[RGK20m3]

I know that this has been discussed before, and may be normal- the tweeter field coil that is in the audio amp power supply runs considerably hotter than the other tweeter; voltage drop across the audio side tweeter field is about 85v, while the other is about 45v.  This equates to 125ma current flowing, of which 60ma is the woofer field.  There is about 25ma through the 6F6 plate and screen, which leaves 40 ma for all the screens on the upper chassis, which seems reasonable. But 10.5 watts seems a lot for the tweeter field to dissipate.......
Why would it be designed (or desirable) to operate this way? I am thinking of shunting the field to reduce the current through the field, which would raise some of the upper chassis voltages. Or, connect the woofer field before the tweeter field with a resistor in series.
What do you think?