The string stretches and builds up tension T . T pulls backwards on and forwards on . Thus continuously loses angular momentum, while continuously gains the same. This means that cannot remain in orbit and must drop down to a yet lower orbit. Similarly, acquires too much angular momentum to stay in orbit and must move outwards.
T goes up, and the process runs away.
This is the essence of the weak-field instability in differentially rotating systems. Introducing other magnetic-field components does not change our argument. It is of course crucial that the spring be weak. If the spring constant is strong enough that there are many vibrations in an orbital time, the stretching scenario we have outlined will not work. Plausible sources for the desirable anamalous viscosity have been identified, therefore, in some well understood circumstances when an inviscid disk would be unstable.