Azimuthal convective flow and density-depleted magnetic field-aligned current co-located in the helium plasma produced in the large plasma device (LAPD-U) at UCLA (Gekelman et al 2016 Rev. Sci. Instrum. 87025105) support an Alfvénic perturbation that is static in the laboratory frame. Electrostatic probes measure the flow and static density perturbations in the 72 cm-diameter, 12 m-long, afterglow plasma, wherein a radially segmented electrode creates the convective flow and an off-cylindrical-axis planar-mesh electrode draws current in a channel parallel to the background magnetic field. This stationary 'wave' is measured as a fixed (in the laboratory frame) ion density structure.