filaments. The efficiency of electromagnetic energy conversion, from optical to THz, reaches its peak when the drive pulse waist size is close to the column radius. The efficiency increases with an increase in the drive pulse wavelength, and reaches the maximum when the drive pulse becomes near-critical for relativistic self-focusing. Numerical examples with sub-Joule, near-infrared terawatt drive pulses

demonstrate the highest conversion efficiency of the order 10^{−5} with the total emitted energy of several microjoules, a few-hundred MV/m electric field at the column surface, and an MV/m field 10 cm away from the source.