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As suggested, slitting the tube should help, although perhaps not as much as using a non-conductive material. If the tube with a slit is supported by conductive material on the ends, some current will still be induced, and may cause some force on the plunger.
I have quite a collection of solenoids, and two solenoid motors, they all have brass tubes in them.Ian S C
Solenoids also don't normally cycle with the frequency that a solenoid motor would require. I should think repeated, rapid switching on and off of the DC current would cause heating similar to that with AC current.Chuck