Switching of Dislocations in Solid Helium Between Pinned and Unpinned States in the Torsional Oscillator Experiments

The anomalous temperature dependence of the period of a torsional oscillator (TO) containing solid helium can be explained by the dislocation-vibration model. Namely, the dislocations in solid helium vibrate in phase with the torsional oscillation and the TO-period change varies as the square of the average dislocation pinning length which becomes shorter at lower temperature due to pinning of dislocations by He-3 impurity atoms. This dislocation-vibration model is further developed by introducing distribution functions for the network pinning lengths for dislocation segments and by considering the mechanisms of pinning of dislocations by and unpinning of dislocations from He-3 impurity atoms. Experimental data, such as the TO-period change at different He-3 concentrations, the rim-velocity dependence of the TO period, the hysteresis of the TO period with respect to the rim velocity and to the temperature, are analyzed based on the dislocation-vibration model. Above all, the hysteresis is caused by switching of dislocations between pinned and unpinned states.