Performance characterisation of the Hamamatsu R760 photomultiplier tube for the PLUME detector

This paper presents a comprehensive laboratory characterization of the Hamamatsu R760 photomultiplier tubes used in the PLUME detector for the LHCb experiment, systematically evaluating their gain, timing, linearity, dark current, and ageing to establish optimal operating conditions for stable luminosity measurements during LHC Runs 3 and 4.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It's like a giant, high-speed racetrack where protons zoom around and crash into each other billions of times a second. To understand what happens in these crashes, scientists need to know exactly how many crashes are happening. This number is called luminosity.

Enter the PLUME detector. Think of PLUME as a very sensitive "traffic counter" sitting right next to the racetrack. Its job is to count the particles flying out of the crash zone so scientists can calculate the luminosity.

But here's the catch: PLUME doesn't count particles directly. Instead, it uses 48 special light sensors (called Photomultiplier Tubes, or PMTs) to catch the tiny flashes of blue light (Cherenkov light) that particles create when they hit a quartz window. It's like trying to count cars by counting the sparks they kick up as they drive over a special road surface.

This paper is essentially a quality control report for those 48 light sensors before they were installed. The scientists wanted to make sure these sensors were tough, accurate, and wouldn't break down during the next decade of racing.

Here is a breakdown of what they tested, using simple analogies:

1. The "Volume Knob" (Gain)

The Concept: The PMTs need to amplify the tiny flash of light into a signal big enough for computers to read. This amplification is called "gain."
The Test: The scientists turned the "volume knob" (voltage) up and down to see how loud the signal got.
The Result: They found the perfect setting. Even if the light gets very dim, these sensors can turn it up loud enough to hear. They confirmed that the sensors can be tuned to the exact volume needed for the job.

2. The "Stopwatch Drift" (Transit-Time Drift)

The Concept: The particles arrive in very tight groups (bunches) every 25 nanoseconds. The sensor needs to react instantly. If the sensor is slow, it might mix up which group of particles caused the flash.
The Test: They measured how long it takes for an electron to travel from the start of the sensor to the end. They checked if this time changes when they turn the voltage up or down.
The Result: The "stopwatch" is incredibly stable. Even if they change the voltage, the sensor only gets off by a tiny fraction of a second (less than 7 nanoseconds). This is fast enough to keep perfect time with the LHC's race schedule.

3. The "Honest Scale" (Linearity)

The Concept: If one particle creates a signal of "1," then 10 particles should create a signal of "10." The sensor shouldn't get confused and say "100" or "5."
The Test: They shone light of different intensities (like turning a dimmer switch) to see if the sensor's output stayed proportional.
The Result: The sensor is an honest scale. As long as the light isn't blindingly bright (which won't happen in normal operation), the output is perfectly proportional to the input. It won't lie about the number of particles.

4. The "Silent Room" (Dark Current)

The Concept: Even in total darkness, some sensors get "noisy" and create fake signals (static).
The Test: They put the sensors in a pitch-black box to see if they would generate any signals on their own.
The Result: The sensors are very quiet. The "noise" they make is so tiny (less than 20 nanoamps) that it's completely drowned out by the real signals from the particle crashes. It's like trying to hear a whisper in a library, but the whisper is so quiet you can't hear it at all.

5. The "Marathon Run" (Ageing)

The Concept: This is the big one. The LHC will run for many years (Runs 3 and 4). The sensors will be bombarded with particles constantly. Will they get tired and stop working?
The Test: They simulated years of work in a few months. They shone a bright light on the sensors continuously, forcing them to work hard, accumulating a massive amount of "charge" (like running a marathon).
The Result:

• The Fatigue: The sensors did get a little tired. Their sensitivity dropped by about 4 times in the beginning.
• The Fix: But, just like a runner who needs to drink more water to keep going, the scientists found they could just turn up the voltage to compensate.
• The Verdict: Even after simulating the entire lifespan of the experiment, the sensors still had plenty of "headroom." They could be turned up high enough to keep working perfectly without needing to be replaced.

The Bottom Line

The scientists looked at these 48 light sensors and said, "They are ready." They are fast, accurate, quiet, and tough enough to survive the next decade of particle smashing. With a little adjustment to their power settings, they will keep counting the collisions perfectly from the start of Run 3 all the way through Run 4.

Technical Summary

1. Problem Statement

The LHCb experiment at the Large Hadron Collider (LHC) is upgrading for Runs 3 and 4 to operate at a luminosity approximately five times higher than previous runs. To manage this, the experiment employs a luminosity levelling technique, which requires precise, real-time monitoring of the instantaneous luminosity to adjust beam conditions.

The PLUME (Probe for LUminosity MEasurement) detector is the dedicated luminometer for this task. It consists of a hodoscope with 48 Hamamatsu R760 photomultiplier tubes (PMTs) designed to detect Cherenkov light produced by particles in quartz. The critical challenges addressed in this paper are:

• Stability: Ensuring the PMTs maintain stable gain and timing over the full duration of Runs 3 and 4 (approx. 5.5 years).
• Radiation Hardness: Withstanding an expected integrated dose of 80–200 kGy and a neutron fluence of $1 \times 10^{14} \text{ n/cm}^2$.
• Ageing: Verifying that the PMTs can accumulate a total integrated charge of approximately 450 C without permanent failure or requiring replacement.
• Linearity: Ensuring the signal response remains linear despite high particle rates and space-charge effects.

2. Methodology

The authors conducted a comprehensive characterisation campaign on the specific PMTs installed in the PLUME detector under controlled laboratory conditions. The experimental setup included:

• Light Sources: A 405 nm picosecond diode laser (for gain, timing, and linearity) and a 525 nm LED driven by a pulse generator (for ageing).
• Readout Electronics:
  • Keithley 6485 Picoammeter: For dark current and relative gain measurements.
  • DRS4 Evaluation Board: A switched capacitor array (5 GSPS) for digitizing waveforms to measure absolute gain, transit-time drift, and linearity.
  • CAEN SY127: A 40-channel power supply system.
• Test Parameters:
  • Gain: Measured in the Single Photoelectron (SPE) regime using a Poisson-Gaussian fit to charge spectra.
  • Transit-Time Drift: Measured as the time difference between the laser trigger and PMT output pulse across voltages (650–1250 V).
  • Linearity: Tested at operational voltage and +400 V, comparing measured charge against expected charge derived from light intensity ratios.
  • Dark Current: Measured in darkness at 13 voltage steps.
  • Ageing: A continuous illumination campaign accumulating charge up to ~340 C, with periodic interruptions to measure gain recovery and required voltage adjustments.

3. Key Contributions

• Custom Divider Circuit: The paper details the development of a custom resistive voltage divider (developed at IJCLab) to replace the standard Hamamatsu divider, which lacked the necessary linearity for the high photon yields generated by the PLUME's quartz tablets.
• Comprehensive Characterisation: This is the first full characterization of the specific batch of R760 PMTs intended for PLUME, covering gain, timing, linearity, dark current, and ageing in a single study.
• Ageing Simulation: The authors performed an accelerated ageing test that exceeded the charge accumulation expected during Run 3 and approached the total expected for Run 4, providing empirical data on long-term degradation.

4. Key Results

A. Gain and Voltage Dependence

• Absolute Gain: At the maximum supply voltage of 1250 V, the average absolute gain is $1.5 \times 10^7$.
• Voltage Scaling: The gain follows the power law $G(V) = C \cdot \Delta V^\alpha$, with the exponent $\alpha$ measured to be 7.53 (consistent with the expected 7–8 range for 10 dynodes).
• Operating Point: To achieve the target operational gain of $1.5 \times 10^5$, specific bias voltages (starting around 650–800 V) were determined for each PMT.

B. Transit-Time Drift

• The transit time varies with voltage, but the drift ($\Delta t_{transit}$) relative to the reference at 1250 V does not exceed 7 ns across the entire operating voltage range.
• Given the LHC bunch-crossing interval is 25 ns and the PMT signal width is ~10 ns, this drift is acceptable and will not significantly impact timing resolution or signal containment.

C. Linearity

• The PMTs exhibit excellent linearity for integrated charges below 10 pC (the upper limit of the PLUME operational regime), with deviations < 10%.
• At higher charges (~40 pC), deviations reach up to 30% due to space-charge effects, but these are outside the normal operating range.
• Linearity performance was consistent between the operational voltage and a voltage 400 V higher.

D. Dark Current

• Dark current increases with voltage but remains negligible. Even at the maximum voltage (1250 V), the dark current is < 20 nA for all tested units.
• This is orders of magnitude lower than the expected anode current during operation (several $\mu$A), ensuring no significant bias in luminosity measurements.

E. Ageing and Longevity

• Charge Accumulation: The test accumulated 340 C of integrated charge.
• Gain Degradation: Gain initially dropped by a factor of four within the first 40 C, followed by a slow, linear decline.
• Voltage Compensation: To maintain a constant gain of $1.5 \times 10^5$, the required high voltage increased from ~800 V to 1035 V.
• Recovery: A 20-day pause in the ageing process showed no significant gain recovery; degradation was permanent.
• Conclusion: The final required voltage (1035 V) is well below the R760 maximum limit (1250 V), confirming the PMTs can survive the full duration of Runs 3 and 4 without replacement.

5. Significance

This paper provides the critical Quality Assurance (QA) validation required for the deployment of the PLUME detector. By demonstrating that the Hamamatsu R760 PMTs meet all performance criteria—specifically regarding linearity in the low-charge regime, timing stability, and long-term survivability under high charge accumulation—the authors confirm that the PLUME detector is ready to deliver the precise luminosity measurements necessary for the LHCb experiment's physics goals in Runs 3 and 4. The results establish the optimal operating conditions (bias voltages) and confirm that the detector design is robust against the harsh radiation environment of the LHC.