what I have found is that AC based foam cutters do not cut as cleanly as variable DC power supplies, so you should look into getting a variable DC power supply for your project. you can get a really inexpensive one like this (0-30V and 0-3A): http://www.volteq.com/volteq-regulated-variable-dc-power-supply-gps-3030d-30v-3a.html

If you wish to stick to AC based foam cutter, then try to get a variable transformer, or variac, which allows you to lower the voltage if you need less output, and you don't waste any electricity. Volteq has small ones starting at $44.50: http://www.volteq.com/variac-auto-transformer.html

If you still want to continue your own way, I will do the following:

1) make sure without any dimmer, your power is enough to heat up the foam cutter
2) once you are sure of that, you can put in a variable resistor to reduce the voltage on the foam cutter. you need to make sure that the resistor can handle the current you are putting through without getting hot.

One of the UK magazines published a switch-mode foam cutter supply about a year or more ago.

Maybe longer ago than I think, as I can't remember which one.

 

Well, I just finished assembling and testing my $20 LM338-based power supply that I'm going to use in my foam cutter. I'm getting 36+ VDC according to two multimeters! More than I need, so this should work out fine. Gotta reconfigure my "repurposed" Sears battery charger to hold the PS - soon as the ice outside melts and the frigid air goes away so I can use my workshop, ie garage! Sucks not having a basement. Anyway, thanks to all who've read and responded to this thread.

 

The capacitor in the Dimmer is very likely wrong- both for inductive load, and low wattage. Its used to preset the phase angle. For low wattage you can build a primitive dimmer with MAC97. You'd find it needs a certain capacitor value for certain behaviour.