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Charge Collection Efficiency in Air-Vented Plane-Parallel Ionisation Chambers at Ultra-High Dose Rates: A Self-Consistent Garfield++ Monte Carlo Model Including Space-Charge Effects and Ion Recombination

This paper presents a validated self-consistent Garfield++ Monte Carlo model that incorporates space-charge effects and ion recombination to demonstrate that charge collection efficiency in air-vented plane-parallel ionisation chambers at ultra-high dose rates is primarily reduced by electric-field-dependent electron attachment rather than direct recombination.

Original authors: Pierre Gérard Ortega, Gilles De Lentdecker, Quentin Flandroy, Jarrick Nys

Published 2026-06-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Pierre Gérard Ortega, Gilles De Lentdecker, Quentin Flandroy, Jarrick Nys

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Measuring a "Flash" of Radiation

Imagine you are trying to measure the amount of rain falling during a sudden, massive thunderstorm. You have a bucket (an ionization chamber) designed to catch the rain and tell you how much water fell.

In traditional radiotherapy, the "rain" falls slowly and steadily. Your bucket works perfectly. But in FLASH radiotherapy, the radiation comes in an incredibly intense, ultra-fast burst (like a firehose blasting water for a split second).

The problem is that when you blast that much water into a small bucket all at once, the water itself starts to push back. The sheer volume of water creates a "wall" that changes how the rest of the water flows. In the world of radiation, this is called space charge. The paper explains how the authors built a super-accurate computer simulation to understand exactly how this "water wall" messes up the measurement, and they found a surprising reason why the measurement goes wrong.

The Problem: The Bucket Gets Clogged

In a normal radiation beam, the air inside the detector acts like a clean highway. Charged particles (electrons and ions) zip straight to the walls of the bucket to be counted.

But under Ultra-High Dose Rates (UHDR):

The Traffic Jam: So many particles are created instantly that they crowd the air. This crowd creates its own electric force, which distorts the "highway" (the electric field).
The Detour: Sometimes this crowd pushes the electric field so hard that it creates a "no-go zone" where the field drops to almost zero. Other times, it squeezes the field so tight it becomes four times stronger than normal.
The Result: The particles get lost, slow down, or crash into each other before they can reach the bucket wall. This means the machine thinks less radiation hit the patient than actually did. This is called a drop in Charge Collection Efficiency (CCE).

The Solution: A Digital Twin

The authors (Pierre Gérard Ortega and colleagues) took a powerful physics simulation tool called Garfield++ and upgraded it. Think of Garfield++ as a video game engine for physics. They added two new "rules" to the game to make it realistic for these super-fast bursts:

The Crowd Rule (Space Charge): The simulation now calculates how the particles push against each other and bend the electric field in real-time.
The Crash Rule (Recombination): The simulation now tracks when positive and negative particles crash into each other and cancel out (recombine) before they can be counted.

They tested their new "Digital Twin" against real-world math models and other scientists' data, and it matched perfectly.

The Big Discovery: It's Not About Time, It's About "Sticky" Air

For a long time, scientists thought the reason measurements failed during these fast bursts was that the particles stayed in the bucket too long, giving them more time to crash into each other.

The paper's simulation proved this wrong.

Here is the analogy they found:

The Old Idea: The particles were stuck in a traffic jam for a long time, so they had plenty of time to crash.
The New Reality: The particles didn't stay longer; they just got stuck to the "walls" of the air immediately.

The air in the detector contains oxygen. Oxygen is like Velcro.

Normally, the electric field is strong enough to rip the electrons off the oxygen before they stick.
But because the "crowd" (space charge) distorted the electric field, some areas became weak.
In these weak areas, the electrons couldn't escape the oxygen. They got "Velcroed" (attached) to the oxygen molecules instantly.
Once an electron is stuck to oxygen, it becomes a heavy, slow negative ion. These heavy ions are much more likely to crash into positive ions and disappear (recombine).

The Conclusion: The measurement error isn't because the particles lingered; it's because the distorted electric field made the air "stickier," causing electrons to get trapped and lost before they could be counted.

Why This Matters

The authors built a flexible, open-source tool (called GarFLIC) that anyone can use. It allows scientists to simulate exactly how different types of air, different chamber shapes, and different radiation bursts will behave.

By understanding that the problem is really about the "stickiness" of the air (the Free Electron Fraction), they believe we can create better math formulas to fix these measurements in real-time. This means doctors can trust their radiation dose measurements even when using these incredibly fast, powerful FLASH treatments.

In short: They built a super-accurate simulator, found that the "crowd" of particles makes the air sticky, and proved that this stickiness—not the time the particles spend in the air—is the main reason measurements go wrong during ultra-fast radiation bursts.

Technical Summary: Charge Collection Efficiency in Air-Vented Plane-Parallel Ionisation Chambers at Ultra-High Dose Rates

Problem Statement
Ultra-high dose rate (UHDR) irradiation, utilized in FLASH radiotherapy (≥40 Gy s⁻¹), induces significant space-charge effects within plane-parallel ionisation chambers (PPICs). These effects lead to substantial reductions in charge collection efficiency (CCE). While standard analytical models (e.g., Boag's model) account for ion recombination in conventional radiotherapy, they fail under UHDR conditions because they neglect electric-field distortions caused by high charge densities. Existing literature indicates that space charge can locally distort the electric field by factors exceeding four, yet a self-consistent framework to model the interplay between particle transport, electron attachment, ion–ion recombination, and dynamic field evolution has been lacking.

Methodology
The authors extended the Garfield++ Monte Carlo simulation framework to address these gaps. The development involved three primary technical implementations:

Ion–Ion Recombination: The AvalancheMC class was extended to simulate volume recombination (recombination between ions from different tracks) as a Poissonian process. The recombination probability is calculated at each time step based on local ion densities and a specified recombination coefficient ( $\alpha$ ).
Space-Charge Electric Field Calculation: A Poisson solver was implemented within the ComponentGrid class. Using a Particle-in-Cell (PIC) approach, the code deposits charge from simulated particles onto a 3D Cartesian grid. The resulting space-charge density ( $\rho$ ) is used to solve Poisson's equation ( $\nabla^2\phi = -\rho/\varepsilon$ ) via an iterative Gauss–Seidel solver with Successive Over-Relaxation (SOR). This updates the electric field dynamically, accounting for distortions caused by the accumulated charge.
Electron Attachment and Transport: The model couples electron transport with attachment processes. Using Magboltz, electron swarm parameters (mobility and attachment coefficients) are determined for specific gas mixtures (air with varying humidity). The simulation tracks the conversion of free electrons to negative ions, which is highly dependent on the local electric field strength.

The simulation handles arbitrary gas mixtures, atmospheric conditions, and beam structures. To manage computational costs for UHDR doses (involving $\sim 10^9$ physical particles), a particle weight (multiplicity factor) is employed. Parallelisation is achieved by defining global time steps where particle drifts are computed in parallel, followed by a serial step to update density maps and the electric field.

Key Contributions

Self-Consistent Framework: The paper presents GarFLIC (Garfield++ for FLASH Ionisation Chamber), a flexible Monte Carlo tool that self-consistently couples particle transport, attachment, recombination, and dynamic electric-field distortions.
Validation Against Literature: The model was rigorously validated against:
- Fenwick and Kumar: Reproducing CCE and free electron fraction (FEF) in the absence of space charge.
- Kranzer et al.: Reproducing the temporal evolution of electric-field distortions under UHDR pulses.
- Paz Martín et al.: Reproducing FEF evolution, CCE as a function of dose per pulse (DPP), and induced current profiles.
Mechanistic Insight: The study isolates the specific physical drivers of CCE reduction in UHDR regimes, distinguishing between recombination time and attachment dynamics.

Results

Electric Field Distortion: Simulations confirm that under UHDR conditions (e.g., a 2 Gy pulse over 2.5 µs), space charge can locally increase the electric field by more than a factor of four or reduce it to nearly zero. These distortions persist throughout the charge drift phase, even after electron collection.
Free Electron Fraction (FEF): The FEF is shown to be a dynamic variable rather than a constant. As DPP increases, the electric field reduction in large chamber regions increases the electron attachment coefficient, causing a progressive decrease in the FEF.
Charge Collection Efficiency (CCE): The model accurately reproduces the drop in CCE observed in reference studies across various bias voltages and DPPs.
Primary Mechanism of CCE Loss: The simulations indicate that the reduction in CCE under UHDR is not primarily driven by an increased coexistence time of positive and negative ions (which would enhance recombination via time). Instead, the reduction is mainly driven by the decrease in the FEF. The space-charge-induced electric field distortion lowers the local field strength, increasing the probability of electron attachment to oxygen molecules. This generates a higher density of negative ions, which subsequently enhances ion–ion recombination rates.

Significance and Claims
The paper claims that the developed framework provides a robust, flexible, and self-consistent tool for investigating recombination phenomena in ionisation chambers under FLASH conditions. By demonstrating that CCE reduction is largely governed by the evolution of the FEF (driven by field-dependent attachment), the authors suggest that the complex problem of UHDR dosimetry may be simplified. This finding opens the possibility for developing improved analytical models or real-time correction methods for PPICs, potentially moving beyond the limitations of current Boag-based formalisms. The authors explicitly state that these mechanisms are now integrated into the open-source Garfield++ software, available for future research and dosimetry model development.