Are the magnets in tokamaks variable in strength? For example, if the plasma inside is beginning to terminate and collide with the walls of the confinement vessel, can the magnets account for this and realign the plasma?
 A: From the wikipedia explanation of the name,

"тороидальная камера с магнитными катушками" (toroidal'naya kamera s magnitnymi katushkami) — toroidal chamber with magnetic coils,

note the coils at the end.
The magnetic fields used to control the plasma inside tokamaks are generally electromagnets produced by running high currents through wire coils. As such, they're intrinsically variable, though of course they have a finite range, and a maximal field strength past which they're no longer able to control the plasma.
A: As was said by Emilio Pisanty, the magnetic field coils are intrinsically variable. As was also said, they have a finite range. Let's try to elaborate that further:


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*Most modern tokamaks (where modern refers to being recently put into operation) use superconducting magnetic field coils. Superconductors have the property that when the critical magnetic field is reached, they loose their superconductivity. That limits the magnetic field from a technical point of view.

*Certain heating systems only work at their resonant magnetic field strength they are designed for: electromagnetic waves in the microwave regimes, for example, are resonant (in their frequency) to the gyrofrequency of the electrons (the frequency with which the electrons gyrate around the magnetic field lines). And you need those heating systems to bring the plasma temperature in your tokamak to fusion-relevant temperatures. 

*It is true that instabilities occurring in the plasma can be (partly) stabilized by increasing the confining magnetic field. The related quantity is the plasma-ß which is the ratio of kinetic pressure to magnetic field pressure. In a tokamak, it is typically on the order of a few percent. Having in mind an efficient fusion reactor, you are trying to maximize the plasma-ß (e.g. by shaping the plasma), trying to get as much plasma as possible per magnetic field, since magnetic field costs money. And that is another limitation: costs (more precisely it's the area enclosed by a magnetic field which is getting expensive very quickly).

A: Yes. Changing currents in the magnetic coils used to shape the poloidal field is done constantly by feedback control systems. A good example is active stabilization of the vertical instability. All tokamak plasmas with elongated cross sections are unstable to vertical perturbations, but unlike most plasma instabilities, the growth rate is small enough that we can actually catch it. A simple measurement of the plasma's position, fed into a PID controller for the coil commands, is usually enough.
