1, The electrons are being " generated" because the +ion , is a little bit of gas that is deficient in electrons. When this alights on the cathode, an electron jumps into the "hole". this electron is supplied from the external power supply, so current is seen to flow.
2, The currents are caused by the out gassing of contaminants, so are totally linked to the cleaness and chemical purity of the materials of the construction.
We used to do gas tests on high vacuum klystrons, these are large transmitting valves. From memory, the supply was 3 KV, the manufacturers spec was 20 micro amps, the typical currents were tiny less then 5 micro amps. If you left the supply on, the free ions drifted down to one end of the tube, leaving none free, so the current then went down to absolutely nothing.
Frank