After searching my store of artefacts I saw a length of flexible plastic curtain rail. Now this variety is supplied rolled and the spare piece I found still exhibited the curvature of the roll. Isn't it great when you find something that is screaming out to be used for a different purpose you have in mind.
The guitar string (E 1st) was looped at both ends and held with nut and bolt to the ends of the curtain rail. The string is held taught by the springy curtain rail - and that is all there is to it.
The battery charger I have was clipped onto the bolts and set for 6V motorcycle mode. The wire gets hot enough to melt the polystyrene but not hot enough to melt the plastic curtain rail.
In the picture I have used the baseboard of a new 'n' gauge project as a work bench and the wire of the cutter overhangs the edge. The yoke is resting on some insulating foam so that the electrics don't come into contact with the railway track. Polystyrene to cut is simply offered up to the wire and carefully pushed through it, which requires no force whatsoever.
Why do I need to cut polystyrene? Well, it is the foundation of the landscape for the new railway. The contours of the land can be formed quickly and easily with polystyrene blocks.