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The early optical afterglow emission of several gamma-ray bursts (GRBs) showsa high linear polarization degree (PD) of tens of percent, suggesting anordered magnetic field in the emission region. The light curves are consistentwith being of a reverse shock (RS) origin. However, the magnetizationparameter, $\sigma$, of the outflow is unknown. If $\sigma$ is too small, anordered field in the RS may be quickly randomized due to turbulence driven byvarious perturbations so that the PD may not be as high as observed. Here weuse the "Athena++" relativistic MHD code to simulate a relativistic jet with anordered magnetic field propagating into a clumpy ambient medium, with a focuson how density fluctuations may distort the ordered magnetic field and reducePD in the RS emission for different $\sigma$ values. For a given densityfluctuation, we discover a clear power-law relationship between the relative PDreduction and the $\sigma$ value of the outflow. Such a relation may be appliedto estimate $\sigma$ of the GRB outflows using the polarization data of earlyafterglows.

Magnetized Reverse Shock: Density-fluctuation-induced Field Distortion, Polarization Degree Reduction, and Application to GRBs