MHD equilibria with flows in uniform gravity. II. A class of exact 2-D loop-like solutions

Details MHD equilibria with flows in uniform gravity. II. A class of exact 2-D loop-like solutions MHD equilibria with flows in uniform gravity. II. A class of exact 2-D loop-like solutions

Aug 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...275..613t&link_type=abstract

Astronomy and Astrophysics, Vol. 275, p. 613 (1993)

Astronomy and Astrophysics

Astrophysics

20

Mhd, Sun: Corona, Sun: Chromosphere, Sun: Magnetic Fields, Stars: Coronae

Scientific paper

We present a novel class of two-dimensional MHD equilibria which emerge as exact solutions of the coupled transfield and Bernoulli nonlinear equations governing the dynamics of steady flows along magnetic lines in an atmosphere that is horizontally compressible and vertically stratified in the presence of a uniform gravitational field. The topology of the solutions is analysed in detail and is found to be controlled by a classical sonic and a novel X-type critical point corresponding to a new characteristic speed for MHD wave propagation in an inhomogeneous medium. A subclass of low Alfvén numbers loop-like solutions is found for a mildly stratified atmosphere; for very strong stratification no solutions exist while for moderate stratification only periodic solutions are allowed. The results of the study are compared with those of models without flows and models with low Alfvén number flows while the approach followed here extends that of treating the flux tube as rigid, or slender. Among our conclusions is that an increase of the magnitude of the flow speed increases the height of the loops, while for stronger flows there are no equilibrium solutions and it is conjectured that the loop is disrupted. Thus, the general trends emerging from this analysis may be contrasted with solar observations wherein, for example, some solar loops extend over heights much higher than those predicted by models without flows. Then, in the quiet Sun and in chromospheric or coronal loops with plasma-β and Alfvén number not much smaller than unity, the above nonlinear effects of the flows should be taken into account.

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