Spatial quasi-periodic variations of the plasma density and magnetic field in zebra radio sources

Context. Radio bursts and their fine structures are an integral part of solar flares. Fine structures in particular are used for diagnostics of solar flare processes. The so-called zebras belong to the most important of such fine structures. Aims. We analyze seven zebra events in order to search for spatial variations in the plasma density and magnetic field in zebra-stripe sources. Methods. We used an improved method for estimating the gyroharmonic numbers of zebra-stripe frequencies. We compared observed zebra-stripe frequencies with those calculated in the zebra model. The differences in these frequencies vary and thus show spatial variations in the plasma density and magnetic field. Results. In six out of seven analyzed zebras, we found a rather high correlation coefficient (about 0.7 and higher) between spatial variations in the density and magnetic field and a strictly periodic function. These density and magnetic field variations are explained by the torsional or sausage magnetoacoustic waves in the loop in which zebra-stripe sources are located. We present the wavelengths of these waves in dependence on the zebra frequency and estimate their periods.