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Physics 681: Solar Physics and Instrumentation – Lecture 21

Physics 681: Solar Physics and Instrumentation – Lecture 21. Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research. Magnetism. Fields and Conducting Matter The Induction Equation Electrical Conductivity on the Sun Frozen Magnetic Field The Magnetic Force

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Physics 681: Solar Physics and Instrumentation – Lecture 21

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  1. Physics 681: Solar Physics and Instrumentation – Lecture 21 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research

  2. Magnetism • Fields and Conducting Matter • The Induction Equation • Electrical Conductivity on the Sun • Frozen Magnetic Field • The Magnetic Force • Flux Tubes • Concentration of Magnetic Flux Tubes • Observational Evidence for Flux Tubes • Vertical Thin Flux Tubes • Curved Thin Flux Tubes • Thermal Structure of Photospheric Tubes • Sunspots • The Solar Cycle Center for Solar-Terrestrial Research

  3. Fields and Conducting Matter • Magnetic features: sunspots, sunspot fine structure, filaments, prominences, … • Magnetism on the Sun occurs on all scales! (small flux tubes to mean field) • Maxwell’s equations (magnetic permeability μ = 4π 10-7 Vs/Am) • Ohm’s law Center for Solar-Terrestrial Research

  4. Induction equation • Magnetic diffusivity • Magnetic Reynolds number • High conductivity: • Electrical conductivity of a fully ionized gas Center for Solar-Terrestrial Research

  5. ln Λ ≈ 5 for the solar interior, ln Λ ≈ 10 for the chromosphere, and ln Λ ≈ 20 for the corona • Conductivity is large: • The temperature in the solar photosphere/chromosphere is low  hydrogen and helium are neutral BUT heavier elements with low ionization potentials still donate electrons  collisions of electrons with neutrals  conductivity is greatly reduced • Conductivity for weak ionization • Large horizontal gradients (e.g., sunspots) • Collisions are rare and magnetic fields are strong  anisotropy • Plasma turbulence reduces conductivity Center for Solar-Terrestrial Research

  6. Kopecký and Soytürk (1971) Center for Solar-Terrestrial Research

  7. Frozen Magnetic Fields • High conductivity σ = 1 V/A (in sunspots), typical velocity v = 1 km/s, and scale height l = 100 km  frozen field lines • Total magnetic flux • Differential flux at two instances separated by an infinitesimal time interval dt Center for Solar-Terrestrial Research

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