---
title: FAERIE Simulation Framework
url: https://www.emergentmind.com/topics/faerie
type: topic
---

# FAERIE Simulation Framework

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 [2409.02185].

## 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 [2409.02185].

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 [2409.02185].

## 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** [2509.14407].

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 [2409.02185].

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 [2509.14407].

## 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 [2509.14407].

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 [2409.02185].

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
$$
f_{x,y,z}(x,y) = \epsilon_0 c\int_0^{t}E_{x,y,z}^{2}(t,x,y)\,{\rm d}t,
$$
with total fluence \(f_{\rm tot}=f_x+f_y+f_z\), and the radiation energy over an observer layer is
$$
E_{\rm rad} = \int_{x_{\rm min}}^{x_{\rm max}}\int_{y_{\rm min}}^{y_{\rm max}} f(x,y)\,{\rm d}x\,{\rm d}y.
$$
These studies report that the **in-air component** has a relatively narrow spectrum with a peak below about \(100\,{\rm MHz}\), whereas the **in-ice component** has a broader spectrum with a peak around \(\sim 400\,{\rm MHz}\). 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 [2601.06417].

## 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
$$
n(z) = A - B \exp(-C|z|),
$$
where \(|z|\) is the depth below the surface. For South Pole ice, one FAERIE description gives
$$
A=1.775,\quad B=0.43,\quad C=0.0132.
$$
For Greenland ice, a **double-exponential** form is used because firn densification changes around \(|z|=14.9\,\mathrm{m}\):
for \(|z|<14.9\,\mathrm{m}\),
$$
A=1.775,\quad B=0.5019,\quad C=0.03247,
$$
and for \(|z|>14.9\,\mathrm{m}\),
$$
A=1.775,\quad B=0.448023,\quad C=0.02469.
$$
These profiles determine ray bending, arrival times, and the mapping between emission geometry and deep-antenna footprints [2409.02185].

At the air–ice boundary, propagation follows **Snell’s law**,
$$
n_1 \sin i_1 = n_2 \sin i_2.
$$
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
$$
\theta_c^{\rm air}\sim 1^\circ,\qquad \theta_c^{\rm ice}\sim 50^\circ,
$$
which helps explain why the in-ice component forms a compact annular structure while the in-air component produces a broader transmitted footprint [2409.02185].

The characterization studies then exploit this geometry operationally. For Greenland-like simulations, they use a **3D antenna grid of 4704 antennas** at depths \(0\ {\rm m}\), \(60\ {\rm m}\), and \(100\ {\rm m}\), with the deeper layers shifted to remain centered on the footprint after refraction. They also report representative Cherenkov-ring distances for a \(10^{17.5}\) eV, \(34^\circ\) shower of about
$$
r_{\rm cer}^{\rm air}\sim 45\,{\rm m},\qquad r_{\rm cer}^{\rm ice}\sim 145\,{\rm m},
$$
and note that the in-ice footprint is generally confined within about \(\pm 200\) m [2601.06417].

## 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 [2509.14407].

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 \(n_{\rm ice}=1.78\), in-ice shower maximum depth \(d_{\rm max}=6\,\mathrm{m}\), and Cherenkov angle \(\theta_c=43^\circ\). For the forward simulation they assumed a **proton primary** with energy fixed to **\(10\) PeV**, not as a unique measurement of the event energy but as a working hypothesis for topology validation [2509.14407].

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 \(2^\circ\)** and that simulated channel-dependent delays match the observed delays with **residuals less than 5 ns** across channels [2601.02718].

Polarization behavior provided supporting, though not decisive, evidence. The pulse amplitude per channel was defined as
$$
A_{\rm pulse} = \sqrt{A_{env}^2-V_{\rm rms}^2},
$$
where \(A_{env}\) is the peak of the Hilbert envelope and \(V_{\rm rms}\) 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, \(\chi^2\), 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 [2509.14407].

## 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 \(|z|=100\,\mathrm{m}\) was roughly estimated as
$$
\Delta t \sim 100\,\mathrm{m}\times \frac{n_{\rm ice}}{c} \sim 470\,\mathrm{ns},
$$
assuming \(n_{\rm ice}=1.4\), and the double-pulse rate was defined as
$$
r_{\rm double} = \frac{N_{\rm double}}{N_{\rm trig}}.
$$
At \(10^{17.5}\) eV and \(100\) m depth, one characterization study reports that the double-pulse fraction reaches up to about **40%** of triggered events in the \(y\)-channel, with the rate peaking near \(\theta \sim 34^\circ\) [2601.06417].

Polarization is presented as one of the sharpest discriminants. The field decomposition is
$$
E^{\rm Vpol}=E_z,\qquad E^{\rm Hpol}=\sqrt{E_x^2+E_y^2},
$$
and the corresponding radiation-energy ratio \(E_{\rm rad}^{\rm Hpol}/E_{\rm rad}^{\rm Vpol}\) 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 [2601.06417].

The literature is also explicit about current limitations. FAERIE is computationally expensive: one characterization paper reports **\(\sim 10^4-10^5\ {\rm CPU\ hours}\) 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 \(50^\circ\). 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 **\(\sim 1^\circ\)**, 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 [2509.14407].

Source: https://www.emergentmind.com/topics/faerie