## 1 Introduction
### Radio Waves Propagation in the Ionosphere
The GNSS satellite networks (Global Navigation Satellite System) and innovative methods related to them and radio occultations (RO) have been initiated or used for research purposes, aimed at better understanding of the ionosphere layers. These include the FORMOSAT-3/COSMIC system (Formosa Satellite Mission 3-Constellation Observing System for Meteorology, Ionosphere, and Climate) and the successor of this system, the currently implemented FORMOSAT-7/COSMIC-2 RO. All these tools provide not only the determination of electron density and TEC (Total Electron Content) parameter, but also a support for numerical forecasts of cosmic weather. The LOFAR system fits perfectly into this trend, which in the LOFAR2.0 phase will be used mainly for purposes related to space weather research. Currently, the LOFAR4 SW (LOFAR for Space Weather) project is being implemented under European Union (EU) program Horizon 2020. The International Validation and Combination Center located at the University of Warmia and Mazury is an important part of the International GNSS Service's (IGS) Ionospheric Working Group. The Center collects ionospheric data provided by eight International Associated Analysis Centers (CODE/Switzerland, ESOC/Germany, JPL/USA, UPC/Spain, CAS/China, WHU/China, NRCan/Canada and DGFI-TUM/Germany), validates it and combines into final, combined IGS product. Maps provided by SRRC/UWM with high spatial (1 \(\times\) 1 degree) and temporal (5 min.) resolution will be used in close future by the LOFAR Telescope for ionosphere calibration process. In our LOFAR pulsar observations we intended to focus on the role of point changes in the state of the ionosphere in a specific direction in the sky that may be caused by various disturbances in the ionosphere, such as different-scale Travelling Ionosphere Disturbances (TIDs) [10; 11], plasma bubbles, plasma patches, field-aligned irregularities (FAIs), and down to very small plasma density fluctuations causing radio signal scintillations. It was also found that the turbulent spatial structure of the ionospheric electron density can be described by a Kolmogorov structure function:  
\[\varphi_{\mathrm{ij}}=(S_{\mathrm{ij}}/S_{0})^{\beta}, \tag{1}\]  
where \(\varphi_{\mathrm{ij}}\) is the phase variance between two points, \(S_{\mathrm{ij}}\) is the distance between the points, and \(S_{0}\) is the diffractive scale at which the phase variance is 1 rad. For index \(\beta\) equal to 5/3 the pure Kolmogorov turbulence occur. At 150 MHz and mid latitudes the standard diffractive scale ranges from 2 and 40 km. The conditions, under which the scale for LOFAR station approach to about 1 km (the Fresnel scale) are called a scintillation. In the case of astronomical research, scintillations are very undesirable because they prevent accurate measurements. This type of disturbance, as well as the TIDs, leads to a change in the observed value of TEC (total electron content) parameters from one to several units [12]. In our case, when it comes to the observation of meter radio waves, this relationship between the point of view of extraterrestrial sources of radio radiation becomes crucial and directly affects the obtained measurement results. For our specific low frequency LOFAR observations, this physical phenomenon causes changes in the effective antenna beam direction which may cause the pulsar to deviate from the beam center. The change of direction of view \(\Delta\phi\) depends on the wavelength \(\lambda\) and on the TEC like \(\Delta\phi=-25\cdot\lambda\cdot\Delta\)TEC. This causes a drop of the expected telescope sensitivity and in extreme cases (with unusually large TEC values) the source may be outside of the observed telescope beam altogether. All this makes the problem important for astrophysical measurements with telescopes operating on long radio waves.