From Pascal.Demoulin@obspm.fr Fri May 30 09:26:57 2003 Date: Fri, 30 May 2003 15:07:09 +0200 From: Pascal Demoulin To: Kanya Kusano Cc: 'Jongchul Chae' , 'mitch Berger' , 'Pablo Mininni' , 'Richard Canfield' , 'Alexander Nindos' , 'BC Low' , 'Jim Klimchuk' , 'Marcelo Lopez-Fuentes' , 'Sarah Gibson' , sakurai@solar.mtk.nao.ac.jp, 'Terry Forbes' , "'Brian T. Welsch'" , dana@mithra.physics.montana.edu, magara@mithra.physics.montana.edu, apevtsov@nso.edu, haimin@sundog.caltech.edu, yjmoon@bbso.njit.edu, "[ISO-2022-JP] \"'?^[$B;3^[(B ^[$B1{L@^[(B'\"" , 'Cristina Mandrini' , 'Lidia Driel-Gesztelyi' , "[ISO-2022-JP] \"^[$B??1I>k^[(B ^[$BD+90^[(B\"" Subject: Re: 2 new papers on magnetic helicity Dear Kanya, In present mail I finish to answer to our e.mail of mai 27 (the one with five figures). GOOD NEWS: I am AGREEING with you ! Can you believe it !!! :)= Indeed in this e.mail you go a long way forward ahead to your ApJ paper, explaining clearly your view ! Well done ! So I will basically made below small comments. > The helicity flux (E x A_p) and the energy flux (E X B) are generated > by the > electric field E. Therefore, the variation which we must find for the > measurement of the helicity and energy fluxes is NOT the velocity, BUT > the > electric field E. AGREE ! Indeed only the two tangential components of E, so Et (because one can presently used only the normal component of the induction equation. So, to be clearer, I would wrote: Et = Vt x Bn + Vn x Bt = Wt x Bn + Wn x Bt So, we have the equation > (Vt-Wt) x Bn + (Vn-Wn) x Bt = nabla xi, ......... <3> (Vt-Wt) x Bn + (Vn-Wn) x Bt = nabla_t xi, ......... <3> OK, I agree that the solution the normal component of the induction equation is unique if one can measure the velocity component along Bt X Bn. That is a new and nice result !!! > The second point is that the measurement of the perpendicular velocity > (fF') > is much easier than that of the parallel velocity (Ff), because it > does not > diverge even if the elevation angle of the field line (theta) is small. > Therefore, the LCT may provide more precise results for the > perpendicular > velocity compared to the parallel velocity. YES !! Excellent point ! > Once the perpendicular > velocity is measured, the induction equation derives the correct > answer, > however large the error in the parallel velocity is. YES > Therefore, we do NOT need to measure the > perpendicular velocity in order to derive the energy flux! YES !! Another excellent point !!! > Sec.4 Demonstration Your application to observations is really nice !! OK ! As you do, it will be better to first apply again to AR 8100 to show better the evolution of the method. A last comment: the splitting of dotH in dotH_t, dotH_n (the same for E) with your method, looks to me no longer useful, it even could even be dangerous to keep it .... as it can create a miss-understanding as follow ! We have so far no reason to think that dotH_n is due only to emergence of flux, of course there should be a fraction which is coming from emergence, but this fraction is unknown... Indeed, there are, a priori, extreme cases where dotH_n come only from horizontal plasma motions. More over this fraction is likely to evolve strongly with the AR age... What your analyze does indeed show is that when you use both LCT and induction equation dotH separates naturally in a two different components: perpendicular (along Bt X Bn) and locally parallel to the plane Bt, Bn. Let call it respectively perp and par, then dotH = dotHperp + dotHpar with both terms having a different origin from the technic used (resp. LCT and induction equation) but also from the physics: dotHperp is not coming from emergence (vertical plasma motion) dotHpar mix-up vertical and horizontal plasma motions (and we cannot separate them ... but that is not needed to get the helicity and energy flux). The amount of dotHperp with respect to dotHpar could have implications for the models (e.g. transfer of H by emergence or torsionnal Alfven waves... ?). > It suggests that the major part of helicity may be carried by the > vertical motion and the > parallel motion. Looks very interesting to see how general this is ! So, after some oscillations... the convergence rate was fast ! Thanks a lot. That is a simulating discussion ! My best wishes, Pascal *====================================================================* Pascal Demoulin Phone: 33 1 45 07 78 16 Observatoire de Paris Fax: 33 1 45 07 79 59 section Meudon, LESIA, Bat. 14 http://www.solaire.obspm.fr/demoulin/ F-92195 Meudon Principal Cedex Pascal.Demoulin@obspm.fr France *====================================================================*