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Surely the power input is dictated by the Poynting flux at the base, and so any saturation level of loop tangling has nothing to do with it? Otherwise one would have to be extracting energy out of the corona itself, rather than the convection zone. <div><br></div><div>Hugh</div><div><br><div><div>On Mar 6, 2009, at 8:12 AM, Klimchuk, James A. (GSFC-6710) wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Mitch,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> <blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Dear All,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I have been away from coronal heating for a number of years, so I am</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">asking for some guidance.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Here is my problem:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The Parker model for heating relied heavily on energy storage</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">throughout a coronal loop. In the absence of reconnection the field</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">lines within</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">a loop would become increasingly tangled: the free energy within a</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">loop then increases as time squared, giving a power input increasing</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">linearly with time. Throw in reconnection,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">and the system reaches a steady state at some saturation time t_sat.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Here the heating power is linear in t_sat. Physically, t_sat tells you</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">the time needed to stress the field up to levels where reconnection</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">takes off, as in the secondary instabilities of Dahlburg, Linton and</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Antiochos. The curious thing is that the heating rate goes down if</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">reconnection is more easy to trigger, because the saturation time is</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">smaller for easy reconnection.</div> </blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Yes, this has always been a fascinating result.<span class="Apple-converted-space"> </span>If the energy release</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">process were highly efficient, the corona would be much cooler.<span class="Apple-converted-space"> </span>The</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">process must have a "switch-on" property whereby it remains dormant</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">while magnetic stresses build to substantial levels and then turns on.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The nice thing about the secondary instability is that it occurs at the</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">right level of stress to produce the observed temperatures and loss</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">rates.<span class="Apple-converted-space"> </span>(By the way, the secondary instability work is Dahlburg,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">KLIMCHUK, and Antiochos!!!)<span class="Apple-converted-space"> </span>Note that this switch-on property is</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">generic.<span class="Apple-converted-space"> </span>It must apply to flares, CMEs, and any magnetically driven</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">process.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> <blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Having grown up with these ideas, it is difficult to reconcile myself</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">with the newer observations suggesting the location of heating mostly</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">at the base of loops. This causes two problems: first, is there enough</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">volume of stressed field in the chromosphere/transition region to</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">store the saturation level energy (yes, I know B is stronger down</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">there, but still...). Secondly, reconnection may be too easy down</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">there because of lower magnetic Reynolds numbers. Can someone convince</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">me that you can still get 10^7 ergs/cm^2-sec active region heating</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">rates?</div> </blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">You raise a valid concern.<span class="Apple-converted-space"> </span>The integral of B^2 over the transition</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">region volume is small.<span class="Apple-converted-space"> </span>Note that B is the shear component of the</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">field, since we are interested in the free energy available to heat the</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">plasma.<span class="Apple-converted-space"> </span>One might be even more concerned about the chromosphere, which</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">is also not very thick and which has much greater heating requirements.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">The situation there is helped by the fact that the field may be more</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">highly concentrated in discrete flux tubes (at least in the low</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">chromosphere).<span class="Apple-converted-space"> </span>For a given magnetic flux, the volume integral of</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">magnetic energy goes as one over the filling factor.<span class="Apple-converted-space"> </span>Say we take a</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">magnetic flux density of 100 G, a chromospheric thickness of 2x10^8 cm,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">and a filling factor of 10%.<span class="Apple-converted-space"> </span>The energy per unit area is then 10^12</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">erg/cm^2.<span class="Apple-converted-space"> </span>For the transition region (h ~ 2x10^7 cm, f ~ 1), the number</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">is more like 10^10 erg/cm^2.<span class="Apple-converted-space"> </span>To satisfy the coronal energy budget of</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">10^7 erg/cm^2/s^1 in active regions, the field must be "recharged" every</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">1000 s.<span class="Apple-converted-space"> </span>Maybe this isn't so bad, since stresses can propagate down from</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">the corona (ultimately they come from the photosphere motions).</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Cheers,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Jim</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> <blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Best Wishes</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Mitchell Berger</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">On Fri, Mar 6, 2009 at 2:13 AM, Brooks, David (Forn Natl)</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><<a href="mailto:dhbrooks@ssd5.nrl.navy.mil">dhbrooks@ssd5.nrl.navy.mil</a>> wrote:</div> <blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Dear All,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">A good example (I would say that...) of hot loops in locally</div> </blockquote></blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">unipolar</div> <blockquote type="cite"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">regions</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">as seen by SOT (that Harry mentioned) is video 4 in our paper:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="http://www.iop.org/EJ/article/1538-4357/689/1/L77/23039.html">http://www.iop.org/EJ/article/1538-4357/689/1/L77/23039.html</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">It also shows that dynamic events in the chromosphere/transition</div> </blockquote></blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">region</div> <blockquote type="cite"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">cluster</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">around the active region neutral line in mixed flux regions. These</div> </blockquote></blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">are the</div> <blockquote type="cite"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">resolvable events that Jim referred to that don't reach high</div> </blockquote></blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">temperatures.</div> <blockquote type="cite"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Best wishes,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">David Brooks</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Loops mailing list</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:Loops@solar.physics.montana.edu">Loops@solar.physics.montana.edu</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="https://mithra.physics.montana.edu/mailman/listinfo/loops">https://mithra.physics.montana.edu/mailman/listinfo/loops</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> </blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Loops mailing list</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:Loops@solar.physics.montana.edu">Loops@solar.physics.montana.edu</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="https://mithra.physics.montana.edu/mailman/listinfo/loops">https://mithra.physics.montana.edu/mailman/listinfo/loops</a></div> </blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Loops mailing list</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:Loops@solar.physics.montana.edu">Loops@solar.physics.montana.edu</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="https://mithra.physics.montana.edu/mailman/listinfo/loops">https://mithra.physics.montana.edu/mailman/listinfo/loops</a></div> </blockquote></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">+++++++++++++++++++++</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br class="khtml-block-placeholder"></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">In medias res</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:hhudson@ssl.berkeley.edu">hhudson@ssl.berkeley.edu</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">+1 (510) 643-0333</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">AST:7731^29u18e3</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></span></span> </div><br></div></body></html>