  The formation of the radial electric field, $E_{\rm r}$ in the SOL has been
experimentally studied for attached divertor conditions in stellarator W7-X.
The main objective of this study is to test the validity in a complex 3D island
divertor of simple models, typically developed in tokamaks, relating $E_{\rm
r}$ to the sheath potential drop gradient at the target. Additionally, we
investigate the effect of the edge $E_{\rm r}$ shear on the reduction of
density fluctuation amplitude, a well-established phenomenon according to the
existing bibliography. The main diagnostic for measurements in the SOL is a
V-band Doppler reflectometer that can provide the measurement of the $E_{\rm
r}$ and density fluctuations with good spatial resolution. Three-dimensional
measurements of divertor parameters has been carried out using infrared
cameras, with $\lambda_{\rm q}$ resulting a suitable proxy for the
model-relevant $\lambda_{\rm T}$. In the investigated attached regimes, it is
shown for the first time that the formation of the $E_{\rm r}$ in the SOL
depends on parameters at the divertor, following a $E_{\rm r} \propto T_{\rm e}
/\lambda_q$ qualitatively similar to that found in a tokamak. Then, from the
analyzed plasmas, the observed $E_{\rm r}$ shear at the edge is linked to a
moderate local reduction of the amplitude of density fluctuations.
