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The superfluid two-stream instability

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ABSTRACT. This paper provides the first study of a new dynamical instability in superfluids. This instability is similar to the two-stream instability known to operate in plasmas. It is analogous to the Kelvin-Helmholtz instability, but has the distinguishing feature that the two fluids are interpenetrating. The instability sets in once the relative flow between the two components of the system reaches a critical level. Our analysis is based on the two-fluid equations that have been used to model the dynamics of the outer core of a neutron star, where superfluid neutrons are expected to coexist with superconducting protons and relativistic electrons. These equations are analogous to the standard Landau model for superfluid helium. We study this instability for two different model problems. First we analyse a local dispersion relation for waves in a system where one fluid is at rest while the other flows at a constant rate. This provides a proof of principle of the existence of the two-stream instability for superfluids. Our second model problem concerns two rotating fluids confined within an infinitesimally thin spherical shell. The two model scenarios are physically distinct: in the first model the two fluids are coupled ‘chemically’ and the instability sets in through acoustic waves, while in the second problem the fluids are only coupled via the entrainment effect and the instability is associated with the superfluid r modes. The two scenarios illustrate that the instability mechanism is generic, and that it may set in through various modes of oscillation. We briefly discuss whether there are conditions, e.g. in the inner crust of a mature neutron star, where the coupling between the two fluids is sufficiently strong that the instability sets in at a relative flow small enough to be astrophysically plausible.

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