FAERIE Simulation Framework

• FAERIE is a hybrid Monte Carlo framework that models both in-air geomagnetic and in-ice Askaryan radio emissions from cosmic ray air showers using established codes like CORSIKA, CoREAS, and GEANT4.
• It captures distinct signal features such as bean-shaped and annular lateral patterns, timing differences, polarization, and spectral peaks that are key for experimental interpretation.
• FAERIE supports calibration and background discrimination in deep-antenna neutrino detectors while also highlighting computational challenges and modeling limitations.

Searching arXiv for FAERIE and closely related papers to ground the article. FAERIE is the Framework for the simulation of Air shower Emission of Radio for In-Ice Experiments, a hybrid Monte Carlo framework developed to model radio signals from cosmic-ray-induced air showers as observed by deep antennas embedded in polar ice. Its defining feature is a mixed-medium treatment in which a downward-going cosmic ray can emit radio in the atmosphere, send part of that radiation through the air–ice boundary, deposit shower particles into the ice, and generate a secondary in-ice cascade whose radio emission is then propagated to buried receivers. In the arXiv literature, FAERIE is used primarily in the context of ultra-high-energy neutrino experiments such as ARA and RNO-G, where cosmic rays are simultaneously a dominant background, a calibration source, and a proof-of-principle target for in-ice radio detection (Chiche et al., 2024).

1. Experimental setting and scientific role

FAERIE addresses a problem specific to radio neutrino detectors with deep in-ice antennas. These instruments are designed to detect Askaryan radio emission from neutrino-induced cascades in ice, but they are also exposed to radio signals from cosmic-ray showers. Two classes of cosmic-ray signal are relevant. The first is in-air cascade emission transmitted into ice: the extensive air shower radiates in the atmosphere and part of that radiation refracts through the air–ice boundary. The second is in-ice cascade emission: sufficiently energetic shower particles survive to the surface, enter the ice, and initiate a secondary cascade that radiates in the denser medium. FAERIE was introduced precisely to model both channels within a single event description, rather than treating atmospheric radio emission and in-ice Askaryan emission as separate simulation problems (Chiche et al., 2024).

This mixed-medium capability matters because the cosmic-ray flux is much larger than the neutrino flux, so cosmic rays are expected to appear earlier and more often than neutrinos in deep-antenna arrays. The same signals therefore have two opposite experimental meanings. They are a major background to neutrino searches, but they are also a valuable calibration source and a proof-of-principle target for validating the in-ice radio detection chain. A recurring conclusion of the FAERIE-based studies is that the observed morphology depends strongly on shower geometry: vertical showers can produce both transmitted in-air and secondary in-ice signals, whereas inclined showers are increasingly dominated by the transmitted in-air component (Chiche et al., 2024).

2. Hybrid simulation architecture

FAERIE is described as a hybrid framework that integrates several established codes. For the atmospheric cascade it uses CORSIKA 7.7500. For radio emission from the air shower it uses CoREAS, specifically a modified version of CoREAS that evaluates electric fields at antenna positions in the ice. For the shower core entering the ice and the subsequent in-ice cascade it uses GEANT4 10.5. In one conference description, the in-ice radio signal is generated with a code originating from the T-510 experiment; in the ARA double-pulse analysis, the emphasis is instead on the modified CoREAS, GEANT4, and detector-level coupling. Across these descriptions, the common point is that FAERIE is not only an air-shower radio code and not only an in-ice Askaryan code: it is a full air-to-ice simulation chain (Ali et al., 17 Sep 2025).

Both the atmospheric and in-ice radio calculations are based on the endpoint formalism, written in one FAERIE description as

$E_{\pm}(\Vec{x}, t) = \pm \frac{1}{\Delta t} \frac{q}{c} \left( \frac{\widehat{r} \times [\widehat{r} \times \Vec{\beta}^{\star}]} {|1-n \Vec{\beta}^{\star} \cdot \widehat{r}|R} \right),$

with $q$ the particle charge, $\Delta t$ the track duration, $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$, $n$ the refractive index, $\widehat{r}$ the source–observer direction, and $R$ the source–observer distance. In ice, $R$ is reinterpreted as the geometrical path length obtained from ray tracing rather than a straight Euclidean distance. FAERIE therefore couples particle-level tracking, radio-emission calculation, and refractive propagation in a single formalism (Chiche et al., 2024).

The framework outputs time-domain electric-field traces at antenna positions. In the ARA analyses, these traces are passed into AraSim, which applies the detector response and produces time-domain voltage traces comparable to measured ARA waveforms. That interface is central in practice because the experimental observables are de-dispersed voltage waveforms in sixteen receiver channels, not idealized electric fields. The workflow thereby extends from shower physics through waveform formation to reconstruction-level comparison (Ali et al., 17 Sep 2025).

3. Emission channels and signal phenomenology

FAERIE models two physically distinct radio-emission channels. The first is the in-air geomagnetic emission, generated by the deflection of electrons and positrons in the Earth’s magnetic field and associated with a time-varying transverse current. At South Pole, where the geomagnetic field is nearly vertical, this emission is expected to be predominantly horizontally polarized for inclined showers when projected onto ARA antennas. One ARA proceedings paper notes that geomagnetic emission accounts for roughly 90% of the total observed in-air radio signal. The second channel is the in-ice Askaryan emission, generated after the shower core enters the upper ice and develops a net negative charge excess that radiates coherently in a Cherenkov-like cone. In the ARA geometry this Askaryan emission can project into both HPol and VPol channels (Ali et al., 17 Sep 2025).

The two components exhibit distinct footprint morphologies. In FAERIE simulations, the in-air component produces the familiar bean-shaped lateral pattern that reflects interference between geomagnetic and charge-excess emission. The in-ice component is more annular or ring-like, reflecting the in-ice Cherenkov geometry and the predominance of charge-excess emission in the dense medium. For vertical showers at moderate depth the two components can cover similar lateral scales because the in-air source is farther away, while for inclined showers the total field becomes very similar to the in-air component alone because too few energetic particles survive to create a strong in-ice cascade (Chiche et al., 2024).

The later characterization studies extend this phenomenology to timing, polarization, spectrum, and radiation energy. For each antenna, FAERIE can output the three field components separately for the in-air and in-ice parts,

$$E_x^{\rm air}(t),\; E_y^{\rm air}(t),\; E_z^{\rm air}(t),$$

and

$$E_x^{\rm ice}(t),\; E_y^{\rm ice}(t),\; E_z^{\rm ice}(t).$$

The corresponding energy fluence is defined as

$q$0

with total fluence $q$1, and the radiation energy over an observer layer is

$q$2

These studies report that the in-air component has a relatively narrow spectrum with a peak below about $q$3, whereas the in-ice component has a broader spectrum with a peak around $q$4. They also find that many antennas can observe a double pulse, with the in-air pulse arriving first and the in-ice pulse arriving later (Chiche et al., 10 Jan 2026).

4. Propagation, firn, and refractive geometry

A central ingredient of FAERIE is that neither the atmosphere nor the firn–ice column is treated as homogeneous. In ice the refractive index is modeled as

$q$5

where $q$6 is the depth below the surface. For South Pole ice, one FAERIE description gives

$q$7

For Greenland ice, a double-exponential form is used because firn densification changes around $q$8: for $q$9,

$\Delta t$0

and for $\Delta t$1,

$\Delta t$2

These profiles determine ray bending, arrival times, and the mapping between emission geometry and deep-antenna footprints (Chiche et al., 2024).

At the air–ice boundary, propagation follows Snell’s law,

$\Delta t$3

FAERIE includes ray tracing through the refractive gradient and, for emitters and receivers in the ice, finds two ray solutions: a direct path and a path reflected at the air/ice boundary. This is particularly relevant for the in-ice cascade, whose radio signal can reach a buried antenna either directly or after reflection. A broader geometrical point emphasized in the FAERIE literature is that the Cherenkov angle is much larger in ice than in air, qualitatively

$\Delta t$4

which helps explain why the in-ice component forms a compact annular structure while the in-air component produces a broader transmitted footprint (Chiche et al., 2024).

The characterization studies then exploit this geometry operationally. For Greenland-like simulations, they use a 3D antenna grid of 4704 antennas at depths $\Delta t$5, $\Delta t$6, and $\Delta t$7, with the deeper layers shifted to remain centered on the footprint after refraction. They also report representative Cherenkov-ring distances for a $\Delta t$8 eV, $\Delta t$9 shower of about

$\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$0

and note that the in-ice footprint is generally confined within about $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$1 m (Chiche et al., 10 Jan 2026).

5. Reconstruction-level use in the ARA double-pulse candidate

FAERIE became central to the interpretation of an isolated double-pulse cosmic-ray candidate recorded by ARA Station-2. In that event, several de-dispersed channels showed two impulsive excursions separated by tens of nanoseconds. Clear double pulses were reported in channels 0, 1, 4, 5, 7, 9, 12, and 13, and the first pulse was visible in nearly all channels except 6 and 8. A key empirical observation was that the time separation between the two pulses was not the same in every channel, which disfavors a single source with an intrinsic universal double pulse and instead suggests two distinct emission vertices with different propagation paths to each antenna (Ali et al., 17 Sep 2025).

The analysis workflow separated the two pulses and reconstructed each independently with the standard ARA interferometric reconstruction algorithm, cross-checked with AraVertex. The first pulse was interpreted as geomagnetic emission in air and the second as Askaryan emission in ice. From the independently reconstructed directions, the authors inferred a preferred shower geometry using Snell’s-law reasoning for the first pulse and Cherenkov-based geometry for the second. The assumptions used in the proceedings text were explicit: bulk ice refractive index $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$2, in-ice shower maximum depth $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$3, and Cherenkov angle $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$4. For the forward simulation they assumed a proton primary with energy fixed to $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$5 PeV, not as a unique measurement of the event energy but as a working hypothesis for topology validation (Ali et al., 17 Sep 2025).

FAERIE then generated time-domain electric-field traces for that geometry, AraSim converted them into detector-level voltage waveforms, and the same reconstruction procedures used on data were applied to the simulation. The proceedings study reports that the simulated event reproduced the channel-by-channel relative signal arrival times of the recorded event and that the reconstructed vertices of the simulated geomagnetic and Askaryan components agreed with those of the first and second observed pulses. A later ARA preprint describes this agreement more quantitatively, stating that reconstructed vertex directions from simulation and data agree with residuals smaller than $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$6 and that simulated channel-dependent delays match the observed delays with residuals less than 5 ns across channels (Ali et al., 6 Jan 2026).

Polarization behavior provided supporting, though not decisive, evidence. The pulse amplitude per channel was defined as

$\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$7

where $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$8 is the peak of the Hilbert envelope and $\Vec{\beta}^{\star}=\Vec{v}^{\star}/c$9 is estimated from a pre-signal region. Summing over channels, the event gave an HPol/VPol power ratio of 1.513 for the first pulse and 0.922 for the second pulse, consistent with the expectation that the first pulse is geomagnetic and the second Askaryan. At the same time, the ARA analyses are explicit that the validation is not based on a formal likelihood, $n$0, or Bayesian posterior. The procedure identifies a preferred event topology from reconstruction outputs and then checks that FAERIE-generated showers at that topology reproduce the observed directional and timing structure (Ali et al., 17 Sep 2025).

6. Calibration, veto design, and present limitations

Beyond the ARA double-pulse candidate, FAERIE is used to derive practical observables for cosmic-ray identification and cosmic-ray/neutrino discrimination. The recurring handles are surface activity, bean-shaped lateral distributions, geomagnetic polarization, double-pulse time traces, depth-dependent delays, and, for more vertical events, evidence of a second in-ice component. In Greenland-like studies, the delay between a surface antenna and a deep antenna at $n$1 was roughly estimated as

$n$2

assuming $n$3, and the double-pulse rate was defined as

$n$4

At $n$5 eV and $n$6 m depth, one characterization study reports that the double-pulse fraction reaches up to about 40% of triggered events in the $n$7-channel, with the rate peaking near $n$8 (Chiche et al., 10 Jan 2026).

Polarization is presented as one of the sharpest discriminants. The field decomposition is

$n$9

and the corresponding radiation-energy ratio $\widehat{r}$0 differs strongly between the two signal classes. For the in-air component this ratio is very large, while for the in-ice component it is much smaller; one FAERIE study states that the difference reaches more than two orders of magnitude at the radiation-energy level. This suggests a direct route to neutrino discrimination in the zenith range where neutrino-induced events are expected to be Askaryan-like but cosmic-ray events are increasingly in-air dominated (Chiche et al., 10 Jan 2026).

The literature is also explicit about current limitations. FAERIE is computationally expensive: one characterization paper reports $\widehat{r}$1 per simulation, which is why some libraries contain only one shower per energy/zenith bin and treat shower-to-shower fluctuations with a much smaller auxiliary sample. Several studies use only proton primaries, only one azimuth, and a flat-Earth approximation that limits zenith angles to about $\widehat{r}$2. Some characterization results are presented only at the electric-field level, without full detector response, gain, digitization, or realistic noise. In the ARA event interpretation, amplitude matching is not emphasized because shower-to-shower fluctuations are described as of order unity, the Askaryan component is highly collimated at $\widehat{r}$3, and the effect of known density variations in the upper ice layers has not yet been evaluated. The broader implication is that FAERIE already provides a physically realistic bridge between cosmic-ray radio phenomenology and in-ice detector analysis, but that its present use remains strongest in timing, directional reconstruction, and mixed-medium topology testing rather than in precision amplitude fitting (Ali et al., 17 Sep 2025).