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A novel segmented multigap pressurized gas ionization chamber is being developed for optimization of the luminosity of the Large Hadron Collider (LHC). The ionization chambers are to be installed in the front quadrupole and 0° neutral particle absorbers in the high luminosity interaction regions (IRs) and sample the energy deposited near the maxima of the hadronic/electromagnetic showers in these absorbers. The ionization chambers are instrumented with low noise, fast pulse-shaping electronics to be capable of resolving individual bunch crossings at 40 MHz. In this paper, we report the initial results of our second test of this instrumentation in a super proton synchrotron (SPS) external proton beam. Single 300 GeV protons are used to simulate the hadronic/electromagnetic showers produced by the forward collision products from the interaction regions of the LHC. The capability of instrumentation to measure the luminosity of individual bunches in a 40 MHz bunch train is demonstrated.