Stability of Astrophysical Beams

by Ralph Lierheimer Fiedler

Under the supervision of Professor Thomas W. Jones


The stability of a plasma bean traveling through a confining external medium is studied in an astrophysical context. Empirical relations have been obtained relating the growth rates of small boundary perturbations to the beam Mach number, the ratio of internal to external sound speed and the perturbation wavenumber (see Table I). Pinching mode instabilities are found to be the least stable mode for subsonic flow, whereas helical mode instabilities are the least stable for supersonic flow. An axial magnetic field acts to significantly destabilize a beam, over the hydrodynamical case, only if the beam is supersonic and the magnetic field pressure is on the same order, or greater than , the plasma gas pressure.
The least stable wave modes, as evaluated by the empirical relations, were used to estimate an upper limit to the distance a beam can travel before non-linear effects become important. Comparing observations of extended extragalactic radio sources with the distance limit provides information on the Mach number and sound speed ratio, that is, assuming beams exist in these sources (see the Applications section). Agreement in the values of the Mach number and sound speed ratio obtained using the distance limit and other independent methods suggests that the beam model is consistent with the observations of some extended radio sources (NGC 6251, for example).
Preliminary calculations of boundary instabilities, where a helical magnetic field is assumed within the beam, show, at least for supersonic flow, that increasing the magnetic filed pitch angle form zero degrees to 20 degrees, while keeping the field strength at the boundary constant, has less than a 5% effect on the perturbation growth rates as derived for an axial magnetic field.