Hydrogen plasma from a thetatron gun has been directed into the entrance of a solenoid so that a tenuous low-β plasma stream is guided along the magnetic field lines. The main parameters of the plasma and field are n similar 3 × 10¹¹ cm^-3, B = 2 kG and ion energy similar 800 eV. A simple theory is presented which predicts an electrostatic instability caused by the anisotropy in the distribution of the transverse component of ion velocity; this anisotropy arises because the ion gyro-radius (similar 0.5 cm) is of the same order as the radius of the plasma stream (similar 2 cm). The instability is similar to the `loss-cone instability' and the properties by which it is characterized are provided.Experimental results are described which confirm the existence of an instability and support the theoretical predictions. The frequency ω/2π(similar 40 Mc/s) has been measured and the transverse wavelength has been estimated using double electric probes with different electrode separations. An increase in longitudinal electron energy has been demonstrated by varying the bias on an ion probe. The existence of standing waves is inferred from low frequency fluctuations on both the ion probe output and the rectified high frequency signal. It is suggested that the instability may account for the anomalous loss of diamagnetism which is often observed in similar plasma streams.