Homogeneous carbon nanotube suspensions are studied in the semidilute regime, which is permitted by the use of an effective polysiloxane surfactant, PySi70, as a liquid matrix. We study such suspensions under an AC electric field by optical microscopy, transient light transmission and impedance spectroscopy. Optical microscopy shows the formation of long-range microscale columnar order as a result of a fast field-induced phase separation. The aggregation process is found to be reversible and repeatable, with nanotubes re-dispersing into a homogeneous solution, in a diffusive manner, in the seconds following removal of the electric field. The suggested role of the induced dipolar forces is consistent with the relatively fast columnar formation and characteristic concentration of maximum field-response. The equilibrium columnar structure provides fast field-induced control of the transparency and dielectric response, while avoiding electrical breakdown.