Plasma Instabilities in Electron-Positron Pair Beams from Blazars

The non-detection of an electromagnetic cascade in the electron-positron plasma beams from blazars has led many physicists to invoke an intergalactic magnetic eld that de ects charged particles away from our eld of view. In this thesis we look at a dierent explanation. Namely that the beams loose their energy through plasma instabilities rather than the inverse Compton scattering which would create the cascade. We use a covariant formalism to calculate the linear response tensor of the plasma. Using this tensor we nd the absorption coecient for particles distributed according to the Jüttner distribution and for a dierent distribution based on simulations. The absorption coecient is found to diverge for specic values of the phase velocity when the electric eld of the mode vanishes. This is unphysical, which means there is some issue with the calculations. The issue is identied as the assumption that the imaginary part of the frequency, known as the absorption coecient, is small. This assumption contradicts the results making the calculations invalid. To solve this problem one would have to redo the calculations avoiding this assumption