High-precision beam profile measurement with a microchannel-plate detector in the high magnetic field of the WISArD experiment

This paper presents the development and characterization of a compact microchannel-plate detector for the WISArD experiment at ISOLDE/CERN, demonstrating its ability to achieve sub-millimeter beam profile measurements with pincushion distortion correction under a 4 T magnetic field to support the extraction of the beta-neutrino angular correlation coefficient with 0.1% uncertainty.

The Gist

Imagine you are trying to take a perfect photograph of a tiny, invisible speck of dust (a radioactive atom) as it flies through a room. But there's a catch: the room is filled with an incredibly powerful, invisible magnetic force field (like a giant, invisible magnet) that tries to twist and bend everything that moves through it.

This is the challenge faced by the WISArD experiment at CERN. They want to study how certain atoms decay to understand the fundamental rules of the universe. To do this, they need to know exactly where the atoms are landing. If they are off by even a tiny fraction of a millimeter, their calculations about the universe's secrets will be wrong.

Here is the story of how they built a special "camera" to solve this problem, explained simply.

1. The Problem: The "Magnet Monster"

The experiment needs a very strong magnetic field (4 Tesla) to work. Think of this magnetic field as a giant, invisible tornado.

• The Issue: Standard cameras (detectors) used to see these atoms rely on electrons flying through the air to create an image. But in this "magnetic tornado," the electrons get twisted and squashed, making the camera blind or very blurry.
• The Space Issue: The camera also has to fit inside a very tight, narrow tube (the "detection tower"). It's like trying to install a high-tech dashboard in a car that only has a tiny glovebox to work with.

2. The Solution: A "Sandwich" Camera

The team built a custom detector using Microchannel Plates (MCPs).

• The Sandwich: Imagine a sandwich made of three layers of special glass that are covered in millions of tiny, microscopic tunnels (channels). When an atom hits the first layer, it triggers a chain reaction, multiplying the signal like a row of falling dominoes.
• The Secret Sauce: To survive the "magnetic tornado," they made the tunnels in the glass very narrow and tilted them at a specific angle. This forces the electrons to stay on track even when the magnetic field tries to push them sideways.
• The Shape: Because space was so tight, they couldn't use a round camera sensor. They had to use a square one.

3. The Distortion: The "Funhouse Mirror"

Using a square sensor caused a new problem. In physics, when you use a square resistive grid to find a position, the image gets warped, looking like a pincushion (the edges bulge out, and the corners get squished).

• The Analogy: Imagine drawing a perfect grid on a rubber sheet and then stretching the corners. The lines curve, and a square hole looks like a distorted diamond.
• The Fix: The scientists wrote a clever computer program (a mathematical "spell") to look at the distorted image and mathematically "un-stretch" it. They used a calibration mask (a stencil with tiny holes) to teach the computer exactly how the distortion works, allowing them to reconstruct the true, straight image.

4. The Test: Running in the Storm

They tested this camera in two ways:

1. In the Quiet Room: First, they tested it with a stable beam of atoms without the magnetic field. They proved they could see the atoms with incredible precision (better than the width of a human hair).
2. In the Tornado: Then, they turned on the 4 Tesla magnetic field.
   • The Challenge: The magnetic field made the camera less sensitive (dimmer). To fix this, they cranked up the voltage (the "power") to the camera, like turning up the brightness on a flashlight in a dark storm.
   • The Result: Even in the strongest magnetic field, the camera still worked! It could see the beam clearly, though the image was a bit fuzzier than in the quiet room.

5. The Big Win: Seeing the Invisible

Finally, they used this camera to look at the actual radioactive beam (32Ar) during the real experiment.

• The Result: They mapped the beam's shape perfectly. They found out exactly how wide the beam was and where its center was.
• Why it Matters: Before this, they were guessing the beam's location with a margin of error that was too big. Now, they know the location with sub-millimeter accuracy.

The Bottom Line

This paper is about building a tiny, rugged, "funhouse-mirror-fixing" camera that can survive inside a giant magnetic storm. By doing so, the scientists can now measure the decay of atoms with the extreme precision needed to test if our current understanding of the universe (the Standard Model) is complete, or if there are hidden secrets waiting to be discovered.

They turned a "blurry, distorted mess" into a "crystal-clear map," ensuring that their next big discovery won't be ruined by a tiny measurement error.

Technical Summary

1. Problem Statement

The WISArD experiment at ISOLDE/CERN aims to measure the modified beta-neutrino angular correlation coefficient ($\tilde{a}_{\beta\nu}$) in the beta decay of $^{32}\text{Ar}$ with a precision of 1‰. This measurement is crucial for probing physics beyond the Standard Model.

• The Challenge: The extraction of $\tilde{a}_{\beta\nu}$ relies on Monte-Carlo simulations that are highly sensitive to the spatial location of the radioactive decay source. Previous proof-of-principle experiments suffered from a systematic error of $\Delta\tilde{a}_{\beta\nu} = 4‰$ due to a 3 mm uncertainty in the beam implantation position and radius.
• Constraints: To reduce this uncertainty, a new beam diagnostic tool with sub-millimeter accuracy is required. However, the detector must operate within the WISArD detection tower, which is housed inside a superconducting magnet providing a 4 Tesla (T) magnetic field. The available space is extremely limited (max diameter 12 cm, max thickness 15 mm).
• Technical Hurdle: Standard Microchannel Plate (MCP) detectors suffer significant gain reduction (up to one order of magnitude) in strong magnetic fields (1 T) because the field shortens electron trajectories, reducing secondary emission. Furthermore, standard position-sensitive anodes (e.g., delay lines, backgammon) require electron cloud spreading, which is suppressed by the 4 T field.

2. Methodology and Detector Design

Detector Architecture

The team developed a compact, custom MCP detector designed specifically for the WISArD constraints:

• MCP Stack: Three MCPs arranged in a Z-stack configuration (providing higher gain than standard Chevron stacks).
• MCP Specifications: Hamamatsu F1551-01 plates with a 12 µm channel diameter and an 8° bias angle. These smaller channels and angles were chosen to mitigate gain loss in the 4 T field.
• Anode: A custom-made square-shaped resistive anode (16 mm × 16 mm) fabricated by mixing graphite powder with glyceride-based paint on a PEEK substrate. This geometry is compact and compatible with high magnetic fields, unlike larger commercial alternatives.
• Readout: The anode has four corners connected to charge preamplifiers. A 2D position is calculated based on the charge division ratio at these corners.
• Calibration: A permanent aluminum mask with a 1.4 mm pitch pattern (holes) is fixed in front of the first MCP to provide online calibration and act as a Faraday cup for beam tuning.

Image Reconstruction and Calibration

The raw position data from a square resistive anode suffers from pincushion distortion and gain non-uniformity (particularly at the corners). The authors developed a multi-step reconstruction algorithm:

1. Logarithmic Correction: Applied to the normalized corner charges to correct for gain differences and reduce pincushion distortion.
2. Geometric Modeling: A 2D function was fitted to the calibration mask image. The transmission of the mask was modeled using linear functions defining the hole contours, convoluted with a 2D Gaussian to account for detector resolution.
3. Bilinear Interpolation: A mapping function was created to transform the distorted detector coordinates into the physical mask coordinates, achieving sub-millimeter accuracy.

Testing Conditions

• Stable Beam: Characterized using a 30 keV $^{39}\text{K}^+$ beam at ISOLDE (0 T to 4 T).
• Radioactive Beam: Tested with the actual $^{32}\text{Ar}$ beam during the 2025 run at 4 T.
• Voltage Adjustment: To compensate for magnetic field-induced gain loss, the MCP bias voltage was increased from -2.0 kV (0 T) to -3.2 kV (4 T).

3. Key Contributions

• Custom Detector Design: Successfully integrated a compact, Z-stack MCP with a custom square resistive anode into a high-field (4 T), space-constrained environment.
• Advanced Reconstruction Algorithm: Developed a robust image reconstruction method that corrects for the inherent geometric distortions of square resistive anodes and gain non-uniformities, enabling high-precision position reconstruction.
• Magnetic Field Characterization: Systematically quantified the impact of the 4 T magnetic field on MCP gain and spatial resolution, establishing the necessary voltage compensation strategies.
• Systematic Error Reduction: Demonstrated a beam profiling system capable of reducing the beam position uncertainty from millimeters to sub-millimeters, directly addressing the primary systematic error source in the WISArD experiment.

4. Results

Performance in Magnetic Fields

• Gain Loss: The magnetic field significantly reduced MCP gain. A threshold voltage was observed below which no signal was detected, roughly estimated as $V_{min} \approx -1.8 - 0.2 \times B$ (kV).
• Resolution:
  • 0 T: Achieved a spatial resolution of $\delta x = 0.061$ mm and $\delta y = 0.063$ mm.
  • 1 T to 3 T: With increased bias voltages (-2.2 kV to -2.6 kV), the resolution degraded to approximately 0.15 mm.
  • 4 T: At the nominal operating voltage of -3.2 kV, the resolution was maintained at a level sufficient for the experiment, though the 4 T scan data showed some inhomogeneity due to beam confinement.
• Position Accuracy: The reconstruction algorithm successfully corrected distortions. The mean deviation between reconstructed hole positions and nominal mask positions at 1 T was negligible ($\Delta x \approx -0.012$ mm, $\Delta y \approx -0.039$ mm).

$^{32}\text{Ar}$ Beam Profile Measurement

• Using the calibrated detector at 4 T, the $^{32}\text{Ar}$ beam profile was measured and fitted to a 2D Gaussian distribution.
• Beam Parameters:
  • Center: $\mu_x = -0.05(8)$ mm, $\mu_y = 0.41(6)$ mm.
  • Widths: $\sigma_x = 1.05(7)$ mm, $\sigma_y = 0.61(8)$ mm.
• Impact on Physics: The uncertainty in the beam profile was propagated to the $\tilde{a}_{\beta\nu}$ measurement using Geant4 simulations. The resulting systematic uncertainty contribution was $(\Delta\tilde{a}_{\beta\nu})_{beam} = 0.7(1)‰$.

5. Significance

This work successfully overcomes the critical bottleneck of the WISArD experiment. By developing a specialized detector and reconstruction method, the team reduced the systematic uncertainty related to the beam profile from 4‰ (previous limit) to 0.7‰. This improvement brings the total experimental uncertainty well within the 1‰ target required to definitively test the Standard Model and search for exotic currents in nuclear beta decay. The methodology serves as a blueprint for high-precision ion beam diagnostics in high-magnetic-field environments.