Abstract: Apparatus and method for operating a downhole sucker rod pump in which a downhole linear motor is controlled by a surface digital computer. The motor includes a number of coil sections circumfusing and spaced along the length of a non-magnetic tube, and an armature positioned coaxially inside the tube. The armature section includes a central mandrel of a non-magnetic material and a number of laminated armature sections circumfusing and spaced along the length of the mandrel. The tube is sized substantially the same as the production tubing, and the armature is not physically connected to the tube, such that the armature and the attached pump can be removed without removing the tubing. The coils are energized by electric power supplied by three electric conductors running from the surface.