The luminous efficacy of the mercury discharge is directly related to the vapour pressure at which it operates, and Figure 3 below details the precise relationship for one particular design of lamp. The first lamps operated at a relatively low pressure of less than one torr and had an efficacy of 17.9 lm/W, just to the right of point B on the graph below, so it is obvious that there was considerable room for improvements in efficacy.
The data here relates to a tube of 27mm diameter with the discharge current being held constant at 4 Amperes (Krefft & Summerer, 1934). For each lamp the precise values will be slightly different, but the general principles are illustrated here.
Figure 3 - Effects of Mercury Vapour Pressure on Luminous Efficacy
Mercury Pressure 0.01 to 0.1 torr (Region A-B)
At the lowest pressure indicated on the graph above (point A), the majority of the mercury radiation is in the ultra-violet part of the spectrum. The temperature of the discharge is low and not a great deal higher than the tube wall, thus with such a small temperature gradient the loss of energy by thermal conduction is minimal and this ultra-violet generation is very efficient. However, the lack of radiation in the visible part of the spectrum means that lamps operating in this pressure region attain an efficacy of only some 10 lm/W.
As pressure increases, so does the luminous efficacy and it reaches a maximum at 0.1 torr (point B) where approximately 20 lm/W can be attained. The reason for the increase is that self-absorption of the mercury resonance lines in the ultra-violet part of the spectrum begins to become significant, with the effect that the relative intensity of other lines in the visible part of the spectrum increases, hence luminous efficacy rises.
Although such an inefficient discharge might at first seem to be particularly useless for lighting applications (even incandescent lamps can do better!), it should be remembered that fluorescent phosphors can be used to convert invisible ultra violet radiation into useful light. This is the principle of operation in the fluorescent tube in which a discharge generating the maximum amount of ultra-violet is highly desirable, so the typical mercury vapour pressure is around 0.005 torr. At such a pressure, the efficacy of generating the 253.7nm ultra-violet resonance line is at its maximum. However in this text, only the higher pressure mercury discharges are of interest and detailed information on the fluorescent lamp will be found under that category.
Mercury Pressure 0.1 to 5 torr (Region B-C)
Above 0.1 torr the luminous efficacy (and UV generation) begins to fall again. The reason here is that with increasing pressure, there are more mercury atoms in the tube and the probability of energy being lost due to elastic collisions between a speeding electron and a mercury atom increases. See Figure 4. With more mercury atoms in the discharge tube the electrons must follow a more tortuous path from one electrode to the other, with energy being lost at each collision. Only some of these collisions are sufficiently powerful to lead to ionisation and light generation, many just result in heat losses. As pressure rises, so does this energy loss mechanism hence luminous efficacy begins to suffer. The result of more frequent collisions is that the gas temperature rises to approximately 500°C by point C. With such a hot discharge core a considerable amount of the energy input is transferred as heat by thermal conduction to the tube wall, representing a loss of energy so efficacy falls.
Figure 4 - Higher pressures mean increased energy losses through atomic collisions
Mercury Pressure 5 to 100 torr (Region C-D)
Interestingly, a minimum is reached at point C when the pressure is about 5 torr (but depending on the tube diameter) where a fascinating phenomenon begins to occur. Above this pressure the discharge, which completely fills the entire tube diameter at lower pressures, gradually begins to contract inwards towards the axis of the tube until eventually an annular dark region exists between the discharge and the tube wall (see Figure 5). The pressure at which the discharge detatches itself from the tube wall is generally considered to be the point which differentiates the so-called low pressure lamps from all other medium or high pressure lamps.
Fig. 5 - End views showing diffuse low pressure & constricted high pressure discharges
As pressure increases the discharge becomes more and more constricted, hence the dark space surrounding it also grows. This dark region affords some thermal insulation between the discharge and the tube wall, and it very conveniently reduces the significance of the conducted heat losses. Because the discharge is better insulated its temperature can rise and it soon escalates to approximately 6000°C, at which most modern mercury lamps operate. The relative intensity of the mercury lines begins to increase as the discharge contracts but without significant heat losses, the effect being that once again, luminous efficacy rises with increasing pressure.
In addition by this point, the temperature at the core of the discharge has reached a level where temperature radiation begins to set in, and a small amount of continuum appears in the mercury spectrum - literally, this radiation is generated by the incandescence of heated mercury vapour. The increase in luminous efficacy beyond what was previously thought to be a minimum at C was first observed by Küch and Retschinsky in 1906.
Mercury Pressure >100 torr (Beyond D)
As pressure continues to rise, the extra radiation is mainly the result of the high temperature of the discharge - consequently a greater amount of continuum radiation is seen. The luminous efficacy at first rises very rapidly beyond point D, but asymptotically reaches a high value as pressures of 100,000 torr or so are reached (approximately 130 atm.) and the luminous efficacy may be as great as 70 lm/W.
High pressure mercury lamps for general lighting applications operate in the pressure range above point D, typically around 4,000 to 8,000 torr (5-10 atmospheres pressure). This is the maximum attainable for a low cost general lighting lamp and is not all that far away from the maximum point shown on the graph. While the luminous efficacy at higher pressures might seem attractive, very large amounts of energy are dissipated in these lamps which require expensive constructions and forced cooling, which make them impractical for all but the most specialised applications.