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Understanding Plasma Physics: Theory and Calculations in Ionized Fluids

Explore the complexities of plasma physics in California, where solar plasma phenomena, ionized gas, and magnetic fields are observed. Learn about MHD principles, Liouville and Boltzmann equations, and generalized transport equations for kinetic modeling. Simplify kinetics and delve into transport equations for a comprehensive understanding of plasma properties.

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Understanding Plasma Physics: Theory and Calculations in Ionized Fluids

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Presentation Transcript

  1. Meanwhile, somewhere in California

  2. Solar plasma • Convection is complicated • Temperature is very high • Completely or partially ionized gas -> • Charges (protons and electrons) are present • + Magnetic field is somehow generated and observed • Quite dense • -> Need a good description of ionized fluid (plasma), since solving ~1030 equations of motion for each charged particle is not realistic…

  3. MHD • Start with basic principles: 6D volume in phase space, distribution function • Derive general transport equation • Calculate 0,1,2-momenta for velocity • Average over different particle types • Add induction equation for magnetic field • Simplify

  4. Some kinetics - Distribution function for particles f(ri,pi,t) in 6-dimensional space of coordinates and momenta. We can write a “conservation” equation for it. Liouville equation Collisions change the “conservation”: Boltzmann equation (BE) BE in vector form

  5. Simplifying kinetics - We want to get rid of velocity part of space. To do it we integrate BE for particle type a over an arbitrary volume in v-space d3V. We also multiply BE by a function of v, Χ(v). Where the averages <> are Generalized transport equation for Χ.

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