Magnetic Flux Emergence Zhang & Low

1. Magnetic Flux EmergenceZhang & Low Paper II. used “field flipping” trick to study “current sheet” (CS) and “relaxed” (RX) fields, w/J = 0: “pot’l w/in domains” Here, use LFFF fields (|J|>0), again comparing CS & relaxed fields, this time subject to constraint of H conservation. Goal: Learn about changes in energy & topology from emergence & relaxation.

2. Outline • Briefly review helicity • Cursory review of procedure • Cursory review of results • Majority of time: Discussion!

3. Helicity • Woltjer’s Theorem: min E field for given helicity has constant a • Taylor explains behavior in reverse field pinch experiments: B evolves toward LFFF -- a diffuses toward constant distribution. • NB: field does not relax to potential!

4. Helicity, p. 2 – Use w/Solar? • Need relative helicity for gauge invariance if B field crosses boundary surface. • Q: Do CS fields contain helicity? • Antiochos: on Sun, unlike lab experiments, “everything can’t reconnect w/ everything” • So: a can’t diffuse – Taylor’s idea N/A! • Further: a seems to concentrate, not diffuse! • Q: When the Sun’s field relaxes (reconnects), what’s it do with that helicity? • Low: the role of CME’s is to carry away helicity!

5. Procedure – Field Flipping a la Paper II.

6. Procedure – LFFF Flipping in Paper III. • Same idea, w/an extra step: • Fig. 2, RHS: Find LFFF with “emerged field” • Fig. 2, LHS: Find LFFF w/o “emerged field,” then flip sign of field w/in flux surface dilineating “emerged” & “preexising” fields • Flipping alters helicity (but not energy), so a in un- and flipped fields must be found to keep same H and match same BC. (Fig. 4)

7. Comments on Procedure • Free boundary problems are tough, hence the field flipping trick. • Confined field within volume 1.0 < r < 4.0. Q: Does this limit conclusions that can be drawn from this work? Prob’ly not. • Emerged/preexisting ratio of .44 seems more plausible than 3.4 case.

8. Results • Fig. 6: Have cases where flux rope forms. • Fig. 8: Found case where twist in emerged field’s rope flips sign after relaxation! • Fig. 12: found case with highest energy in lowesta field (cf., Berger 1985)

9. Implications & Discussion • Page 485, 2d col., final para: Mechanism of concentrating twist in flux rope formation? • Page 488, 2d col., final para: “Take Home:” Items a) & b). • “Idealization:” (3) is prob’ly only relevant in Chen’s model of CME’s – timescales of relaxation in other models << timescales of photospheric evolution

10. More Discussion Points • Page 492, 2d col.:Something or other about some Hudson guy’s “Implosion” idea