Fast simulation of the whole-sky CMB map in the presence of primordial magnetic field

We present a novel method for generation of sets of the Cosmic Microwave Background (CMB) anisotropy maps, which reproduces the $\Delta \l=2$ correlations associated with Alfv\'en turbulence. The method is based on the non-linear transformation of the CMB maps, which is obtained from the Monte Carlo simulation of the statistically isotropic Gaussian signal. Our method is computationally fast and efficient. We have applied two estimators (the cross-correlation estimator in multipole domain for $\l+1,m$ and $\l-1,m$ modes and circular phase moments) to test the statistical properties of derived maps. Both of these statistics confirm the effectiveness of our generation method. We believe that our method can be useful for fast generation of the non-Gaussian maps in the presence of the primordial magnetic field, and be a valuable tool for the non-Gaussianity investigation of the CMB in the framework of the future PLANCK data analysis.