From Pascal.Demoulin@obspm.fr Tue May 27 17:50:54 2003 Date: Wed, 14 May 2003 17:05:37 +0200 From: Pascal Demoulin To: Kanya Kusano 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, chae@cnu.ac.kr, haimin@sundog.caltech.edu, yjmoon@bbso.njit.edu Subject: Re: 2 new papers on magnetic helicity Dear Dr Kusano, In the previous mail, I should rather have said: Magnetic helicity has became a hot subject in these past MONTHS !!! :)= (looking for the numerous papers put on the the Max Millenium E-print archive recently !). Thanks, I printed your two new papers....and will read them... Now, about our different views. First, I am not surprised by your reaction. It took me a lot of time to convince myself that it was correct, in particular when the magnetic flux is increasing ! Next let go step by step to see where we really disagree.... and finally see if we can converge (hopefully !). > Please note that the method using the induction equation is different > from > the case of Doppler measurement. Yes they are different, BUT they have a COMMON PROPERTY: they BOTH aim to measure (or determine) the PLASMA velocity (Vn). In the case of your method this come from your Eq. (18) which is the ideal MHD induction equation where Vt and Vn are the plasma velocity components. OK ? The central KEY of our paper (DB03 later), is that tracking methods are following the foot-point of magnetic flux tubes, so they are measuring the velocity (called U) which is a combination of both Vt and Vn: U = Vt - (Vn/Bn) Bt (Eq. 24 in DB03) and it is only U which enter in the induction equation (Eq. 27 in DB03). Written in equations, your Eq. (18) is identical to Eq. 19 in DB03, and vector algebra gives: (with d meaning partial derivative ) dB/dt = nabla.(Vn.Bt-Vt.Bn) (Eq. 20 in DB03) = nabla.( -U .Bn) (Eq. 27 in DB03) In conclusion, if you agree that tracking methods give really the velocity U, there is NOTHING to add in the induction equation (except dissipation). Of course we can discuss the precision, validity of the tracking methods but that is a separate issue (OK ?). > we should not add the vertical velocity onto the helicity and energy > fluxes > (eqs. 25 and 26 in your paper). This is true, and this effect was > already > taken into account in my method > based on the induction equation (ApJ 2002, 577, 501). From above, I clearly DO NOT agree with this: your induction equation is written with the PLASMA velocities ! In your paper, you do the following: in the induction equation dB/dt = nabla.(Vn.Bt-Vt.Bn) you use U as a proxy for Vt, then you get: dB/dt = nabla.(Vn.Bt-U.Bn) ...... but U.Bn ALREADY contain the term Vn.Bt ! So I do still believe that you duplicate the terms due to emergence. I fill sorry, but I cannot change my mind for that reason !! > In your simple case (Fig.2 in your paper), the magnetic flux of each > polarity across the photosphere is not changed. NO ! Not when the top of the flux tube was crossing the boundary. I realize that we should have done a time evolution for the illustration... in order to not give this false impression ! Indeed the magnetic flux of each polarity CAN change. How it will change ? With ideal MHD, by emergence (or submergence) at the inversion lines (Bn=0). There, the foot point velocity: U = Vt - (Vn/Bn) Bt will be divergent (Vn, Bt finite, but Bn->0 ). This is a concern for tracking methods which will miss the period of time when the + and - polarities are very close. In any case, the small bipole will also be missed by the magnetogram..... > In more general case where the magnetic flux changes, it is obvious > that the > vertical velocity should be included into the helicity and energy > fluxes, since any > horizontal motion cannot reproduce the change in total magnetic flux. YES ...for the total magnetic flux..... but NOT for the helicity and energy fluxes ! That's look strange initially, I agree ! But indeed the helicity and energy fluxes are NOT linked directly to magnetic flux emergence ! For example, you can emerge a lot of flux without input of magnetic helicity. The only possible problem that I had suspected (which is indeed not a problem !) could be located where Bn=0 (inversion lines)....the only location where truly NEW magnetic flux could be transfered trough the boundary. Indeed because it is the non-singular U.Bn quantity (and not U) which enter in the helicity and energy fluxes, there is NO problem there too ! I hope that this clarify some points. I am not expecting that you agree directly with every things (may be none ! :)= )..... so I will be pleased to continue the argumentation, in particular because I believe that it is an important issue to derive budgets. As far as I know, this point was missed in all previous papers dealing with observations (even where I am co-author .... I was expecting myself too much from the emerging term !). 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 *====================================================================*