Gain Stability of Electron Multiplier High Voltage Power Supply in Photon Counting Mode
Electron multipliers detect single particles by amplifying individual electrons through secondary emission cascades, producing output pulses of millions of electrons from each input event. In photon counting mode, the detector counts individual photons by detecting the output pulses from the electron multiplier. The counting accuracy depends critically on the stability of the electron multiplier gain, which is determined by the applied high voltage. The power supply must maintain extremely stable output voltage to preserve the pulse amplitude distribution and the counting efficiency over extended measurement periods.
The electron multiplier consists of a series of dynodes, each at successively higher potential, that multiply electrons through secondary emission. An electron striking a dynode surface releases several secondary electrons, which accelerate to the next dynode and produce more secondaries. The total gain is the product of the secondary emission yield at each dynode, typically ranging from thousands to millions depending on the number of dynodes and the applied voltage. The gain increases exponentially with voltage, making the multiplier sensitive to voltage variations.
Photon counting operation discriminates signal pulses from noise by comparing the pulse amplitude with a threshold. Pulses exceeding the threshold are counted as photon events, while smaller pulses are rejected as noise. The threshold setting determines the counting efficiency and the noise rejection. If the gain changes, the pulse amplitude distribution shifts, changing the fraction of pulses that exceed the threshold. Gain decreases cause loss of counting efficiency as pulses fall below threshold. Gain increases cause increased noise counts as small noise pulses exceed the threshold.
The pulse height distribution from an electron multiplier illuminated with single photons has a characteristic shape, with a peak corresponding to the average pulse amplitude and a tail extending to lower amplitudes. The distribution shape depends on the statistics of the secondary emission process. The threshold is typically set in the valley between the noise peak at low amplitude and the signal peak at higher amplitude. The threshold placement optimizes the tradeoff between counting efficiency and noise rejection.
Voltage stability requirements derive from the sensitivity of gain to voltage and the acceptable variation in counting efficiency. The gain varies approximately as the voltage raised to a power, with the exponent depending on the dynode material and geometry. For typical electron multipliers, a one percent voltage change produces a gain change of several percent. The acceptable voltage stability depends on the pulse height distribution and the threshold setting, with typical requirements being stability better than 0.01 percent for high precision measurements.
Sources of voltage instability include temperature drift, line voltage variations, load changes, and time dependent aging effects. Temperature affects the voltage reference, the feedback components, and the high voltage generation circuitry. Line voltage variations couple through the regulation to the output. Load changes occur when the detector current varies with count rate. Aging causes gradual changes in component values over the equipment lifetime. The power supply design must minimize each of these instability sources.
Temperature control or compensation maintains stable operation over the ambient temperature range. Ovenized references maintain constant temperature for the most critical components, eliminating temperature effects at the cost of additional power and warmup time. Temperature compensation circuits adjust the output based on measured temperature, canceling the temperature coefficients of the components. Selection of low temperature coefficient components minimizes the inherent temperature sensitivity.
Line regulation rejects variations in the input power voltage. Linear regulators provide excellent line regulation with simple circuitry but have efficiency limitations. Switching preregulators can provide efficient line regulation with appropriate feedback design. The regulation bandwidth must be sufficient to reject line variations at the relevant frequencies, typically line frequency and its harmonics.
Load regulation maintains constant output voltage despite variations in the load current. The electron multiplier current varies with the count rate, from nanoamps at low count rates to microamps at high count rates. The output impedance of the power supply causes the voltage to vary with current. Low output impedance achieved through feedback maintains stable voltage across the operating current range.
Long term stability over hours to days is critical for photon counting experiments that accumulate counts over extended periods. The voltage must remain stable within the specification throughout the measurement, without drift that would change the counting efficiency. Regular calibration checks verify the stability and detect any drift that requires correction. Reference standards traceable to primary standards provide the calibration reference.
Monitoring and diagnostics enable detection of developing problems before they affect measurement quality. Output voltage monitoring tracks the actual voltage applied to the multiplier. Temperature monitoring indicates the thermal environment of the power supply. Current monitoring measures the multiplier current, indicating the count rate and the multiplier condition. These diagnostics support preventive maintenance and quality assurance for the measurement system.
