From Pascal.Demoulin@obspm.fr Tue May 27 17:53:32 2003 Date: Mon, 19 May 2003 18:14:12 +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'" Subject: Re: 2 new papers on magnetic helicity [Part 1, Text/PLAIN 173 lines] [Unable to print this part] Dear Kanya, I was not expecting such debate.... but I like it since it clarifies several parts .... and we start to have some agreement (as I wrote below).... of course not on every things....but that's a nice start !! My first purpose in our discussion is to ask you to understand my work correctly! I feel very sorry .....but that is exactly what I am trying to do ! I understand better now after your e.mails ! Still, I do not find what you wrote in e.mails in your ApJ paper.... so probably you will need to re-explain your method in the next paper you do on the subject (e.g. in your paper the velocity V "looks" really like a plasma velocity.... and I do not get the foot point motions). It seams to me that your method has now changed of scope (see also below). 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 AGREE that your method is different from the case using the Doppler measurement ! (first agreement ! :)= ). I believe that you now understand my comment, (although you may not yet be convinced totally?) Not yet fully, sorry ! see below. 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. Second agreement ! :)= 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?) Yes, I agree. As it is well explain in Jongchul's note.ps, LCT is able to give only a mean Ut (calculated on the spatial apodizing window used), not a local (pixel) value. So indeed, I am expecting large residual if you compute R at each pixel. Yes, I agree that this R still need to be computed. It is a measure of how well the LCT works. But what to do next with R large ? Three possible options: - improve the LCT algorithm, - "improve the data": use high resolution white light images rather than magnetograms - use the induction equation (third agreement ! :)= ). But in the last case, I do not fully agree with you (nothing is perfect yet !). If theoretically we agree that we should use: dBn/dt = nabla.( -Ut.Bn) (Eq. 27 in DB03) but that Ut is only approximate from LCT method (+ a specific problem at inversion lines where Bn = 0), we have: Ut = Ut(LCT) + u where u is the term missed by LCT method. Then we have to found u which satisfies: dBn/dt = nabla.( -Ut(LCT).Bn -u.Bn) The problem is now different (even if it looks similar) than in your ApJ paper: it is not Bt, but Bn which is present in front of the unknown function. Since the problem is different from the one in your ApJ paper, one should be concerned about the unicity of the solution (not obvious: the unknown, u, has now two components !). Bn=0 can be still a problem, then we can still look for the unknown Ft = u.Bn which satisfy: dBn/dt = nabla.( -Ut(LCT).Bn -Ft) .... but unique solution ??? I guess that you will object that it is the same as your method.... but I believe it is NOT since a term such as un.Bt catch only the vertical motions while a term such as u.Bn catch both vertical and horizontal motions (from Eq. 24 in DB03). Said differently, I found no good reason why LCT would miss ONLY foot point motions associated to vertical motions. 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. OK, fourth agreement ! :)= The main problem is to estimate the magnitude of this flux lost....: significant or not ? The vertical velocity Un in my ApJ paper was introduced originally to compensate that. Sorry, but I should tell you that it is not clear from your ApJ paper (at least for me !). (This is the first motivation of my work.) Same comment as above.... probably needs to be written in a next publication. 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. I probably need to spend more time to check this...since I am not yet (sorry !) convinced that that the vertical velocity vanished automatically from your Eq. (37) (with Vn=0 in our ApJ paper notations) ! 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. I agree that it can indicate that the LCT are not yet precise enough, it is a warning, BUT I still wonder about the Un. Bn term (Vn. Bn in our ApJ paper notations). Because of the reasons above, I still believe that we should add the term of Un, As I say above, if it is a correction to the LCT, why only a vertical component for the velocity ? ....indeed rather both velocity components.... that we can write as a single u horizontal component (from Eq. 24 in DB03). in order to get more precise helicity flux. I hope that you understand my thought! Four agreements at least... not so bad ! :)= Still we have not ended the debate ! My best regards, 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 *====================================================================*