Development of a time calibration system for the KLM upgrade in the Belle II experiment

The authors developed and validated a compact, high-speed time calibration system utilizing a laser diode and GaN FET-based drive circuit, which achieved a 13 ps timing resolution for individual channels and demonstrated its suitability for the large-scale scintillator upgrades in the Belle II experiment's KLM detector.

The Gist

Imagine you are trying to catch a speeding bullet with a camera. To know exactly when the bullet passed, your camera needs to be incredibly precise. If your camera is even a tiny bit slow or fast compared to the others, your measurement of the bullet's speed will be wrong.

This is the challenge facing the Belle II experiment, a massive particle physics lab in Japan. They are upgrading a giant detector called the KLM (which acts like a giant net to catch invisible particles called muons and neutral kaons). This net is made of tens of thousands of long, glowing plastic strips (scintillators). When a particle hits a strip, it flashes with light. To figure out exactly where and when the particle hit, the scientists need to measure that flash with a precision better than 100 picoseconds (that's one-trillionth of a second!).

The problem? With tens of thousands of these strips, tiny differences in the electronics, cables, or even the shape of the strips can throw off the timing. It's like having an orchestra of 50,000 musicians; if they don't all start playing at the exact same split-second, the music sounds terrible.

The Solution: A "Super-Strobe" Clock

To fix this, the team (led by researchers from Nankai University and Fudan University) built a Time Calibration System. Think of this system as a "Master Conductor" that gives every single musician in the orchestra a perfect, synchronized starting signal.

Here is how their invention works, broken down into simple parts:

1. The Light Source: The "Super-Strobe"
Instead of using a slow, flickering light bulb, they use a Laser Diode. Imagine a camera flash so fast and powerful that it freezes a hummingbird's wings in mid-air. This laser emits a tiny, intense burst of blue light.

• The Analogy: Think of it like a master drummer hitting a drumstick. Every time the drumstick hits, it sends a signal to every musician to start playing.

2. The Driver Circuit: The "GaN FET" Muscle
To make the laser flash that fast, you need a switch that can turn on and off incredibly quickly. The team used a special type of electronic switch called a GaN FET (Gallium Nitride Field Effect Transistor).

• The Analogy: Regular switches are like a heavy door that takes a second to open and close. A GaN FET is like a magic door that opens and closes in the blink of an eye. This allows the laser to fire a pulse so short it's almost instantaneous.

3. The Distribution: The "Light Splitter"
The laser fires one beam, but they need to test thousands of channels. They use an optical splitter (like a prism or a fork in a road) to divide that single laser beam into many smaller beams, sending them to different parts of the detector at the exact same time.

• The Analogy: Imagine a single water hose that splits into 50 smaller hoses, all spraying water at the exact same moment to test 50 different sprinklers.

The Results: Precision Beyond Imagination

The team built a prototype and tested it with their glowing plastic strips. Here is what they found:

• The "Single Channel" Test: When they tested just one path of the system, they achieved a timing precision of 13 picoseconds.
  • The Metaphor: If the entire experiment lasted for the age of the universe (13.8 billion years), this system is precise enough to tell you the difference between a second and a fraction of a second that is smaller than the time it takes for a single atom to vibrate.
• The "Orchestra" Test: They checked if all the different channels (the different "musicians") were in sync. They found that the difference between any two channels was less than 250 picoseconds.
  • The Metaphor: In a choir of 50,000 people, this means everyone is singing the note within a tiny fraction of a beat of each other. No one is "off-key" enough to ruin the song.

Why Does This Matter?

Without this system, the Belle II experiment would be like trying to measure the speed of a race car with a stopwatch that has a slow reaction time. The data would be blurry.

With this new laser calibration system, the scientists can now:

1. Synchronize all 50,000+ channels perfectly.
2. Measure the speed of particles with extreme accuracy.
3. Identify rare and mysterious particles that were previously too hard to spot.

In short, they built a "super-precise stopwatch" that ensures the entire giant detector works as one perfect, synchronized machine, allowing them to unlock the secrets of the universe with crystal-clear timing.

Technical Summary

1. Problem Statement

The Belle II experiment at the SuperKEKB collider is undergoing an upgrade to its outermost subsystem, the $K_L$ and Muon (KLM) Detector. The upgrade aims to improve background veto capabilities and enable precise Time-of-Flight (TOF) measurements for $K_L$ meson momentum determination.

• Requirements: To achieve a momentum resolution of $\sim10\%$, the upgraded KLM detector, comprising tens of thousands of scintillator channels, must achieve a time resolution better than 100 ps (with some channels reaching $\sim50$ ps).
• Challenge: Variations in electronic components, cables, and geometric configurations among the massive number of channels introduce timing deviations. A dedicated, compact, and high-precision calibration system is required to correct these deviations and ensure the system meets the stringent timing specifications. Existing laser calibration systems (e.g., in BESIII or MEG II) achieve resolutions of 41–89 ps, but the scale and precision requirements of the Belle II KLM upgrade necessitate a more advanced solution.

2. Methodology

The authors developed a compact, high-speed time calibration system utilizing a laser diode as the light source and a custom Gallium Nitride Field-Effect Transistor (GaN FET) based drive circuit.

A. System Architecture

• Concept: A single laser source is split via an optical splitter to illuminate multiple scintillator channels simultaneously. One channel serves as a reference photodetector ($T_{ref}$), while others ($T_i$) measure the arrival time. The deviation $\delta t_i = T_i - T_{ref}$ is calculated to calibrate the detector.
• Light Source: An Osram PLPT5 447KA laser diode (445 nm, 2 W max). The 445 nm wavelength is chosen to align with the peak Photon Detection Efficiency (PDE) of the Hamamatsu S14160 Silicon Photomultipliers (SiPMs) used in the detector.
• Drive Circuit Design:
  • Timing Generation: An NE555 timer and SN74AHC123ADR monostable multivibrator generate trigger signals.
  • Gate Driving: Signals are processed by an LMG1020 low-side gate driver (capable of 7 A output).
  • Switching: EPC2037 GaN FETs are employed for high-speed switching. GaN technology was selected for its fast turn-on speed, compact size, and low on-resistance, enabling the generation of ultra-short light pulses.
  • Power Supply: A dual-power system uses an LM1117 LDO (5 V) for logic and an LGS6302B5 boost converter (up to 24 V) with an LM317 adjustable regulator for the laser diode.
  • Pulse Shaping: The laser diode circuit acts as an underdamped RLC circuit. A clamping circuit (diode and resistor) is added to suppress reverse current and voltage spikes, ensuring a single, well-defined short pulse.

B. Prototype Construction

• Hardware: A prototype PCB (97 mm $\times$ 86 mm) was built with 8 laser control channels, 2 trigger outputs, and 8 power delivery channels. The laser diode is mounted on a separate small PCB (26 mm $\times$ 21 mm).
• Test Setup:
  • Detectors: Hamamatsu S14160 SiPM arrays (1 $\times$ 4 configuration).
  • Readout: A custom preamplifier (+26 dB gain, 426 MHz bandwidth) and a DT5742 digitizer (5 GS/s sampling rate).
  • Analysis: Timing was extracted using the Constant Fraction Discriminator (CFD) method with a fraction $f=0.2$.

3. Key Contributions

1. GaN FET-Based Driver: The integration of GaN FETs into the laser driver circuit allows for extremely fast switching, which is critical for generating the short, intense optical pulses required for sub-100 ps timing resolution.
2. Compact Scalable Design: The system is designed to be compact and flexible, capable of driving multiple channels simultaneously, making it suitable for the tens of thousands of channels in the KLM upgrade.
3. Optimized Circuit Topology: The implementation of a specific RLC discharge circuit with a clamping mechanism ensures stable, single-pulse emission while protecting the laser diode from oscillation-induced damage.

4. Experimental Results

The prototype was rigorously tested in two stages:

• Single-Channel Resolution (Laser + SiPM):

  • Tested directly with two SiPM arrays facing the laser diode.
  • Result: Achieved a time resolution of $13.52 \pm 0.09$ ps. This confirms the laser driver and diode can produce pulses precise enough to calibrate detectors with $\sim50$ ps resolution.

• Scintillator Channel Calibration:

  • Tested with three 1-meter high-transparency scintillator bars (GaoNengKeDi) coupled to SiPMs via optical fibers.
  • Result: Using one channel as a reference, the other channels showed resolutions of 17 ps and 19 ps. The effective time resolution for a single calibration channel was determined to be $\sim13$ ps.

• Inter-Channel Deviation (Self-Calibration):

  • The consistency among the 8 laser control channels was analyzed by swapping channels while keeping the laser diode and SiPM constant.
  • Result: The maximum deviation between channels was 138 ps, with most measurements falling within 100 ps. The total deviation among all calibration channels remained below 250 ps.

5. Significance

• Meeting Upgrade Requirements: The system's single-channel resolution ($\sim13$ ps) is significantly better than the required detector resolution ($<100$ ps), ensuring the calibration system does not become the limiting factor in the overall timing performance.
• Scalability: The low inter-channel deviation ($<250$ ps) demonstrates that the system can reliably calibrate the tens of thousands of channels in the KLM detector without introducing significant systematic errors.
• Future Impact: This development provides a proven, high-precision solution for the Belle II KLM upgrade, enabling accurate TOF measurements that are crucial for $K_L$ meson momentum reconstruction and background rejection in high-luminosity physics experiments.