# What is the power of the Ljung-Box Test for auto-correlation?

How large sample size should be for Ljung-Box statistic to achieve a power $\ge 0.5$ when number of lags tested is 1? How does the power fall ( assuming an AR(1) process), with increasing number of lags? The LB test is more than 40 years old, surely someone must have answered these questions by now.