Is there a "pinch effect" in a Tokamak? Is there a "pinch effect" in a Tokamak, like in a linear Z-pinch or in a circular pinch (the ZETA machine from the late 50's)? Tokamaks run in a pulsed mode and a powerful circular current is induced in the plasma. This should pinch the plasma.
Are the field lines frozen into the plasma of a Tokamak and does this create (momentarily) a powerful magnetic field? The magnetic field in a Z-pinch is apparently very strong at least for a short while.
 A: 
This should pinch the plasma.

It does, however, in contrast to ZETA, it's a very weak pinch to the point of not being a major component of the fusion action.
The issue with ZETA, and pure pinch in general, is that the instabilities in the plasma are current-driven. So as you increase the current in order to reach higher densities, you're only making the instabilities worse. This was very evident in the earlier pinch machines, which suffered from kink. ZETA was a "stabilized pinch" design, but it turns out that did indeed help with the large-scale pinch, but did nothing to the small-scale "microinstabilities" that had formerly been invisible in the massive whipping plasma.
The basic idea behind the tok is that you keep the ratio of external magnetic force to current below a certain threshold. More specifically, the idea is to ensure the combination of the fields from the two sources "add up" such that the resulting field is highly twisted so that any one line winds around the reactor's short axis faster than along the long axis. Think of a candy cane being more tightly wound. If the twist is more than 1:1, the kink is strongly suppressed.
Unfortunately, there is a downside... unless you make HONKING magnets, the amount of current you can use before you hit this number is relatively small compared to what you want. You want more, because the current heats the plasma, and as it contracts you get adiabatic heating too. So in the tok you need some other form of heating to get to fusion.
The pinch really looked like a cheap way to get to fusion, as the current both confined and heated the plasma. But such was not to be.
