From kusano@hiroshima-u.ac.jp Tue May 27 17:52:13 2003 Date: Thu, 15 May 2003 12:31:14 +0900 From: Kanya Kusano To: 'Pascal Demoulin' 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, "[iso-2022-jp] ^[$B2#;3^[(B ^[$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 Pascal, Thank you for your reply. Here, I briefly write my answer to a question from you. I wrote: > > Please note that the method using the induction equation is different > > from the case of Doppler measurement. You wrote: > 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 ? My answer to this question is NO. This is a key to close a small gap between us. My method based on the induction equation can provide us only the velocity which is consistent with the magnetic evolution (d B_n/d t). Using your notation, that is u_n and u_t, rather than v_n and v_t. You probably misunderstood this point of my paper. As I wrote in my ApJ paper, when you solve the inverse problem of the induction equation ("inverse" means that the velocity is solved when B and dB/dt are given), there is an infinite number of the solutions. However, if you specify the horizontal velocity, the solution of the vertical velocity is unique in the most cases. (That was proven in my ApJ paper.) Therefore, if and only if you use the real plasma velocity for the horizontal motion, my method gives you the real velocity v_n. For simplicity, let us restrict our discussion only to a simplest case, in which the total magnetic flux is not changed. In the case, if you use the tracking velocity U as the horizontal velocity, which satisfies your equation > dB/dt = nabla.( -U .Bn) (Eq. 27 in DB03), then my method gives you the solution that the vertical velocity is vanished everywhere. Thus, the energy and helicity fluxes of the vertical velocity are vanished AUTOMATICALLY. It does not duplicate the flux included in the part of the horizontal velocity. As long as you use the velocity consistent with the induction equation, you do not need worry about the duplication. This is my answer, and I hope and believe that we can achieve an agreement (at least) for this point! Thank you! 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://corona.qm.adsm.hiroshima-u.ac.jp/~kusano/ --------------------------------------------------------