• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

Constant current for heaters?

Strictly speaking, this is not always true. Yes, many receiving tubes were designed for a particular steady state operating voltage. However, with the advent of television and mass market design (including A5 radios), many tubes were designed for a constant steady state operating current and the voltage was just a target. In the GE data sheets, this characteristic is termed the "controlled heater warmup characteristic". Such tubes were specifically designed to operate in a series filament configuration (usually with 300mA or 600mA level). These tubes can still be used with a voltage source of appropriate value, but oftentimes their voltages are approximate.
With tubes designed for series string heater use, such as in AC/DC powered table radios, then the heater current would have to be more closely held to spec to be sure all tubes lit up with the correct voltage across their heaters.
 
People end up chasing there tail never reaching a definative answere.there are tubes specificlly designed for series operation.and there are audio tubes mostly designed for a specific voltage to operate. Back when tubes were designed using a ccs never came into the picture and there are millions of tubes lasting years without fancey current limiting. Your worrying about an issue that does not exist.
Back then, a CCS would have been cumbersome to implement. With today's semiconductor devices, it's much easier to do.
 
There used to be current regulating valves, basically incandescent lamps with a lower operating temperature and a filament with a large positive temperature coefficient. I can't remember what they were called.

The heaters of valve computers were usually turned on gradually. It had some effect on reliability, but it was not very large. An added advantage was the much smaller current surge during start up.