Moderator Informed Compact Positron Optimization

Sophie Crisp, Spencer Gessner

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March 23, 2026

Acknowledgements

PI: Spencer Gessner (SLAC, Stanford)

Undergraduates: Ryland Goldman (UCLA), Arif Ismail (Stanford University)

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This work was supported by the Department of Energy, Laboratory Directed Research and Development program at SLAC National Accelerator Laboratory, under contract DE-AC02-76SF00515.

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Outline

• Motivation: Where are we now?
• Makeup of a slow positron beamline
• Simulations and modeling of a linac based positron source
• Testing at the XTA beamline in the NLCTA bunker at SLAC

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SLAC Once Hosted the World’s Highest Intensity Positron Source

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How can we leverage this expertise and apply it to new scientific challenges?

SLC Positron Target

Positrons for Basic Research

Positron Annihilation Lifetime Spectroscopy

Total Reflection High Energy Positron Diffraction

Laser Cooled Positronium

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Y. Fukuya, J. Phys. D: Appl. Phys. 52, 013002

K. Shu et al., Nature 633, 793–797 (2024)

Positrons enable exciting scientific opportunities, but positron sources have limitations.

Current Positron Sources are Limited by Efficiency

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x 10

* This is just linac sources, but you get the idea

Why is the yield so low?

Schematic of a Linac Based Slow Positron Beamline

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Positron Energy Distribution After Target

Electron Linac

65 MeV e-

High Z Target

e+, e- Particle Shower

Moderator

‘Monochromatic’ e+

Positron Angular Distribution After Target

Remoderator

Lens

Positron Moderation

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Credit: K. Wada

Typically on the order of 10^-4 slow positrons per fast positron*

Lots of ideas to increase e+/e- efficiency

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Moderator Geometry/ Material

Target Geometry

Decelerating Linac

Trapping

Lots of ideas to increase e+/e- efficiency

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Moderator Geometry/ Material:

Tungsten is robust, and you can have complicated geometries

but solid neon gives order of magnitude higher efficiency

Target Geometry:

Potential Conical or Inverse Conical Designs increase fast positron yield- critically, at the desired energy

Decelerating Linac:

Certainly effective, but how much for the increased complexity?

Trapping:

Buffer gas traps are often use to build up positrons to a high number and release all at once, but it’s hard (never been designed or done) to get picosecond timescale beam

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Hessami, Gessner, 2023 https://doi.org/10.1103/PhysRevAccelBeams.26.123402

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Goldman 2025: https://doi.org/10.48550/arXiv.2508.15975

Crisp 2025: https://doi.org/10.48550/arXiv.2508.07549

Efficiency Through the Beamline

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Electron Linac

65 MeV e-

High Z Target

e+, e- Particle Shower

Moderator

‘Monochromatic’ e+

Remoderator

Lens

Max eff: 0.65

Typ: 0.1

Max eff: 0.01

Typ: 1e-5

Eff: 0.01

Increasing moderator efficiency is critical to increasing positron flux.

Positron Moderation is Inefficient

In order to be re-emitted as a moderated positron:

The fast positron must first be ‘stopped’ in the moderator material

without annihilating

at which point it has some probability of getting back to the surface

without annihilating

and being reemitted as a ~3 eV positron

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Stopping

Profile

~microns

Diffusion

Length

~55 nm

Branching

Ratio

~0.3

Reemission Probability

<10^-3

Positron Fate as a Function of Energy

Whether the positrons get stopped within a moderator foil is energy dependent, and so is where

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Left: results from g4beamline simulations of positrons incident on a moderator foil. Stopped positrons contribute to f(z) and thus have a probability of remission as ‘slow’ positrons

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Modeling the Moderation Process

• O’Rourke (Rev. Sci. Instrum. 82, 063302 (2011))
• Using Geant4, model interaction inside converter/moderator
• Since Geant4 cannot model diffusion:
• Allow particles to scatter until they reach KE<50 eV
• Assign probability according to exp(-z/L+) for them to diffuse back to surface, where L+ is the diffusion length (L+ = 55 nm for polycrystalline tungsten, 135 nm for single crystal)
• Assign probability y_0 (0.3) for branching ratio, the proportion of thermalized, surface positrons which are reemitted
• Extract final efficiency

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e+ track inside moderator foil

Modeling the Moderation Process

• O’Rourke (Rev. Sci. Instrum. 82, 063302 (2011))

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JLAB?

Benchmarking Moderation Numbers

• 2500 Angstrom foil
• Points are extracted from Chen et al
• Lines are from simulation

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Benchmarking Moderation Numbers

Moderation is inefficient at the energies of the fast positrons out of the target

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KEK Moderator Efficiency Study

Simulations of a KEK style moderator indicate significant improvements in capture of higher energy positrons

We want more, though!

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Left: remission probability as a function of incoming positron energy (keV)

Data refers to 1985 single crystal exp.

5z and 7z are two different grid based (like KEK) geometries I simulated - clear that the grid allows for more scattering which captures more of the high energy positrons - but this is at the expense of beam size/length

Tailoring positron energy distribution is one way you could increase flux.

Since Moderation is Energy Dependent, Tailoring the Fast Positrons Could Help

Previous work suggests near 2 orders of magnitude improvement in moderation via first decelerating the fast positrons

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Long et al, Study on high flux accelerator based positrons source (2007)

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Reemitted Positron Count

Linac Deceleration Scheme

Using an L-band cavity to decrease the energy of the positrons before the moderated, we obtained a 40x improvement in output positron count

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A: Target

B: AMD

C: L-Band

D: Moderator

Short Pulse Positrons

• With a linac decelerator, we can optimize positron bunches for longitudinal brightness
• ie: number of positrons in a ‘short’ pulse <100 ps

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Other Possibility: take from the ultrafast electron diffraction community and utilize alpha magnet for compression:

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https://arxiv.org/pdf/2508.15975

Ryland Goldman, SULI Intern 2025

Further Moderator Possibilities

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Unsuccessful, but maybe just a methodology problem?

Not for maximization of beam, but maximization of PALS resolution

Further Target Possibilities

Conical targets for enhanced high-current positron sources

Vallis et al., Nuclear Instruments and Methods in Physics Research B 568 (2025) 165854

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Alternatively, for low(er) energy drive: Inverse conical target

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Part of this improvement is due to being in a high magnetic field

Reemitted Fraction

e-

e-, e+, gamma spray

The XTA Accelerator at SLAC is our Testbed for Positron Experiments

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XTA can provide a 65 MeV, 100 pC, 30 Hz e- beam with <10ps pulse length

e- beam direction

Initial XTA Facility Positron Upgrade

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Positron Energy: 1-5 MeV Spot Size: 10 mm x 50 mm

Pulse length: <100 ps Charge: 1 fC/s - 30 fC/s (1e5 e+/s)

XTA can provide a 65 MeV, 100 pC, 30 Hz e- beam with <10ps pulse length (<0.5 W)

Background Depends on Incident Positron Energy

If we stay below 800 keV e+,>10x as many 511 keV gamma rays as not

SNR = (# 511 keV)/(total photons)

*assumes 1:1 signal/photon regardless of energy

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First Science with the SLAC Compact Positron Source

• 10 ps Time of Flight resolution for PET detectors would enhance the SNR, enabling lower dose and quicker measurements

Time of Flight PET Detectors

• Utilizing the entangled nature of the emitted gamma rays enables imaging of dense materials

Ghost Imaging with Gamma Rays

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Schneider et al., Phys. Rev. A 113, 013715 (2026)

Utilize well-timed positrons.

Roadmap for a SLAC Positron Facility

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Takeaways:

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• At the XTA beamline at SLAC, this could provide a positron source of up to 1e6 e+/s, comparable to radioactive source capabilities, in a <100 ps pulse

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• Tailoring the e+ energy spectrum is a promising way to increase slow positron source conversion efficiency, but requires experimental validation of our moderator models

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• In the near term, positron production at SLAC will enable testing of
• novel PET detectors, high SNR ghost imaging
• positron targets and moderators

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That Model Was Missing Something Crucial - The Target

Now, initialize positrons directly in front of the target

Greatly increases efficiency, particularly at 100 keV energy scale

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Tailoring positron energy distribution is one way you could increase flux.

So Where Do the Positrons Go?

A large proportion of the low energy positrons are simply reflected

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