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A Global Effect of Local Time-Dependent Reconnection

A Global Effect of Local Time-Dependent Reconnection. Eric Priest. In Collaboration with Dana Longcope. 1. Introduction - Reconnection on Sun. (a) Solar Flare:. An Effect: seismicflare wave. In photosphere (MDI) (8-100 km/s 70 mins). Chromospheric flare wave:. Coronal Heating:.

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A Global Effect of Local Time-Dependent Reconnection

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  1. A Global Effect of Local Time-Dependent Reconnection Eric Priest In Collaboration with Dana Longcope

  2. 1. Introduction- Reconnection on Sun (a) Solar Flare:

  3. An Effect:seismicflare wave In photosphere (MDI) (8-100 km/s 70 mins)

  4. Chromospheric flare wave:

  5. Coronal Heating: Yohkoh- glowing in x-rays

  6. Hinode X-ray Telescope (1 arcsec):

  7. Close-up How heated?

  8. Coronal Tectonics Model (updated version of Parker nanoflare/topological dissipation) Each ‘Coronal Loop’ --> surface in many B sources • --> web separatrix surfaces • As sources move --> J sheets on surfaces --> Reconnect --> Heat • Corona filled w. myriads of J sheets, heating impulsively (see talk by Haynes and by Wilmot-Smith)

  9. Some j sheets at nulls/separators (see Pontin talk) - there are many nulls in corona ?? “X marks the spot” Many sheets also at QSLs-non-nulls

  10. If reconnection heating coronaat many sheets, 1. How does energy spread out ? -- conduction along B -- waves across B 2.If reconnection time-dependent, how much energy liberated locally/globally? Simple model problem

  11. j 2. Magnetic fields in 2D A - flux function contours are field lines A = const X-point: Bx=B’y, By=B’x By+iBx=B’(x+iy)=B’w current:

  12. branch point branch point branch cut j Current I0 (Green 1965) A Current Sheet ? large r

  13. At large r X-point field

  14. At large r perturbation: line current Most of perturbation energy to distance L ~ ~ Lots of energy far from CS

  15. Suppose sheet reconnects Local process but has global consequences: Decrease I--> Bmust change at great distance How ??

  16. 3. Model for effect of reconnection Linearize about X-point B0 : Assume B1 @ t=0 is due to current sheet current diffuses i.e. reconnection  is “turned on” Assume a small current sheet, i.e. (natural diffusion length) so that sheet rapidly diffuses to circle and dynamics can be approximated by linearising about X

  17. Equations natural variable Use only axisymmetric (m=0) part

  18. (r) I0 r D Natural New Variables I Expect: r

  19. Governing equations I EV I Induction Motion EV I • Natural length-scale: • Combine: I I I wave diffusive

  20. Nondimensionalise I I EV EV I EV I I -----> EV EV EV I ? large r and small r

  21. >> 4. Limits(i)Large r (wave) limit:when I EV I I0 R EV I I I0 telegraphers equations EV

  22. >> I0 t R 4. Limits(i)Large r (wave) limit:when I EV I rightward EV I I I0 telegraphers equations EV leftward (Fast Magneto- Sonic waves) I I0 EV

  23. jd classic diffusion: I0 (from wire @ t=0) r r EV I << (ii)Small r (diffusive) limit:when (i.e. r small) EV I I I EV Current density: Id I0 I I0 I0 jd

  24. (iii) Numerical Solution E=0 E=0 I’=0 I=0 E E E E E I I I I I E I R R=-7 R=20 I EV I EV I , Use a uniform staggered grid in R, advancing I and E alternately (11 orders of magnitude in r)

  25. E=0 5. Numerical Solution E=0 I=0 I’=0 E I E E E E I I I I E I R R=-7 R=20 I EV I EV I Diffn term advanced implicitly in an operator splitting method I I0 I0 initial condition @t=0.001/A I0 EV

  26. Numerical Solution for I (------- diffusive solution) I log r (Departs slightly from diffusive solution at small r)

  27. Numerical Solution I(r) Wave solution R Transition: diffusive to wave solution Diffusive solution t

  28. Numerical solutions forIand Eu I EV I I Wave solution: EV I EV I

  29. Magnetic Field: I Sheath ofCurrentpropagates outleaving I = 0 behind

  30. In wake of sheath -a flow Ev -->v I EV But flow near X does not disappear -- it slowly increases ! EV

  31. I (diffusive limit) A(0,t) A(r,t) Flux function A? A t log r -->X-point Electric field Diffusive soln has E decreasing in time Numerical solution has E const (driven by outer wave soln)

  32. 5. Resolving the Paradox-- a 3rd regime -- at later times - eg in j(r,t): I I jd new regime Diffusive solution j I jd(0,t) ~ log r t

  33. I0 ja/d (r,t) At large t Resolving the Paradox I EV I advection - diffusion j But what is j(r,t)? EV I

  34. I I0 I EV I0 -- produces a steady E (independent of ) New Regime ja/d (r,t) Peak in j at X-point remains

  35. EV Poynting flux Ohmic heating Energetics Magnetic energy I Kinetic energy EV For an annular region (in or out) (negative)

  36. (ii) Large t K.E Heat Energetics (i) K.E Diffusion --> Magnetic energy into Ohmic heat Heat (integrated from t=1/ ) Magnetic energy into K.E

  37. 6. Summary Response to enhanced  in current sheet (CS): (i) Diffusion spreads CS out (ii) Wave (Lorentz force) carries current out at vA - as sheath (iii) Peak in j at X remains --> steady E independent of i.e. fast • Most magnetic energy is converted into • kinetic energy in wave -- • may later dissipate. • Coronal heating -- reconnection + wave

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