Topgun,
Of course you have to do some research yourself,but I'll try to help you with some of my reflexions on the subject,ifever they can be of any help.
NO!You'll never beat the betz limit.
But betz law is defined for some special conditions:rotor is a disk,perpendicular to the wind direction,with no obstruction around the rotor.
So if you choose conditions that don't correspond to the conditions of betz law you can get other results.
One way to achieve it is using helping structures,for exemple you can place the rotor in a hole in a wall that's perp to the wind or in a tube that's parralel to the wind.It's easy to imagine that the rotor can have a bigger rendement at the same wind speed.betz limit is not beaten,but conditions are diffferent than betz law was difined for.
Another way is to change the geometry of the rotor itself.
For exemple vawts are basicly a cilinder,with the axis perp to the wind.
But you can imagine some allongated form or a cilinder with the axe paralel to the wind too,that eventually 'catch all of the wind' (lol).Without beating the betz limit.
So that leaves room for dreaming about having more than 59% rendement per swept area,allthough for the moment the results for a simple disk rotor is better than any other fancy design.
Were just waiting for a matematical genious that can extend betz law to those more complex conditions.
But then there is the reality that windmill builders don't care a damn about yield per swept area.What counts is yield per $ that you put in your mill.And that's where allmost surely any genious,but complicated design will be beaten by a simple disk-form rotor.
cheers,
stonebrain