@dmckee mocked at the idea and pointed to a possible duplicate. However, this question does not specify that the reduced density channel is needed to reduce missile drag, so the question is more general and thus different from the possible duplicate.

Many years ago, my bosses told me to find a way to create reduced density channels in the atmosphere. Such channels can have different applications, but I do not want to discuss them here. So such channels can be created using optical discharge in the air and subsequent heating of the ionized air by electromagnetic radiation. Creating broad channels requires a lot of energy, and one needs short wavelength radiation to create long and narrow channels because of diffraction constraints. Using just one laser beam is problematic, as the plasma density in the optical discharge increases until it becomes opaque for the laser beam, so instead of a long homogeneous channel one often gets a series of short channels.

So, after some search in the dark, I suggested creating reduced density channels by combined action of laser and microwave beams. The microwave beam is much broader than the coaxial laser beam (because of diffraction constraints). For appropriate choice of intensities of the beams, the discharge only takes place near the axis, where the beams overlap. The plasma density is pretty much limited by the critical plasma density for the microwave beam, so the plasma stays transparent for the laser beam, and it is possible to achieve a narrow homogeneous plasma channel. Furthermore, I suspected that a significant part of the relatively inexpensive power of microwave beam can be absorbed in this narrow channel, although the channel's diameter is much less than the diameter of the microwave beam. Heating of the narrow plasma channel reduces the air density in the channel due to aerodynamic processes. My calculations based on a rigorous solution of a diffraction problem confirmed this counter-intuitive conjecture, and I published the first work on this topic (Sov. Tech. Phys. Lett. 17(6), June 1991, p. 396.). Since then, I found more precise conditions of such efficient heating of narrow conducting cylinders by broad electromagnetic beams (arXiv:physics/0405091 and arXiv:physics/0611169) and (together with great co-authors) provided experimental confirmation of the results (arXiv:1109.1626 , arXiv:1208.0066 , Proc. of SPIE Vol. 10185 101850I-1 (2017)).

The image shows a 20 micron diameter platinum wire heated by a 300 micron diameter CO2 laser beam with heating efficiency of tens percent.

Other people (Nature Photonics 8, 706–709 (2014)) demonstrated a plasma channel in the atmosphere created by a thin femto-second laser beam using energy supply from the sides from another laser beam, but they used self-focused first beam and axicon focusing of the second beam.

@dmckee mocked at the idea and pointed to a possible duplicate. However, this question does not specify that the reduced density channel is needed to reduce missile drag, so the question is more general and thus different from the possible duplicate.

Many years ago, my bosses told me to find a way to create reduced density channels in the atmosphere. Such channels can have different applications, but I do not want to discuss them here. So such channels can be created using optical discharge in the air and subsequent heating of the ionized air by electromagnetic radiation. Creating broad channels requires a lot of energy, and one needs short wavelength radiation to create long and narrow channels because of diffraction constraints. Using just one laser beam is problematic, as the plasma density in the optical discharge increases until it becomes opaque for the laser beam, so instead of a long homogeneous channel one often gets a series of short channels.

So, after some search in the dark, I suggested creating reduced density channels by combined action of laser and microwave beams. The microwave beam is much broader than the coaxial laser beam (because of diffraction constraints). For appropriate choice of intensities of the beams, the discharge only takes place near the axis, where the beams overlap. The plasma density is pretty much limited by the critical plasma density for the microwave beam, so the plasma stays transparent for the laser beam, and it is possible to achieve a narrow homogeneous plasma channel. Furthermore, I suspected that a significant part of the relatively inexpensive power of microwave beam can be absorbed in this narrow channel, although the channel's diameter is much less than the diameter of the microwave beam. Heating of the narrow plasma channel reduces the air density in the channel due to aerodynamic processes. My calculations based on a rigorous solution of a diffraction problem confirmed this counter-intuitive conjecture, and I published the first work on this topic (Sov. Tech. Phys. Lett. 17(6), June 1991, p. 396.). Since then, I found more precise conditions of such efficient heating of narrow conducting cylinders by broad electromagnetic beams (arXiv:physics/0405091 and arXiv:physics/0611169) and (together with great co-authors) provided experimental confirmation of the results (arXiv:1109.1626 , arXiv:1208.0066 , Proc. of SPIE Vol. 10185 101850I-1 (2017)).

The image shows a 20 micron diameter platinum wire heated by a 300 micron diameter CO2 laser beam with heating efficiency of tens percent.

Other people (Nature Photonics 8, 297–301 (2014)) demonstrated a plasma channel in the atmosphere created by a thin femto-second laser beam using energy supply from the sides from another laser beam, but they used self-focused first beam and axicon focusing of the second beam.