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(abridged) The polarized thermal radiation at far infrared and submillimeterwavelengths from dust grains in interstellar clouds with irregular magneticfields is simulated. We show that the polarization properties of quiescentclouds and of star-forming regions are consistent with Kolmogorov-liketurbulent magnetic fields that are comparable in magnitude to the uniformcomponent of the magnetic fields. If the beam size is much smaller than thecorrelation length $L_{\rm corr}$ of the fields, the calculated percentagepolarization $p$ decreases to an asymptotic value when the number ofcorrelation lengths $N_{\rm corr}$ through the cloud exceeds a few tens. Forthese values of $N_{\rm corr}$, the dispersion in the position angles$\sigma_\alpha$ is still appreciable--decreasing to only about $20^{\circ}$.However, when the finite size of a telescope beam is taken into account, theasymptotic value of $p$ is reached for fewer correlation lengths (smaller$N_{\rm corr}$) due to averaging over the beam; $\sigma_\alpha$ becames muchsmaller and consistent with the observational data. The smoothing of thepolarization properties due to the combined effect of the thickness of thecloud and the finite size of the beam can be described by a single variablewhich we designate as the generalized number of correlation lengths. Inaddition, we study various factors that may contribute to the decrease in thelinear polarization percentage with increasing intensity that is observed atsubmillimeter and far infrared wavelengths in many, though not in all, darkclouds (the "polarization hole" effect).Comment: ApJ, in pres

Irregular Magnetic Fields and the Far‐Infrared Polarimetry of Dust Emission from Interstellar Clouds