What is the Linear N-rate function
These are basically used along with the Ion chambers, Scintillators etc.
Lin N represents a Linear Amplifier, output of these varies directly to the input which represents the Flux linking through Ion chambers, Neutron Flux monitors ,or a scintillator counter output.
Often gas chambers use them for better range, by using multiple amplifiers like Log N , Lin N  amplifiers together they provide capability measure high and low range of radiation amount and give better resolution in case of nuclear reactors.
In case of Nuclear reactors they are used to operate the Reactor regulation system(Rod controlling system ) with respect to the amount of  Full Power(FP) contributed by Neutron flux in the core, which are detected by these ion chambers.