Mr Chips has realized the most important issue .....The best gauge is the one that cuts the foam without breaking.
This wire needs to be strait ... the longer the wire the more it sags . not just under gravity , but as the foam is pushed onto it horizontally ... The wire needs a heavy duty spring attached outside the cutting zone to keep tension ... as the current is applied the wire gets longer from expansion , and it gets less strong .... You need a wire which is very strong at around 500C .... stainless steel wire might be best , then you can have great tension in it to keep perfectly strait without it breaking.. Keep the temp as low as practical allowing high tension without breakage
Current and voltage are easily sorted , get a variable supply and experiment for the right temp .
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