  Current-carrying flows, in the laboratory and in astrophysical jets, can form
remarkably stable magnetic structures. Decades of experience shows that such
flows often build equilibria that reverse field directions, evolving to an MHD
Taylor state, which has remarkable stability properties. We model jets and the
magnetic bubbles they build as reversed field pinch equilibria by assuming the
driver current to be stiff in the MHD sense. Taking the jet current as rigid
and a fixed function of position, we prove a theorem: that the same, simple MHD
stability conditions guarantee stability, even after the jet turns off. This
means that magnetic structures harboring a massive inventory of magnetic energy
can persist long after the building jet current has died away. These may be the
relic radio "fossils," "ghost bubbles" or "magnetic balloons" found in
clusters. These equilibria under magnetic tension will evolve, retaining the
stability properties from that state. The remaining fossil is not a disordered
ball of magnetic fields, but a stable structure under tension, able to respond
to the slings and arrows of outside forces. Typically their Alfven speeds
greatly exceed the cluster sound speed, and so can keep out hot cluster
plasmas, leading to x-ray "ghosts." Passing shocks cannot easily destroy them,
but can energize and light them up anew at radio frequencies. Bubbles can rise
in the hot cluster plasma, perhaps detaching from the parent radio galaxy, yet
stable against Rayleigh-Taylor and other modes.
