Magnetic fields inside extremely fast shock waves

The aim of my research on magnetic fields in extremely fast shock waves has been to predict the properties of shock waves that move almost with the speed of light. These shocks are created in the tenuous interstellar medium by catastrophic events such as the explosion of stars many times heavier than the Sun. In these shocks the gas density is very low, and particle collisions are too infrequent to be of any importance: we call such shocks 'collisionless'. I have investigated how large electrical currents and magnetic fields can form in such shocks through the electromagnetic interaction of charged particles. After introducing the subject and explaining why it is important, I summarize the basic physics of shock waves, relativity theory, electricity and magnetism. I also give an introduction to Gamma-ray Bursts, an astronomical phenomenon which is thought to involve the kind of shock waves that I describe in this thesis. My research starts with a discussion of the large-scale gas compression in extremely fast shock waves and its effect on magnetic fields. The rest of my thesis focuses on the Weibel plasma instability, a mechanism that generates small-scale magnetic fields inside extremely fast shock waves. This mechanism is a key ingredient of the explanation of how the kinetic energy of the shock wave is converted into radiation with a non-thermal energy distribution, such as the radiation in Gamma-ray Bursts. I describe the dynamics of the particles in the shock front both analytically and by simulating their dynamics and the associated electromagnetic fields with the help of computers. I show that the Weibel instability causes the magnetic energy density to reach about 0.01% of the total energy density in a typical shock wave. The instability of the electrons entering the shock front develops first, and stops when the particles become trapped in the magnetic fields that they generate themselves and when the quiver motions induced by this magnetic field convert their directed kinetic energy into a thermal velocity spread (heat). The instability of the protons entering the shock front develops more slowly and is suppressed because the already heated electrons shield the magnetic fields that the protons produce. The electrical currents formed by the electron and proton flows merge to form larger currents, but the additional amplification of the magnetic field strength is limited because their diameter cannot grow beyond the electron skin depth of the plasma. I also discuss the limitations of my research, in particular the uncertainty whether the magnetic field strength is sufficiently strong to explain the brightness of Gamma-ray Bursts. Future research can clarify this by developing better models for the turbulence that develops when the Weibel instability has reached its end. These models are still difficult to develop because of the large difference in scale between electron interactions and proton interactions.