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Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics

Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics. 20-nov-2008. Sunspot equilibria. Sunspots are colder than surroundings So pressure drops faster with height actually exponentially faster Small effect at depth, and total pressure = known

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Computational Astrophysics: Magnetic Fields and Charged Particle Dynamics

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  1. Computational Astrophysics:Magnetic Fields and Charged Particle Dynamics 20-nov-2008

  2. Sunspot equilibria • Sunspots are colder than surroundings • So pressure drops faster with height • actually exponentially faster • Small effect at depth, and total pressure = known • We specify the total pressure at the bottom • For simplicity; no flows through the vertical boundaries • Enforced as py=0 there • Need boundary conditions for other variables • For weak fields we can just extrapolate

  3. Implementing • Equation of contiuity • Mass conservation in fixed coordinate system: • Boundary conditions: • At the boundaries we take the vertical velocity to vanish (anti-symmetric), while the density is extrapolated in the log

  4. Implementing • Equation of motion • Momentum conservation in fixed coordinates: • Boundary conditions • We extrapolate the log pressure • Assume velocity to vanish (anti-symmetric) • The magnetic field is in the x-y plane, so we need the y-derivative of Bx – extrapolate Bx

  5. Implementing • Magnetic field equations for ideal MHD • Induction equation • Boundary condtions • Only Ez is non-zero (Uz and Bz vanish) – we extrapolate it through the boundaries

  6. Implementing • Magnetic field equations for ideal MH • Electric current density: • Boundary condition • We needwhich we take from extrapolation of Bx

  7. Code pieces for sunspot experimentarium • 2c/exercise2c.pro • events.pro • make_widgets.pro • initial_values.pro • stagger.pro • boundary.pro

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