Plasma lensing interpretation of FRB 20201124A bursts at the end of September 2021

When the radio photons propagate through a non-uniform electron density volume, the plasma lensing effect can induce an extreme magnification to the observed flux at certain frequencies. Because the plasma lens acts as a diverging lens, it can extremely suppress the observed flux when aligned with source. These two properties can theoretically cause a highly magnified Fast Radio Burst (FRB) to faint or even disappear for a period of time. In this paper, we interpret that the significant increase in burst counts followed by a sudden quenching in FRB 20201124A in September 2021 can be attributed to plasma lensing. Based on the one-dimensional Gaussian lens model, we search for double main-peak structures in spectra just before its extinction on September 29, 2021. After the de-dispersion and de-scintillation procedures, we find eight bursts with double main-peaks at stable positions. There are three parameters in our modelling, the height and width of the one-dimension Gaussian lens and its distance to the source. We reformulate them as a combined parameter $\mathrm{P}_0 \propto \left ( \frac{a}{\mathrm{AU}}\right )\sqrt{\frac{\mathrm{kpc}}{D_{\mathrm{LS}}} \frac{\mathrm{pc}\;\mathrm{cm}^{-3}}{N_0} }$. The frequency spectra can give an accurate estimation of $\mathrm{P}_0$ corresponding to $\left ( \frac{a}{\mathrm{AU}}\right )\sqrt{\frac{\mathrm{kpc}}{D_{\mathrm{LS}}} \frac{\mathrm{pc}\;\mathrm{cm}^{-3}}{N_0} } \approx 28.118$, while the time of arrival only give a relatively loose constraint on $a^2/D_{\mathrm{LS}}$. Comparing with the observation dynamic spectra, we suggest that for a plasma lens in host galaxy, e.g., $D_{\mathrm{LS}}\approx 1\mathrm{kpc}$, the width of lens can not be larger than $40\mathrm{AU}$. At last, we estimate the relative transverse motion velocity between the lens and source, $v\approx98\left(\frac{a}{\mathrm{AU}}\right)\mathrm{km/s}$.