Methods have been developed for the computation of the frequency response and stability of helium cooling systems in the frequency range of the density wave instability. While more generally applicable, these methods were developed for a study of superconducting power transmission. Special features are the use of helium thermodynamic properties derived at every point from the exact equation of state, and the full accounting of the effect of compressibility. Classical linear control theory is employed throughout. By using a finite difference approach to the integration of the conservation equations over the space coordinate, the accuracy obtainable is limited only by the computation time available. Examples are given for representative transmission line parameters with the helium at a variety of supercritical pressures. It is concluded that, while density wave instability is a real potential problem in superconducting power transmission lines, it is not difficult to select operating parameters in a safe stable regime.

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