Downhole assembly to mitigate high frequency torsional oscillation, and oscillation mitigation tool suitable for use in a downhole assembly

A downhole assembly including a rotary steerable tool and a high frequency torsional oscillation mitigation tool, the high frequency torsional oscillation mitigation tool having:

• a first end, a second end, and a one-way coupling between the first end and the second end,
• a first connector at the first end and a second connector at the second end, the first connector and the second connector being configured for releasable connection to other downhole components in use,
• the one-way coupling having a first part and a second part, the first part being connected to rotate with the first connector and the second part being connected to rotate with the second connector, the one-way coupling having an engaged condition in which the first part and the second part can rotate together and a disengaged condition in which the first part can rotate relative to the second part,
• the first part being a tubular shaft and the second part being a sleeve surrounding the tubular shaft,
• one of the sleeve and the tubular shaft carrying a number of rollers of circular cross-section, each roller of the number of rollers being located in a recess of the sleeve or tubular shaft respectively, each recess having a floor which is inclined from a radially shallower end to a radially deeper end, and in which the each roller projects from the recess when located at the radially shallower end,
• said each roller of the number of rollers comprising a set of aligned roller elements,
• the high frequency torsional oscillation mitigation tool being located above the rotary steerable tool.