Optical diagnostics using laser fluorescence techniques are used to measure the rms electric field in a superstrongly turbulent, relativistic beam–plasma system. This yields the mapping of ⟨E2⟩ as a function of radial locationrand timet. This ⟨E2(r,t)⟩ allows studies of growth and evolution of turbulent fields, their diffusion, and decay. Fluctuating electric fields occur when a 700 keV, 4 kA, 2 &mgr;sec electron beam propagates into a 20 cm diam, 1.5 m long drift tube filled with 10 mTorr of helium plasma. Stark effect shifts appear in suitable forbidden and allowed transitions, originating from the same upper energy level for the measurement: Hei6632 A˚ and Hei5015.7 A˚. The spectral bandwidth includes the forbidden line and its satellites. Using the ratio of the intensity of the forbidden plus satellite lines, to the allowed line intensity, yields the rms field as the combined field of oscillation near the plasma frequency. Fields up to 28 kV/cm result. These results can be explained by an analytical model of production of strong electric fields by beam–plasma instability, including modulational transfer inkspace, plasma heating, radiation, and wave convection. Comparison between experiment and the numerically integrated model shows good agreement.