Hetero and homo charge Hetero charge means that the polarity of the space charge is opposite to that of neighboring electrode, and homo charge is the reverse situation. Under high voltage application, a hetero charge near the electrode is expected to reduce the breakdown voltage, whereas a homo charge will increase it. After polarity reversal under ac conditions, the homo charge is converted to hetero space charge. Mathematical explanation If the near "vacuum" has a pressure of 10−6 mmHg or less, the main vehicle of conduction is electrons. The emission current density (J) from the cathode, as a function of its thermodynamic temperature T, in the absence of space-charge, is given by Richardson's law: where = elementary positive charge (i.e., magnitude of electron charge), = electron mass, = Boltzmann constant = , = Planck constant = , = work function of the cathode, = mean electron reflection coefficient. The reflection coefficient can be as low as 0.105 but is usually near 0.5. For tungsten, (1 − ř)A0 = , and . At 2500 °C, the emission is 28207 A/m2. The emission current as given above is many times greater than that normally collected by the electrodes, except in some pulsed valves such as the cavity magnetron. Most of the electrons emitted by the cathode are driven back to it by the repulsion of the cloud of electrons in its neighborhood. This is called the space charge effect. In the limit of large current densities, J is given by the Child–Langmuir equation below, rather than by the thermionic emission equation above. Occurrence Space charge is an inherent property of all vacuum tubes. This has at times made life harder or easier for electrical engineers who used tubes in their designs. For example, space charge significantly limited the practical application of triode amplifiers which led to further innovations such as the vacuum tube tetrode. On the other hand, space charge was useful in some tube applications because it generates a negative EMF within the tube's envelope, which could be used to create a negative bias on the tube's grid. Grid bias could also be achieved by using an applied grid voltage in addition to the control voltage. This could improve the engineer's control and fidelity of amplification. It allowed to construct space charge tubes for car radios that required only 6 or 12 volts anode voltage (typical examples were the 6DR8/EBF83, 6GM8/ECC86,