From kusano@hiroshima-u.ac.jp Sun Jun 1 20:09:09 2003 Date: Sat, 31 May 2003 16:37:38 +0900 From: Kanya Kusano To: 'Pascal Demoulin' 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 [The following text is in the "iso-2022-jp" character set] [Your display is set for the "US-ASCII" character set] [Some characters may be displayed incorrectly] Dear Pascal, Thanks very much for your last two mails. I am really happy that we achieved common understandings!! > GOOD NEWS: I am AGREEING with you ! Can you believe it !!! :)= Sure!! I knew that this day is coming!! > SO, FINALLY GOOD NEWS: I agree that the solution to Eqs. > (32, 37) is > unique !!! > (but as you have seen, it was not obvious to me from the > beginning ! :)= ) Yes, I agree! Your argument is precise. Actually, I did not yet directly check the uniqueness of (32, 37) before your mail. I appreciate that!! > > (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 !!! Fine! > 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 Fine, too!! > > Therefore, we do NOT need to measure the > > perpendicular velocity in order to derive the energy flux! > YES !! Another excellent point !!! Thanks! > > Sec.4 Demonstration > Your application to observations is really nice !! OK ! Thanks, again!! > As you do, it will be better to first apply again to AR 8100 to show > better the evolution > of the method. > Yes. At least at the present time, I believe that the combination of the LCT and the induction equation is the best way to measure the helicity and energy fluxes. However, we need some benchmark in order to improve that. AR8100 is a good example, because both the flux emerging (increasing magnetic flux) and the shear motion may be involved. > 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. Yes, I fully agree! I also had clearly realized this point. In fact, the referee of our ApJ paper reminded us that, in my method, there is an ambiguity in the partition of the fluxes between the normal part (dot Hn, dotEn) and the tangential part (dotHt, dotEt) by his/her excellent comment (it was actually very smart referee!), although it is not matter for the measurement of total fluxes. I now no longer think that we should call them the fluxes due to the “vertical” motion and to the “horizontal” motion. Probably, such an explanation in my paper misled you, when you first read it. > 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 ! > Yes, it could be an interesting point for the future study of helicity injection mechanism. > So, after some oscillations... the convergence rate was fast ! > Thanks a lot. That is a simulating discussion ! This series of discussion not only makes many things clear, but also makes us find a couple of new things. Now, in order to summarize that, let me try to draft some report based on the final part of our debate and an additional examination of our method. It may be helpful for the next step of our study. I like to send you it first before the submission to a public archive. Anyway, thanks again Pascal, and all other attendee to this on-line conference over e-mail connection! I do hope that it can contribute your study! PS: Are you coming to helicity session at Sydney in July? Best my regards, Kanya -------------------------------------------------------- Kanya KUSANO, Graduate School of Advanced Sciences of Matter, Hiroshima University Higashi-Hiroshima, Hiroshima 739-8530, Japan Phone:[81] (824) 24-7016 fax: [81] (824) 24-7014 e-mail: kusano@hiroshima-u.ac.jp home page: http://plasma.sci.hiroshima-u.ac.jp/~kusano/ --------------------------------------------------------