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19 | | -\@writefile{toc}{\contentsline {section}{\numberline {1}Week 1. Description of the plasma state, with Paolo Ricci}{1}{section.1}} |
20 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Plasmas in nature and laboratory}{1}{subsection.1.1}} |
21 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Rigorous definition of plasma: Debye length}{1}{subsection.1.2}} |
22 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Plasma definition: frequencies and parameters}{2}{subsection.1.3}} |
23 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Particle motion in a static uniform magnetic field . Plasma magnetic properties}{2}{subsection.1.4}} |
| 19 | +\@writefile{toc}{\contentsline {subsection}{\numberline {0.1}The notes' repository}{1}{subsection.0.1}} |
| 20 | +\@writefile{toc}{\contentsline {subsection}{\numberline {0.2}The course wiki and errata pages}{1}{subsection.0.2}} |
| 21 | +\@writefile{toc}{\contentsline {subsection}{\numberline {0.3}Qni's Julia package}{1}{subsection.0.3}} |
| 22 | +\@writefile{toc}{\contentsline {section}{\numberline {1}Week 1. Description of the plasma state, with Paolo Ricci}{2}{section.1}} |
| 23 | +\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Plasmas in nature and laboratory}{2}{subsection.1.1}} |
| 24 | +\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Rigorous definition of plasma: Debye length}{2}{subsection.1.2}} |
| 25 | +\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Plasma definition: frequencies and parameters}{3}{subsection.1.3}} |
| 26 | +\@writefile{toc}{\contentsline {subsection}{\numberline {1.4}Particle motion in a static uniform magnetic field . Plasma magnetic properties}{3}{subsection.1.4}} |
24 | 27 | \@writefile{toc}{\contentsline {subsection}{\numberline {1.5}Particle motion in given electromagnetic fields: the drifts }{3}{subsection.1.5}} |
25 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {1.6}Plasma confinement based on single particle motion. Magnetic mirrors, stellarators, tokamaks}{4}{subsection.1.6}} |
26 | | -\@writefile{toc}{\contentsline {section}{\numberline {2}Week 2: Kinetic description of plasmas, with Paolo Ricci}{7}{section.2}} |
27 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}From single particle to kinetic description}{7}{subsection.2.1}} |
28 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}2b) Coulomb collisions in plasmas. Bonus module.}{8}{subsection.2.2}} |
29 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}2c) Collisional processes in plasmas}{10}{subsection.2.3}} |
30 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.1}Slowing down of an electron beam}{10}{subsubsection.2.3.1}} |
31 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.2}Plasma resistivity}{10}{subsubsection.2.3.2}} |
32 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.3}Overview of plasma collision frequencies}{11}{subsubsection.2.3.3}} |
33 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}2d) Vlasov equation}{11}{subsection.2.4}} |
34 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.1}Derivation from Boltzmann equation}{11}{subsubsection.2.4.1}} |
35 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.2}Conservation laws for the Vlasov equation}{12}{subsubsection.2.4.2}} |
36 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.3}Interpretation of Vlasov equation}{12}{subsubsection.2.4.3}} |
37 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.4}(Formal) solutions of Vlasov equation}{12}{subsubsection.2.4.4}} |
38 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}The two stream instability!}{12}{subsection.2.5}} |
39 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.1}Simplifications}{13}{subsubsection.2.5.1}} |
40 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.2}Linearisation}{13}{subsubsection.2.5.2}} |
41 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.3}Getting to the two-stream instability}{15}{subsubsection.2.5.3}} |
42 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}2f) Kinetic plasma simulations. The Particle in Cell method}{15}{subsection.2.6}} |
43 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}The various time scales in a plasma}{15}{subsubsection.2.6.1}} |
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45 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.3}Practical PIC}{17}{subsubsection.2.6.3}} |
46 | | -\@writefile{toc}{\contentsline {section}{\numberline {3}Week 3. Fluid description of plasmas, with Paolo Ricci}{18}{section.3}} |
47 | | -\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}From Vlasov to two-fluid}{18}{subsection.3.1}} |
48 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Fluid quantities from the distribution function}{18}{subsubsection.3.1.1}} |
49 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.2}Examples of fluid averaged quantities}{18}{subsubsection.3.1.2}} |
50 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.3}The moments of the kinetic equation}{19}{subsubsection.3.1.3}} |
51 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.4}The continuity equation}{19}{subsubsection.3.1.4}} |
52 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.5}The two fluid model!}{20}{subsubsection.3.1.5}} |
53 | | -\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.6}Two fluid simulation of plasma turbulence}{21}{subsubsection.3.1.6}} |
| 28 | +\@writefile{toc}{\contentsline {subsection}{\numberline {1.6}Plasma confinement based on single particle motion. Magnetic mirrors, stellarators, tokamaks}{5}{subsection.1.6}} |
| 29 | +\@writefile{toc}{\contentsline {section}{\numberline {2}Week 2: Kinetic description of plasmas, with Paolo Ricci}{8}{section.2}} |
| 30 | +\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}From single particle to kinetic description}{8}{subsection.2.1}} |
| 31 | +\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}2b) Coulomb collisions in plasmas. Bonus module.}{9}{subsection.2.2}} |
| 32 | +\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}2c) Collisional processes in plasmas}{11}{subsection.2.3}} |
| 33 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.1}Slowing down of an electron beam}{11}{subsubsection.2.3.1}} |
| 34 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.2}Plasma resistivity}{11}{subsubsection.2.3.2}} |
| 35 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.3}Overview of plasma collision frequencies}{12}{subsubsection.2.3.3}} |
| 36 | +\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}2d) Vlasov equation}{12}{subsection.2.4}} |
| 37 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.1}Derivation from Boltzmann equation}{12}{subsubsection.2.4.1}} |
| 38 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.2}Conservation laws for the Vlasov equation}{13}{subsubsection.2.4.2}} |
| 39 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.3}Interpretation of Vlasov equation}{13}{subsubsection.2.4.3}} |
| 40 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.4}(Formal) solutions of Vlasov equation}{13}{subsubsection.2.4.4}} |
| 41 | +\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}The two stream instability!}{13}{subsection.2.5}} |
| 42 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.1}Simplifications}{14}{subsubsection.2.5.1}} |
| 43 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.2}Linearisation}{14}{subsubsection.2.5.2}} |
| 44 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.3}Getting to the two-stream instability}{16}{subsubsection.2.5.3}} |
| 45 | +\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}2f) Kinetic plasma simulations. The Particle in Cell method}{16}{subsection.2.6}} |
| 46 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}The various time scales in a plasma}{16}{subsubsection.2.6.1}} |
| 47 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.2}Simulation approach - Particle in Cell (PIC) method}{17}{subsubsection.2.6.2}} |
| 48 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.3}Practical PIC}{18}{subsubsection.2.6.3}} |
| 49 | +\@writefile{toc}{\contentsline {section}{\numberline {3}Week 3. Fluid description of plasmas, with Paolo Ricci}{19}{section.3}} |
| 50 | +\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}From Vlasov to two-fluid}{19}{subsection.3.1}} |
| 51 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.1}Fluid quantities from the distribution function}{19}{subsubsection.3.1.1}} |
| 52 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.2}Examples of fluid averaged quantities}{19}{subsubsection.3.1.2}} |
| 53 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.3}The moments of the kinetic equation}{20}{subsubsection.3.1.3}} |
| 54 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.4}The continuity equation}{20}{subsubsection.3.1.4}} |
| 55 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.5}The two fluid model!}{21}{subsubsection.3.1.5}} |
| 56 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.1.6}Two fluid simulation of plasma turbulence}{22}{subsubsection.3.1.6}} |
| 57 | +\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The two-fluid dispersion relation}{22}{subsection.3.2}} |
| 58 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.1}Linearization and fourier mode analysis - a review}{22}{subsubsection.3.2.1}} |
| 59 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2}Linearization of Maxwell equations}{23}{subsubsection.3.2.2}} |
| 60 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.3}Linearization of two-fluid equations}{23}{subsubsection.3.2.3}} |
| 61 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.4}The two-fluid dispersion relation}{24}{subsubsection.3.2.4}} |
| 62 | +\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Two fluid waves, parallel and perpendicular propagation}{24}{subsection.3.3}} |
| 63 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.1}Two fluid cold plasma dispersion relation}{24}{subsubsection.3.3.1}} |
| 64 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.2}Waves propagating parallel to $\ensuremath {\mathbf {B_0}}$}{25}{subsubsection.3.3.2}} |
| 65 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.3}Waves propagating perpendicular to $B_0$}{25}{subsubsection.3.3.3}} |
| 66 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.3.4}The main takeaway}{26}{subsubsection.3.3.4}} |
| 67 | +\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Properties of two-fluid waves (Resonanses, cutoffs, etc)}{26}{subsection.3.4}} |
| 68 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.4.1}Properties of right and left handed waves}{26}{subsubsection.3.4.1}} |
| 69 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.4.2}Whistler waves}{27}{subsubsection.3.4.2}} |
| 70 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.4.3}Cut-off and resonance frequencies}{28}{subsubsection.3.4.3}} |
| 71 | +\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.4.4}Properties of waves propagating perpendicular to $B_0$}{28}{subsubsection.3.4.4}} |
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