Magnification Factor
In ueniology, the magnification factor, or M, is the ratio of the increase in magical energy produced by the sink in a field amplifier to the energy consumed by the amplifier. If M is less than 1, the field amplifier will consume more energy than it provides to the sink, known as underamp. If M is equal to 1, this is known as equilibrium. If M is greater than 1, the sink is said to be overamped.
Since magnification is inversely proportional to lattice saturation, M will decrease as the energy fed to the amplifier increases. Eventually, the M of an overamped system will fall to equilibrium, an energy level known as the critical point.
Inflection
It is possible for a source of magical energy, such as a ue transducer, to be used as the sink in an amplifier. In this case, the amplifier would increase the amount of magical energy produced by the source. Inflection occurs when the system reaches overamp. At this point, the system produces more magical energy than it consumes. When M equals 2, the system is said to have reached super-equilibrium. At that point, the extra energy produced can be siphoned off to power the amplifier, making the system self-sustaining.
Super-inflection occurs when the magnification factor of a self-sustaining system passes 2. At that point, the energy produced by the source and amplifier exceeds the energy consumed, increasing energy flow to the amplifier, which further increases the output of the source. This creates runaway feedback loop, causing a sudden increase in magical energy that rises until the amplifier saturates and M falls down to 2 and the system reaches super-equilibrium.
The ratio of initial output to super-equilibrium output is the inflection factor.
Equations
M is equal to
where
- Ud is the density of the ue field within the sink
- Uc is the ambient density of the ue field
- A is the alignment coefficient
- S is the lattice saturation coefficient
The density of the field inside the sink relative to ambient is similar to the field amplifier's magnitude. The only difference is that, depending on the size and position of the sink, the average density of the field inside it may be substantially higher than average inside the entire wave lattice.