The ion fluctuation axial profile is measured by Thomson scattering in an inhomogeneous laserproduced plasma. The electron temperature and plasma drift velocity at the location of the measured ion waves and the plasma density profile are simultaneously measured. The measured ion fluctuation profile is compared to the profile predicted by convective growth of the stimulated Brillouin scattering instability calculated from the measured hydrodynamic profiles. PACS numbers: 52.35.Fp, 52.35.Mw, 52.40.Nk, 52.50.Jm Stimulated Brillouin scattering (SBS) is a parametric instability in a plasma in which an electromagnetic wave interacts with an ion acoustic wave to produce a scattered electromagnetic wave [1 -5]. SBS has been a concern in inertial confinement fusion (ICF) applications as a potential cause of decreased laser-target couphng efficiency. The instability continues to be of interest in a scientific sense because the seeding and saturation mechanisms are not well understood.Although Thomson scattering [6,7] has been used extensively to identify ion waves in interactions between plasmas and 10.6 p, m wavelength lasers [8,9], the plasma and laser parameters for ICF targets will be substantially different. SBS in short-wavelength laserplasma interactions has been studied via scattered light spectra near the incident laser wavelength, and, although there has recently been evidence of seeding of SBS by the two-plasmon decay (TPD) instability at n, /4 [10],the interpretation of spectra is confused by the role of the (unknown) expansion velocity profile. Applications [11,12] of convective gain theory have shown its difficulty in predicting the spectra and signal levels of experiments.In this Letter, we discuss an experiment in which we have determined both the plasma hydrodynamic profiles and the ion acoustic fluctuation profile (using the Thomson scattering technique) in a plasma produced by a laser with a wavelength, A"of1. 064 p, m irradiating a solid carbon target. This means that, for the first time, we can compare an experimental ion wave fluctuation spatial profile to a theoretically predicted one. We find that the spatial dependence and quantitative level of the density fluctuations are adequately modeled for densities above n, /4 by convective gain theory, provided the instability is assumed to grow from laser light scattering from ion acoustic fluctuations. Although Thomson scattering from SBS ion waves has been observed before, this was done in CO2 laser produced plasmas which have significantly different hydrodynamic profiles, and, in general, the instability is strongly coupled whereas most theory to date has assumed weak coupling. Also, the emphasis in those experiments was on measuring growth rates of SBS.The experiment was conducted using the Janus laser facility at the Lawrence Livermore National Laboratory. The plasma was produced using a 1 ns full width at half maximum Gaussian laser pulse (A, = 1.064 p, m) which irradiated a solid carbon target. The laser spatia1 profile is nominally square topped (t...