F-4 take off - and yes lot of smoke these engines did
and
Jet engines smoke is due to incomplete combustion of the fuel that goes through it. The afterburner completes the combustion ( thence you don't see smoke in AB but a lot at MIL power). Jet engine technology has come a long way from the old F-4C/D and KC-135A days. The F-4E had a smoke kit TCTO on it that reduced the smoke output considerably.
I found that on the web- relevant and interesting stuff:
The smoke comes from the engine when it is at or near MIL power. (Which is top shaft speed/power the engine can run.) The engines will smoke at MIL more than any other setting. MIL is the point at which the maximum amount of fuel is being fed to the engine's combustion chamber. This is the point when the engine is running the hottest. MIL is full power on the basic engine without AfterBurner (AB). AB only adds fuel downstream of the actual gas turbine engine. It is (in effect) like a rocket being fed oxygen by the jet engine, and raw fuel that is mixed and ignited for extra heat. (thrust)
It has nothing to do with the afterburner. Even in SEC (Secondary) mode (Where the augmentor is inhibited) there will be smoke at MIL power.
the smoke will subside when the throttle is reduced. (or AB is selected)
Just before the engine goes into AB it nears MIL, at this point it is running almost wide open. The engine is trying to accelerate at the fastest possible rate. To accelerate a turbine engine you add fuel. When the burner kicks in, the smoke goes away as the flame of the augmentor cleans up the exhaust of the engine. (The smoke still enters the augmentor duct, but it burns off before it can emerge.)
When you cancel 'burner, the smoke will return as it is still pouring from the engine at MIL. When the throttle is pulled back towards mid-range the smoke does subside as the engine isn't trying to make so much power.
"Older" engines, ones with more cycles/hours on them, tend to smoke a little more than "newer" ones. This is do to more excessive clearances within the compressor section. To compensate for the lower efficiency of the compressor, the engine's temperature is increased by it's control system. This is done by adding more fuel into the combustion chamber. You have a less efficient compressor (lower compression) and you add more fuel for heat to compensate, and you'll get more smoke.
Watch this F-86 video, 1:00-1:20, you'll see how the older jets smoked at MIL too.