Plasma, a gas of charged particles exhibiting collective behaviour, can be found everywhere in our vast Universe. The characteristics of plasma in very distant parts of the Universe can be similar to characteristics in our solar system and near-Earth space. We can therefore gain an understanding of what happens in astrophysical plasmas by studying processes occurring in near Earth space, an environment much easier to reach. Large volumes in space are filled with plasma and when different plasmas interact distinct boundaries are often created. Many important physical processes, for example particle acceleration, occur at these boundaries. Thus, it is very important to study and understand such boundaries. In Paper I we study magnetic nulls, regions of vanishing magnetic fields, that form inside boundaries separating plasmas with different magnetic field orientations. For the first time, a statistical study of magnetic nulls in the Earth’s nightside magnetosphere has been done by using simultaneous measurements from all four Cluster spacecraft. We find that magnetic nulls occur both in the magnetopause and the magnetotail. In addition, we introduce a method to determine the reliability of the type identification of the observed nulls. In the manuscript of Paper II we study a different boundary, the shocked solar wind plasma in the magnetosheath, using the new Magnetospheric Multiscale mission. We show that a region of strong current in the form of a current sheet is forming inside the turbulent magnetosheath behind a quasi-parallel shock. The strong current sheet can be related to the jets with extreme dynamic pressure, several times that of the undisturbed solar wind dynamic pressure. The current sheet is also associated with electron acceleration parallel to the background magnetic field. In addition, the current sheet satisfies the Walén relation suggesting that plasmas on both sides of the current region are magnetically connected. We speculate on the formation mechanisms of the current sheet and the physical processes inside and around the current sheet.

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The complete set of Kubo conductivity tensors are computed for two- and three-dimensional linear magnetic null systems using collisionless single-particle simulations. Chaos regions are constructed for each case, along with the complete Lyapunov spectrum. It is found that stochastic frequency mixing of particle bounce motion, as well as gyromotion, contribute significantly to the conductivity. For many cases, the conductivity curve is well approximated by power-laws, resulting in a divergent value of the direct-current conductivity, while others can be described by a sum of Maxwellian curves. The energy dissipation of these systems is also briefly discussed.