Time Jitter Analysis of High Voltage Power Supply for Electron Multiplier in Time Resolved Measurements
Electron multipliers serve as sensitive detectors for charged particles, photons, and ionizing radiation in applications ranging from mass spectrometry to particle physics. These devices amplify single particle events through secondary electron emission, producing output pulses with amplitudes suitable for electronic processing. Time resolved measurements utilize the precise timing of detector pulses to extract information about event sequences, particle velocities, or decay lifetimes. The timing precision achievable depends critically on the stability and characteristics of the high voltage power supply powering the electron multiplier, with time jitter being a key parameter that limits the temporal resolution of measurements.
Time jitter refers to the statistical variation in the delay between the arrival of a particle at the detector input and the generation of the output pulse. This jitter arises from stochastic processes in the electron multiplication cascade and from variations in the electronic processing. The total timing uncertainty is the quadrature sum of the detector jitter and the electronics jitter, with the detector contribution being significant in high precision timing applications. Minimizing the detector jitter requires optimization of the electron multiplier operating conditions, particularly the applied voltage.
Discrete dynode electron multipliers consist of a series of electrodes called dynodes, each at successively higher positive potential relative to the previous stage. Electrons from the photocathode or input stage strike the first dynode, releasing secondary electrons that are accelerated toward the next dynode. This process repeats through the dynode chain, with the electron population growing at each stage until the final anode collects the amplified pulse. The total gain depends on the secondary emission yield at each dynode and the number of stages, typically achieving gains of millions for single particle detection.
The transit time through the electron multiplier depends on the electron velocities between dynodes and the geometry of the electron paths. Higher accelerating voltages between dynodes produce faster electrons and shorter transit times. The transit time spread, or jitter, arises from variations in the electron trajectories and velocities. Electrons emitted from different positions on a dynode surface travel different path lengths to the next dynode. Electrons emitted with different initial velocities have different transit times even for the same path length. These variations accumulate through the multiplier stages, producing the overall timing jitter.
The high voltage power supply determines the interdynode voltages and therefore the electron transit times. Higher total voltages produce higher interdynode voltages, faster electrons, and shorter transit times. The transit time spread also decreases with increasing voltage, as the relative variation in electron velocities becomes smaller when the initial thermal velocities are small compared to the accelerated velocities. Operating the electron multiplier at the highest voltage consistent with gain and lifetime requirements minimizes the timing jitter.
Voltage stability affects the timing jitter through variations in the interdynode potentials. Fluctuations in the power supply voltage cause corresponding variations in the electron transit times, adding to the intrinsic jitter of the multiplication process. The frequency spectrum of the voltage noise determines how it affects timing measurements. Low frequency noise below the signal bandwidth causes slow drifts in the transit time that may be tracked and compensated. Higher frequency noise within the timing measurement bandwidth directly adds to the timing jitter.
The voltage divider network that distributes the total voltage among the dynodes affects the timing performance. Resistive dividers provide fixed voltage ratios regardless of the current drawn by the multiplier stages. During a pulse, the electron current between dynodes momentarily loads the divider, potentially causing voltage sag that affects the pulse transit time. The divider resistance values must be low enough to supply the pulse current without significant voltage drop, while being high enough to limit the static power dissipation. The bypass capacitors on divider stages provide low impedance for the pulse currents, maintaining stable voltages during the pulse transit.
Pulse processing electronics contribute additional timing jitter that must be considered in the overall system design. The threshold discriminator that detects the pulse arrival time exhibits jitter due to noise on the input signal and the finite rise time of the pulse. Lower thresholds reduce the walk error from pulse amplitude variations but increase susceptibility to noise. Constant fraction discriminators provide timing that is relatively independent of pulse amplitude, reducing the walk contribution to jitter. The overall timing resolution is optimized by matching the detector and electronics characteristics.
Time to digital converters or time to amplitude converters measure the time intervals between detector pulses with high precision. These devices digitize time intervals with resolution limited by their clock frequency and interpolation techniques. Resolutions of picoseconds are achievable with modern instrumentation, making the detector jitter the limiting factor in many applications. The high voltage power supply must provide stability commensurate with these measurement capabilities to avoid degrading the system performance.
Applications requiring precise timing include time of flight mass spectrometry, where the mass to charge ratio is determined from the flight time of ions through a drift region. The timing jitter of the detector sets a lower limit on the mass resolution achievable with this technique. Lifetime measurements in nuclear physics determine decay constants from the distribution of time intervals between correlated events, with timing jitter broadening the measured lifetime distribution. Laser ranging and lidar applications measure distances from the round trip time of light pulses, with timing jitter limiting the distance resolution.
Characterization of timing jitter requires measurement of the time distribution for a known input signal. Pulssed light sources with known timing characteristics provide input events for photomultiplier tubes. Particle beams with known time structure enable characterization of particle detectors. The measured time distribution width reveals the total jitter, which can be decomposed into detector and electronics contributions through variation of the measurement configuration. Correlation of the jitter with operating voltage and other parameters guides optimization for specific applications.
