The Influence of Plasma Lensing Magnification on the Luminosity Function of Fast Radio Bursts

Small-scale clumps of ionized gas have been suggested by observations in the interstellar medium and the circumgalactic medium. The propagation of radio signals can be deflected by these plasma clumps, i.e., plasma lensing. One observable consequence is the magnification and demagnification of background sources. These effects distort the observed luminosity function and potentially introduce bias into population studies. In this work, we investigate these effects on fast radio bursts using Gaussian plasma clumps distributed across multiple lens planes within a small field of view. The central electron density for each clump is sampled from uniform, lognormal, and Gaussian distributions. Two analytical models are employed to mimic the intrinsic luminosity function. Our results show that plasma lensing can modify the observed luminosity functions. On one hand, our model shows that radio sources may be demagnified below the detection threshold, and the strength varies between ∼1% and 15% depending on the ionized gas model and the source redshift. On the other hand, magnification can produce anomalously bright sources at the high luminosity end. Both effects introduce potential biases in inferred source properties. The lensing strength correlates with the power spectrum of free electron density. However, scattering effects in the host galaxy or in the Milky Way can suppress the plasma lensing effects.