Presumably by controlling the heat dissipated in getting the electron
emitter up to the temperature where it would emit electrons.
IIRR - and I was never directly involved with that part of the
electron microscope - that wasn't normally directly controlled. The
circuit would be floating at an anything up to -30kV, which would make
it more than a little interesting.
Lower temperatures produce far too few electrons (as you
already know very well, the electrons are produced both from
thermal emission _and_ field effect), lessens the beam
intensity, and reduces the rate at which work can get done
(beam sweeping rate.) Which impacts productivity. By quite
a lot with even small changes. Higher temperatures works
great for beam intensity, but quickly destroys the emitter.
(Which is also treated with Lanthanum hexaboride, memory
serving.) The trick is to accurately temperature over time
without drift. And we are talking on the order of tenths of
a Kelvin to perhaps one Kelvin, where possible. Now think
about the local (dI/I)/(dT/T) problem at those temperatures
T, if done pyrometrically, even assuming emissivity doesn't
change over time.
Early solutions were to use inordinately expensive current
drive power supplies (better than 0.1%.) They may drift a
little and need recalibration but that's less important
because the tips themselves age faster still. But the
reality is that the temperature at the tip is the thing to be
controlled, not the current driving it. The tip temperature
needs to be closed up within the control loop. Periodic
adjustment using disappearing filament methods and calibrated
(expensive) tungsten standards achieves bringing temperature
into the loop, if done manually and frequently. The problem
is... well, all the problem in doing that. It means other
specialized power supplies for the standard lamp, careful
logging of lamp usage and recalibration as needed, regular
procedures done frequently, etc.
Variations in lifetime might be as much as a factor of 50X
for the exact same system, depending on customer procedures.
And at the high expense of replacement, it becomes urgent to
find an easier way to achieve more uniform experiences.
Jon