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Physics 681: Solar Physics and Instrumentation – Lecture 22. Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research. The Magnetic Force. Lorentz force (non-relativistic Ohm’s law = magnetohydrodynamic approximation)

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physics 681 solar physics and instrumentation lecture 22

Physics 681: Solar Physics and Instrumentation – Lecture 22

Carsten Denker

NJIT Physics Department

Center for Solar–Terrestrial Research

the magnetic force
The Magnetic Force
  • Lorentz force (non-relativistic Ohm’s law = magnetohydrodynamic approximation)
  • The volume force can be divided into a magnetic pressure gradient and a magnetic tension
  • Magnetic flux tube applies a lateral pressure to the gas into which it is embedded
  • Typical pressure 104 Pa can be balanced by B ≈ 0.15 T
  • In sunspots we see at deeper layer  2  104 Pa  B ≈ 0.3 T
  • Magnetic tension is the tendency of lines of force to shorten themselves  restoring force to perturbations

Center for Solar-Terrestrial Research

magnetic flux tubes
Magnetic Flux Tubes
  • Converging plasma motion is capable of concentrating magnetic flux
  • Cellular flows (granulation, mesogranulation, supergranulation, and giant cells)
  • Kinematic approximation (the flow v is given, the Lorentz force is neglected)
  • 2D, stationary flow consisting of rolls
  • Magnetic Reynolds number Rm = ul / η = 250
  • Boundary conditions: field is vertical at all times at all boundaries
  • Field lines become deformed  diffusion term in the induction equation is no longer negligible  field line reconnection  magnetic flux is expelled from the interior and accumulated in sheets near the cell edges

Center for Solar-Terrestrial Research

slide4

Clark and Johnson (1967)

Galloway and Weiss (1981)

Center for Solar-Terrestrial Research

slide5
Steady state: time scale of field decay d 2 / η equals time scale of advection l / u
  • Final flux after field concentration
  • Field amplification is rapid l / u (turnover time)
  • Expulsion of flux is slower 5( l / u ) and depends on Rm
  • Flux sheets may exist (chain-like crinkles)
  • Equipartition between kinetic and magnetic energy densities (dynamic regime)
  • Regions of motion and regions of fields mutually exclude each other
  • Critical flux
  • Field BP corresponds to an equilibrium between magnetic and gas pressure

Center for Solar-Terrestrial Research

slide6

Galloway and Weiss (1981)

Center for Solar-Terrestrial Research

slide7
Surface density ρ = 3  10-4 kg/m3, velocity of granules u = 2.0 km/s  equipartition field Be = 0.04 T
  • Observed fields are a factor 3 larger  convective collapse (convective instability in the presence of a magnetic field)
  • Stable flux tube exist for a minimum field of 0.1 T capable of suppressing the convective instability
  • The magnetic field is very weak for the major fraction of the solar surface
  • Locally stronger fields of >0.1 T in flux tubes
  • Solar magnetic fields are intermittent
  • Pores are sunspots lacking a penumbra (B ≈ 0.15 T, lifetime ≈ 1 day, size ≈ 5 arcsec)
  • Magnetic knots (B ≈ 0.1-0.2 T, “line gaps” in spectra, lifetime ≈ 1 hour, size 1-2 arcsec, IR observations, abundant near sunspots, ≈ 10 knots per 100 granules, knots have predominantly the opposite field of sunspots, flux is balanced)
  • Unresolved fields  filling factor (d ≈ 100-200 km)

Center for Solar-Terrestrial Research

slide8

http://www.kis.uni-freiburg.de/~steiner/

Center for Solar-Terrestrial Research

slide9

Lin and Rimmele (1999)

Center for Solar-Terrestrial Research

slide10

Wang et al. (1998)

Center for Solar-Terrestrial Research

slide11

http://nsosp.nso.edu/dst/images/fill1.gif

Center for Solar-Terrestrial Research

slide14

Langhans et al. (2002)

Center for Solar-Terrestrial Research

slide15

http://dotdb.phys.uu.nl/DOT/Showpiece/movies.html

Center for Solar-Terrestrial Research