Plasma physics emerged in the early 20th century and became a focal point for research after the Second World War due to the potential uses of nuclear fusion.The reasons for this varied from the creation of hydrogen bombs to fusion for energy production. Moreover, with recent developments in semiconductors and nanoscale objects, where quantum effects are non-negligible, a theory of quantum plasma wasrequired. Plasmas can be split into two main regimes, Classical and Quantum, each requiring a separate theory. In this thesis, we introduce the kinetic theory of plasmas. We study the two regimes separately and obtain a description of the plasmas in terms of a phase-space distribution function; a distribution 𝑓 in the classical case, and the quantum analogue in the Wigner function 𝑊. These are governed by the classical Vlasov equation and the quantum analogue in the Wigner equation. The introduction of the Wigner function in Wigner’s article [5] in 1932, made it easier to connect the two theories since theyboth reside within the phase space. To show that the quantum theory is equivalent to the classical theory with the addition of quantum effects, we used perturbation theory, with a perturbation in the form of an electrostatic linear wave. This results in two dispersion relations, one for each regime. These are equal except for a single term, which can be interpreted as quantum effects. This confirms that the two theories are equivalent in the classical limit. Moreover, we introduce the density matrix, a way to describe systems with statistical mixtures of quantum states. This enables us to derive the set of equations known as the BBGKY-hierarchy. In turn, this hierarchy allows us to reduce the number of particles we need to consider, something that comes in handy when dealing with many-particle systems, which otherwise can be close to impossible.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:umu-225095 |
| Date | January 2024 |
| Creators | Lundström, Sebastian |
| Publisher | Umeå universitet, Institutionen för fysik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
Page generated in 0.0021 seconds