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Field diameters in eyepieces determine how much of the telescope's field you see. The image scale is on the scope's field and the eyepiece acts like a magnifier for the portion of the field of the scope seen.
Barlows expand the image scale of the primary so the eyepiece sees less field. That's why the field seen is smaller and at a higher magnification. The eyepiece is seeing a telescope with a longer focal length.
All eyepieces perform better when the rays entering the bottom are closer to parallel than converging. PowerMates and other telecentric multipliers make the converging rays enter the eyepiece closer to parallel and improve the performance of many eyepieces while providing an expansion of the image scale at the same time.
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