Interaction of stellar winds in binary star systems Binary star systems are fairly common but I am unable to find any information on how the stars interact with one another on aspects other than gravitational affects.  Using Alpha Centauri as the candidate system, what possible effects could happen where their stellar winds reach one another?
Would a cloud of magnetized gas form? Would there be a highly radioactive area between them? Could it form a sort of micro-nebula between the stars?
Systems like this are known as colliding-wind binaries (CWBs), and they do produce some interesting effects. When winds collide, they create shocks, which in turn heats up gas. The most notable result is x-ray emission, which tends to happen whenever you have non-negligible shock heating in stellar winds; there is certainly additional thermal and non-thermal (e.g. synchrotron) radiation at other parts of the spectrum. I don't know if this would lead to significant structure formation - bear in mind that hot stars with strong winds may also generate more prominent outflows and nebulae through unrelated mechanisms; Eta Carinae is a great example.
This actually poses a problem for people trying to study stellar winds in x-rays. We can derive a lot of information from spectroscopic observations of winds - composition, temperature distribution, mass-loss rates - for simple cases when x-ray emission arises from the line deshadowing instability (Owocki, Castor &amp; Rybecki 1988), leading to embedded wind shocks (EWS).
Magnetic fields complicate matters by forming shocks as plasma is forced to travel along field lines, and colliding-wind binaries make it very difficult to study the individual winds because much of the emission is now coming from the CWB shock front and not purely the EWS model. I don't really know how folks studying CWBs disentangle the effects - when I was working on stellar winds, we mostly just ignored all magnetic and O+O binary stars in the sample!