From kusano@hiroshima-u.ac.jp Tue May 27 17:52:59 2003 Date: Sat, 17 May 2003 01:11:28 +0900 From: Kanya Kusano To: 'Pascal Demoulin' , 'Jongchul Chae' Cc: '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'" 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] Hello again! Pascal, As Prof.Chae wrote, I also think that your and Mitch's paper is nice, and I really believe that your paper is (at least theoretically) correct, except your comment to my paper. My first purpose in our discussion is to ask you to understand my work correctly! Let me tell you again, using my method, the helicity injection is NOT duplicated, since the vertical velocity Un is consistent with the magnetic evolution, i.e. dBn/dt = nabla.(Un.Bt-Ut.Bn). It is different from the case using the Doppler measurement, in which the directly observed velocity Vn is not consistent with the LCT result, i.e. dBn/dt not= nabla.(Vn.Bt-Ut.Bn). I believe that you now understand my comment, (although you may not yet be convinced totally?) By the way, I would like to progress our discussion to the next step. You showed that, if the LCT perfectly works, and if we can measure the velocity Ut, which satisfies the equation Ut = Vt - (Vn/Bn) Bt (Eq. 24 in DB03), Ut makes the correct fluxes of energy and helicity without any additional terms. Yes, I agree and I have never criticized this idea. However, in spite of that, I think that we SHOULD add the flux term of Un. Using your word, it is due to the limitation of the LCT. I know that it is out of scope of your paper (DB03). But, your paper suggested us a way to check how well does the LCT works. If (Eq. 24 in DB03) is correct, then dBn/dt = nabla.( -Ut.Bn) (Eq. 27 in DB03) Here, we should check how small the residual R=dBn/dt + nabla.(Ut.Bn) is. For Ut to give the precise flux, the residual R have to be negligiblly small. (OK?) I actually did that in the beginning of my study a couple of years ago, and found that the residual is substantially large (unfortunately!). There may be a lot of reasons. But, I guess that it is mainly due to that the LCT could not reproduce the infinite velocity, which should appear when the flux emerges on the magnetic neutral line, as you wrote. In fact, the residual is large particularly near the neutral lines. It means that the LCT does not work well. I know that the infinite velocity is not a real singular, as you wrote, because the electric field is finite. However, if the LCT cannot make the infinite velocity, then the electric field is vanished on the neutral line, and some amount of the fluxes is lost. The vertical velocity Un in my ApJ paper was introduced originally to compensate that. (This is the first motivation of my work.) Let me say again that if (Eq. 27 in DB03) is satisfied, the inverse problem of the induction equation gives the solution Un=0, because of the uniqueness of solution. However, my work indicated that the helicity and energy fluxes from Un was as large as the fluxes from Ut, and even the sign of the helicity injection is changed by the Un term, It implies that the LCT (at least in my analyses) is less reliable for the helicity and energy fluxes. Because of the reasons above, I still believe that we should add the term of Un, in order to get more precise helicity flux. I hope that you understand my thought! Best regards Kanya