Electron Beam Propagation and Radio-Wave Scattering in the Inner Heliosphere using Five Spacecraft

Solar energetic particles such as electrons can be accelerated to mildly-relativistic velocities in the solar corona. These electrons travel through the turbulent corona generating radio waves, which are then severely affected by scattering. The physical interpretation of the discrepancies between the actual and observed radio sources is still subject to debate. Here, we use radio emission observed by an unprecedented total of five spacecraft, to track the path of radio sources from the low corona to the inner heliosphere (15-75 R$_{\odot}$) generated during a solar event on 4 December 2021. In this study we use the Bayesian multilateration technique known as BELLA to track the apparent path of radio sources observed by Parker Solar Probe, STEREO A, Wind, Solar Orbiter and Mars Express. To validate the accuracy of the tracked path, we used Nan\c{c}ay Radioheliograph interferometric imaging at 150 MHz, which was found to agree with the estimated footpoints predicted by BELLA. We also further validated our results using ACE in-situ measurements. We found that the apparent radio sources followed the path of a Parker Spiral, with an associated solar wind velocity of approximately 493 km s-1 (consistent with the corresponding speed observed at 1 au at the relevant longitude) and connected to 75$^\circ$ longitude East at the solar surface. Finally, we made quantitative estimates of the scattering of radio waves that were found to be in good agreement with contemporary models of scattering. This work shows conclusive evidence that the disputed cause of the widely observed `higher than expected' electron densities at interplanetary distances is due to radio wave scattering, and provides a more detailed understanding of the propagation of radio waves emitted near the local plasma frequency in turbulent plasmas.