10bp4 or fp4
 

Which 10 inch crt was made to operate without an ion trap like the 12 inch version, I may be looking for the 10 inch one that don't need an ion trap.

The 10FP4 is the aluminized one that needs no trap. Assuming it was never rebuilt with a bent gun at some point.

I thought the bent gun is the one that requires an ion trap. The 12lp4 has a crooked gun and that needs an ion trap.

It is, but rebuilders may have used a bent gun to replace the original straight one.