Constant voltage, variable current source
From the data sheet, you want a controllable current source, controllable between 0 and 1A (up to 2A if you like) with a maximum open circuit voltage of 12v.

The damper is obviously a coil. It specifies the resistance as 5 ohms at ambient, 7 ohms at maximum temperature (yes, copper does has that much of a change of resistance with temperature).

As an alternative, at least for playing with on the bench, you could use a variable 0-6v power supply. But be warned that as the temperature changes, the changing resistance will alter the current drawn, which will alter the damping effect. It's because of this we tend to drive current-sensitive loads with constant current rather than constant voltage sources.

In use, the output voltage of the current source will be whatever the load imposes. If you have programmed it to (say) 500mA, and at the present coil temperature the resistance is 6 ohms, then the output voltage will be 3v steady state, though the coil inductance will make it glitch to other levels during current changes. Make sure your supply is protected against reverse voltage. If it is suddenly programmed to a reduced current, the damper inductance will continue to draw the original current monentarily, dragging the output voltage negative. A diode across the output to source this extra current may be sufficient to protect against this problem.

The inductance is not specified, but they do say response within 15mS, though that's to changes in the field. Not well specified.

The 12v is not well specified, it appears to be a maximum voltage, though it doesn't say this. It also says that the electrical characteritics are typical, not to be used for a specification.

The braking force is a function of current, which can be up to 1A for 30 seconds, and 2A intermittently. Neither well specified, what's inermittent, what do you do after 30 seconds? Wait until it's cooled down, how long, to what temperature, drop current below what, monitor coil resistance to assess temperature?

Did I mention that it doesn't appear to be all that well specified?