Vacuum 4 potential charge current density

So it is also possible to use the form (139) for the vacuum charge current density, a form that eliminates any geometric unit such as Ar that is not fully relativistic. However, A is, strictly speaking, a potential energy difference and not a field. 

The term —g2m2A /X implies that the electromagnetic 4-potential has acquired mass. Simultaneously there appear two other terms. All four vacuum charge current densities produce vacuum energy through the equation... 

Field emission potential diagram. Large electric fields induce barrier narrowing, which increases the number of electrons tunnelling from the Fermi level in the metallic, electron-rich, surface into the vacuum. Variations in the density of occupied states, N E), and current density, J[E), as a function of electron energy. Surface contamination and charging effects (Schottky rounding) can be seen to drastically alter the potential profile. 

There are two principal types of ionisation gauge, viz. the hot cathode type in which electrons are emitted by a heated filament, and the cold cathode type in which electrons are released from the cathode by the impact of ions. In both cases the vacuum is measured in terms of the ion current. The electrons are accelerated by a potential difference (usually about 2000 V) across the ionisation tube (see Fig. 6.22). Positively charged ions are formed by the electrons striking gas molecules. The number of positive ions produced is a function of the gas density (i.e. the pressure) and the electron current ie which is normally held constant. The ions are collected at a negatively charged electrode and the resulting ion current it is a direct measure of the gas pressure. The hot cathode version is the most sensitive of the two and can be used to measure vacua down to about 10 10 torr ( 10 8 N/m2). 

---