Turret: Getting a constant rotation speed

After doing a tornado twins tutorial, I have code which makes a turrent rotate toward the player. Which is good. But the rotation speed is not constant - the closer it gets to aiming directly at the player, the more it slows down the rotation of the turrent.

I would like it to just use a constant rotation speed until it achieves a perfect aim at the player.

I think the following is the relevant code, but I am not sure. May the unity gods forgive me…

if (LookAtTarget)
{
	var rotate = Quaternion.LookRotation(LookAtTarget.position - transform.position);

	transform.rotation = Quaternion.Slerp(transform.rotation, rotate, Time.deltaTime * damp);
}

Yes, that is the relevant code. If you want it to rotate at a constant speed, replace that line with this:

// assuming you have a variable called 'rotationSpeed'
transform.rotation = Quaternion.RotateTowards(transform.rotation, rotate, rotationSpeed * Time.smoothDeltaTime);

Looks like an error which occurs at runtime, then the script isnt used.
I also experienced problems i was working on for hours, next day open unity again, and everything is working fine…