Laser beams that directly drive a cylindrical implosion are used to create a measurable region of mixed material in a compressible plasma state, for the first time in a convergent geometry. The turbulence driven by the Richtmyer–Meshkov instability by shock passage across a density discontinuity mixes marker material that is radiographically opaque. The width of the mix layer is compared between a system with large surface roughness and an initially smooth system. The experiment is described and results are compared to multi-dimensional numerical simulation, including three-dimensional turbulence calculations. The calculations adequately match the observations provided the measured initial conditions are used.