<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear Bernd,<div><br></div><div>Thanks for your feedback, which is always interesting from your side.</div><div>What are you up to with STEREO plus magnetic modeling ?</div><div>I hope to see you at the COSPAR meeting in Bremen,</div><div>where we could discuss things.</div><div><br></div><div>Cheers,</div><div>Markus</div><div><br></div><div><br><div><div>On Jun 22, 2010, at 1:13 AM, <a href="mailto:binhest@mps.mpg.de">binhest@mps.mpg.de</a> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><br>Dear Marcus,<br><br>thanks for the hint to your recent loop paper. I browsed through it<br>but I stumbled already on page three where you outline your philosophy:<br>You want to test, how close you can fit a potential field to a set of<br>(stereoscopically derived) field lines. The answer could have bee given<br>without numerical tests: as close as your parameter space allows. </div></blockquote><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Well, within a specific model, such as with unipolar charges or dipoles,</div><div> <span class="Apple-tab-span" style="white-space:pre"> </span>you can approximate a set of coronal loops only within a certain tolerance.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Once you reach a best fit, you cannot get closer, regardless how many</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>free parameters you add. For instance, if an observed loop is a "square",</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>every model consisting of multiple "semi-circles" cannot improve the fit</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>by adding more semi-circles. So, how close you can fit the data depends</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>very much on your chosen parameterization. In this study we tried with</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>buried magnetic charges, but it was not clear a priori if we get a closer</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>match to the STEREO loops than standard extrapolation models. </div><br><blockquote type="cite"><div>The<br>same would hold for a NLFField.</div></blockquote><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>They also have constraints from the photospheric field that does not</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>allow for a better fit than what we measured with the misalignment angles.</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>We wanted to see if the misalignment is due to a wrong boundary condition</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>or due to the inadequacy of NLFFF models.</div><br><blockquote type="cite"><div> The field you find is probably not<br>unique, because you may superpose potential fields which vanish along<br>the field lines.</div></blockquote><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Of course, one best-fit solution is not unique, there are many solutions</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>with similar small misalignment.</div><br><blockquote type="cite"><div> Hence from a successful fit no conclusion can be drawn about the nature of the true field.<br></div></blockquote><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>You are right, we cannot tell whether the true field is potential or not,</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>but we can narrow down the degree of non-potentiality and</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>have a more accurate magnetic field model that is useful for</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>many modeling tasks (like hydrodynamic modeling of an active region).</div><br><blockquote type="cite"><div>At the end of subsection 2.1: I do not know the paper by Gary (2010), </div></blockquote><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Gary's paper contains PTA (parameteric Transform Analysis) that</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>is a general magnetic field deformation concept that can be applied</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>to any model. </div><br><blockquote type="cite"><div>but Conlon and Gallagher (2010) is not NLFFF.<br></div></blockquote><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>You are right, he uses only LFFF (I have to correct that, thanks!)</div><br><blockquote type="cite"><div>And finally: What do you mean by "Abelian"? Commonly this term is used for a</div></blockquote><blockquote type="cite"><div>group property indicating the the group operation is commutative. What does "Abelian" mean for a magnetic vector field ?<br></div></blockquote><div><br></div><span class="Apple-tab-span" style="white-space:pre"> </span>Abelian in the sense of commutative and linear. I wanted to emphasize</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>that we can model the superposition of many unipolar charges or dipoles</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>in any commutative permutation (irregardless of the order) and preserve</div><div><span class="Apple-tab-span" style="white-space:pre"> </span>the divergence-free condition. </div><div><blockquote type="cite"><div><br>Many regards<br><br>Bernd<br><br><br> ======================================================================<br> M M PPPP SSS Dr. Bernd Inhester<br> MM MM P P S Max-Planck-Institut for Solar System Research<br> M M M PPP SS 37191 Katlenburg-Lindau, Germany<br> M M P S Phone:+49 5556 979477 Fax:+49 5556 979240<br> M M P SSSS Email: <a href="mailto:binhest@mps.mpg.de">binhest@mps.mpg.de</a><br> ======================================================================<br><br><br><br><br>On Fri, 18 Jun 2010, Markus J. Aschwanden wrote:<br><br><blockquote type="cite">Dear Loop Aficionados,<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">In case you are interested in magnetic modeling of loops ....<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">Cheers,<br></blockquote><blockquote type="cite">Markus<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">Aschwanden,M.J. and Sandman, A.W. 2010, Astronomical Journal, ... (in press)<br></blockquote><blockquote type="cite">URL1="<a href="http://www.lmsal.com/~aschwand/eprints/2010_bootstrap.pdf">http://www.lmsal.com/~aschwand/eprints/2010_bootstrap.pdf</a>"<br></blockquote><blockquote type="cite">Bootstrapping the coronal magnetic field with STEREO: Unipolar potential field modeling<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite">____________________________________________<br></blockquote><blockquote type="cite">Dr. Markus J. Aschwanden<br></blockquote><blockquote type="cite">Solar & Astrophysics Laboratory<br></blockquote><blockquote type="cite">Lockheed Martin Advanced Techology Center<br></blockquote><blockquote type="cite">Org. ADBS, Bldg. 252<br></blockquote><blockquote type="cite">3251 Hanover St., Palo Alto, CA 94304, USA<br></blockquote><blockquote type="cite">Phone: 650-424-4001, FAX: 650-424-3994<br></blockquote><blockquote type="cite">URL: <a href="http://www.lmsal.com/~aschwand/">http://www.lmsal.com/~aschwand/</a><br></blockquote><blockquote type="cite">e-mail: <a href="mailto:aschwanden@lmsal.com">aschwanden@lmsal.com</a><br></blockquote><blockquote type="cite">_______________________________________<br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote><blockquote type="cite"><br></blockquote>_______________________________________________<br>Loops mailing list<br><a href="mailto:Loops@solar.physics.montana.edu">Loops@solar.physics.montana.edu</a><br>https://mithra.physics.montana.edu/mailman/listinfo/loops<br></div></blockquote></div><br><div>
<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 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; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-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; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 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; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-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; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 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; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>____________________________________________</div><div>Dr. Markus J. Aschwanden</div><div>Solar & Astrophysics Laboratory</div><div>Lockheed Martin Advanced Techology Center</div><div>Org. ADBS, Bldg. 252</div><div>3251 Hanover St., Palo Alto, CA 94304, USA</div><div>Phone: 650-424-4001, FAX: 650-424-3994</div><div>URL: <a href="http://www.lmsal.com/~aschwand/">http://www.lmsal.com/~aschwand/</a></div><div>e-mail: <a href="mailto:aschwanden@lmsal.com">aschwanden@lmsal.com</a></div><div>_______________________________________</div><div>____________________________________</div><br class="Apple-interchange-newline"></span></span></span></span><br class="Apple-interchange-newline">
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