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Microwave Background Signals from Tangled Magnetic Fields

An inhomogeneous cosmological magnetic field will create Alfven-wave modes that induce a small rotational velocity perturbation on the last scattering surface of the microwave background radiation. The Alfven-wave mode survives Silk damping on much smaller scales than the compressional modes. This, in combination with its rotational nature, ensures that there will be no sharp cut-off in anisotropy on arc-minute scales. We estimate that a magnetic field which redshifts to a present value of $3\times 10^{-9}$ Gauss produces temperature anisotropies at the 10 micro Kelvin level at and below 10 arc-min scales. A tangled magnetic field, which is large enough to influence the formation of large scale structure is therefore potentially detectable by future observations.