MHD SELF-SIMILAR SOLUTIONS FOR COLLIMATED JETS E. TRUSSONI Osservatorio Astronomico di Torino, Pino T.se, ITALY C. SAUTY Observatoire de Paris, DA EC, Meudon, FRANCE AND K. TSINGANOS University of Crete, FORTH, Heraklion, GREECE The MHD modelling of jets in axisymmetric geometry requires the treat- ment of the Bernoulli and the transfield equations, that can be treated following a self-similar approach. This technique is based on two main as- sumptions: i) the physical variables are factorized; ii) a suitable scaling law in one direction is prescribed. Solutions self-similar in the r direction (in a spherical frame of reference) have been studied to model collimated winds from disks (Blandford and Payne 1982). Here we present solutions self-similar in the direction, suitable to study the collimated wind around the polar axis of a rotating object (Tsinganos and Trussoni 1991, Sauty and Tsinganos 1994). Our basic assumptions are: - The magnetic flux function, that describes the poloidal components of velocity and magnetic field, is expressed as A(r, ) oc /(r)sin 2 0. - The density and the pressure of the plasma are assumed to scale linearly with A: p(r, ) oc 1 + A and P(r, ) oc P Q (r) (1 + KfA). Accordingly, the surfaces with equal poloidal Alfv n number M are spherical. The original MHD equations then reduce to three ordinary differential equations for the four variables M, / , P 0 and Pi ( KfA). To close the system we need further assumptions, that define two classes of solutions: 1) P 0 and Pi are related, i.e. KfA const; the unknown is / and the shape of the streamlines is deduced. For these solutions a characteristic integral exists (e): it is e > 0 or e < 0 whether the volumetric energy along the polar axis is lower or higher than along the fieldlines, respectively. 2) P 0 and P\ are kept unrelated, then the function / must be prescribed. By assuming / oc R n we can choose streamlines radially expanding (n 0) 455 R. Ekers et al. (eds.), Extragalactic Radio Sources, 455-456. 1996 IAU. Printed in the Netherlands. available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0074180900081444 Downloaded from https://www.cambridge.org/core. IP address: 18.206.13.133, on 04 Jun 2020 at 03:46:29, subject to the Cambridge Core terms of use,