MADMAX: Axion, Solar, Collider & LLM

• MADMAX is a polysemous designation covering a dielectric haloscope for axion dark matter, a solar image-enhancement operator, a collider significance tool, and an LLM red-teaming framework.
• In axion dark matter research, MADMAX employs a stack of dielectric disks in a strong magnetic field to boost and tune axion-induced electromagnetic signals with precise mechanical and electromagnetic controls.
• Across its varied applications, MADMAX leverages directional filtering in solar imaging, likelihood-based significance in collider phenomenology, and modular attack strategies in LLM security to optimize signal extraction and discovery.

MADMAX is a technical designation used for several unrelated constructs across contemporary research literature. The name most prominently denotes the MAgnetized Disk and Mirror Axion eXperiment, a dielectric-haloscope program for the direct detection of dark-matter axions in the high-mass regime (Majorovits, 2017). In solar image processing, Madmax or the OMC operator denotes a direction-adaptive spatial filter built from maxima of convexities for tracing thin chromospheric structures in Hinode/SOT Ca II H filtergrams (Tavabi et al., 2011). In collider phenomenology, MadMax denotes a MadGraph5 add-on for identifying the phase-space regions that carry maximum discovery significance (Plehn et al., 2013). A distinct hyphenated acronym, MAD-MAX, denotes “Modular And Diverse Malicious Attack MiXtures” for automated LLM red teaming (Schoepf et al., 8 Mar 2025).

1. Principal meanings and nomenclature

The shared label “MADMAX” is therefore polysemous. In the astroparticle literature, the term usually refers to a dielectric haloscope for axion dark matter; in solar physics it denotes an image-enhancement operator; in collider analysis it denotes a likelihood-based significance tool; and in LLM security the hyphenated form MAD-MAX denotes a jailbreak-generation framework.

Domain	Expansion or form	Function
Axion dark matter	MAgnetized Disk/Disc and Mirror Axion eXperiment	Dielectric haloscope with dielectric disks in front of a mirror
Solar image processing	Madmax / OMC operator	Directional maximum-convexity filter for thin bright solar structures
Collider phenomenology	MadMax	Parton-level tool for maximum-significance phase-space analysis
LLM security	MAD-MAX	Automated black-box red-teaming method

The axion literature itself contains acronymic variants. The standard expansion is “MAgnetized Disk and Mirror Axion eXperiment” or “MAgnetized Disc and Mirror Axion eXperiment”, while the foundations paper also uses “MAgnetized Dielectric Mirror Axion eXperiment” (Majorovits, 2017, Knirck, 2017). This variation is nomenclatural rather than conceptual: the cited papers describe the same dielectric-haloscope program.

2. Dielectric-haloscope MADMAX for axion dark matter

In axion physics, MADMAX is a proposed direct-detection experiment aimed at the QCD axion dark-matter region above the reach of conventional microwave cavity haloscopes, especially the mass range $40$–$400\,\mu\mathrm{eV}$, corresponding roughly to $10$–$100$ GHz (Majorovits, 2017). The motivation is twofold: axions arise from the Peccei–Quinn solution to the strong-CP problem, and they are also compelling cold dark-matter candidates. The high-mass window is especially relevant to post-inflationary Peccei–Quinn scenarios, for which masses around $100\,\mu\mathrm{eV}$ are repeatedly emphasized as well motivated (Collaboration et al., 2019).

The experimental principle is the dielectric haloscope. A mirror is placed on one side of a stack of parallel dielectric disks inside a strong magnetic field parallel to the disk surfaces. At each boundary between materials with different dielectric constants, the axion-induced electric field is discontinuous, and electromagnetic waves are emitted to satisfy Maxwell boundary conditions. By choosing the disk spacings appropriately, these emissions interfere constructively and can also form resonant structures, producing a large enhancement of the emitted power (Knirck, 2017).

This enhancement is encoded in the boost factor,

$\beta^2 = \frac{P_{\rm sig}}{P_0},$

where $P_{\rm sig}$ is the power emitted by the full booster and $P_0$ is the power from a mirror-only configuration (Garcia et al., 2024). The central operational degree of freedom is the set of disk separations: changing them tunes both the center frequency and the bandwidth of the boost curve. The literature emphasizes an area law,

$\int \beta^2\, d\nu_a = \text{const.},$

so peak boost and bandwidth are traded against one another rather than independently optimized (Collaboration et al., 2019).

The baseline full-scale concept uses about 80 dielectric disks, a $\sim 10$ T dipole magnet, and an aperture of order $400\,\mu\mathrm{eV}$0 (Collaboration et al., 2019). The design goal is to reach $400\,\mu\mathrm{eV}$1 over bandwidths of order $400\,\mu\mathrm{eV}$2–$400\,\mu\mathrm{eV}$3 MHz, with cryogenic microwave radiometry based on HEMT preamplification, heterodyne down-conversion, and FFT-based spectral analysis (Majorovits, 2017, Beurthey et al., 2020). A major conceptual advantage over resonant cavities is that the conversion volume is described as nearly axion-mass independent, so sensitivity can be improved by increasing the transverse area without the severe volume penalty that affects high-frequency cavity haloscopes (Ivanov et al., 5 Mar 2026).

3. Prototype program and first dark-matter searches

The prototype program was built to validate the dielectric-haloscope principle experimentally. A first proof-of-principle booster consisted of a copper mirror and up to five sapphire disks. Its electromagnetic response was characterized through reflectivity and group-delay measurements, and the reported conclusion was that the setup successfully realizes the predicted one-dimensional electromagnetic response for a small-scale dielectric haloscope booster (Egge et al., 2020). The same paper reports percent-level repeatability in the resulting boost factor and establishes group delay as the practical tuning observable.

Subsequent prototype development split into closed and open booster geometries. The closed prototype used three sapphire disks of 20 cm diameter in a casing and was operated in the 1.6 T Morpurgo dipole magnet at CERN; the open prototype used three 30 cm disks and enabled an in situ bead-pull determination of the boost factor (Pralavorio, 2024). The closed booster achieved peak values around $400\,\mu\mathrm{eV}$4 with about 15% uncertainty, while the open booster reached $400\,\mu\mathrm{eV}$5, again with roughly 15% uncertainty (Pralavorio, 2024).

Low-temperature operation was enabled by a dedicated non-magnetic G-10 glass-fiber cryostat. Using continuous circulation of gaseous helium, the MADMAX prototype was cooled reproducibly to temperatures below 10 K for more than 24 hours, including a 29 hour run below $400\,\mu\mathrm{eV}$6 K in the Morpurgo magnet. This made possible, for the first time, both calibration of the booster response at low temperature and a dark matter axion search in a magnetic field at low temperature (Kreikemeyer-Lorenzo et al., 2024).

The first physics result from a MADMAX prototype was a dark photon dark matter search with a three-sapphire-disk plus mirror booster. The scanned mass range was

$400\,\mu\mathrm{eV}$7

No signal was observed. Assuming unpolarized dark photon dark matter with local density $400\,\mu\mathrm{eV}$8, the experiment excluded

$400\,\mu\mathrm{eV}$9

over the full scanned mass range and

$10$0

at $10$1 at 95% CL (Egge et al., 2024).

The first axion dark matter search with a dielectric haloscope followed with the CB200 closed booster in the Morpurgo magnet. The search covered the mass ranges 76.56 to 76.82 $10$2 and 79.31 to 79.53 $10$3 over 14.5 days of data collection. No axion signal was detected, and the experiment set a 95% CL upper limit on the axion-photon coupling down to

$10$4

surpassing previous constraints in the targeted mass windows under the stated assumptions (Garcia et al., 2024). The analysis framework for this first axion search was subsequently formalized in a closed-haloscope sensitivity model that includes geometric imperfections and receiver noise (Ivanov et al., 5 Mar 2026).

4. Electromagnetic modeling, tolerances, and hardware realization

MADMAX required a progression from 1D transfer-matrix descriptions to full-wave treatments. An early finite-element framework solved the Maxwell-axion equations for arbitrary geometries and materials, and was benchmarked on a circular perfectly conducting surface, a single dielectric disk, and a partly dielectric-filled waveguide (Schütte-Engel, 2018). These studies made explicit that finite-size devices exhibit diffraction and near-field effects absent from idealized 1D infinite-plane models.

A major refinement came from 3D calculations for dielectric haloscopes with finite-diameter disks. For ideal systems with perfectly flat, parallel and isotropic dielectric disks of finite diameter, the emitted power is reduced by up to $10$5 relative to earlier 1D calculations because of a geometrical form factor, not because of absorption or diffraction loss (Knirck et al., 2021). The same study found that the outgoing field is beam-like rather than plane-wave-like and that the fundamental mode matches a Gaussian beam with a frequency-independent $10$6 matching ratio and waist $10$7, where $10$8 is the disk diameter (Knirck et al., 2021). This directly constrains the quasi-optical readout.

The 3D analysis also derived concrete design requirements for a benchmark configuration with $10$9 bandwidth around $100$0. To keep the emitted power within 20% of the ideal 3D case, the cited tolerances are: maximum tilt $100$1 divided by the disk diameter, disk planarity $100$2 min-to-max or better, and surface roughness $100$3 min-to-max (Knirck et al., 2021). Realistic halo velocities of $100$4 and magnetic-field inhomogeneities of order 10% were found to have negligible impact on sensitivity for the studied benchmark (Knirck et al., 2021).

Because iterative optimization over many disk positions is computationally costly, surrogate modeling has also been studied. A proof-of-principle deep-learning approach trained a 1D convolutional network on 169,260 dielectric-haloscope configurations, each sampled at 300 frequency points, to predict the boost factor from the disk configuration and frequency (Jung et al., 2022). The network generally reproduced peak position and bandwidth well but did not fully capture fine peak substructure; in the baseline training, 89% of predictions achieved a boost score below about 0.3, and the authors present the method as a surrogate for optimization rather than a replacement for detailed electromagnetic modeling (Jung et al., 2022).

Mechanical realization was pursued in parallel. A custom piezo-electric stick-slip linear stage was qualified down to 4.5 K and up to 5.3 T, with performance considered sufficient for MADMAX disc positioning (Garutti et al., 2023). The OB200 demonstrator then provided the first mechanical realization of a tunable dielectric haloscope. It used one movable 200 mm sapphire disk, three piezoelectric motors, laser-interferometric feedback, and closed-loop control. Tested in magnetic fields up to 1.6 T and at cryogenic temperatures down to 35 K, it achieved target positioning better than 5 $100$5, motor agreement within a few micrometers, and final stability better than 1 $100$6, matching the quoted MADMAX mechanical requirements (Collaboration et al., 2024).

For the analysis of the first axion search, a simplified but realistic closed-booster model treated the CB200 system as a transmission-line network dominated by the TE$100$7 mode and included effective geometric imperfections, receiver noise, and impedance mismatch (Ivanov et al., 5 Mar 2026). In this description the transverse overlap factor was

$100$8

and fitted boost factors reached approximately

$100$9

with combined relative uncertainty of about 9% to 14%, depending on frequency (Ivanov et al., 5 Mar 2026). This suggests that experimentally useful sensitivity estimates can be obtained without resorting to full 3D simulation for every fit iteration.

5. Madmax as a solar image-enhancement operator

In solar physics, Madmax denotes a spatial image-enhancement filter, also called the OMC operator for Operator Maximum Convexities, designed to make very thin, bright, hair-like structures stand out against noisy backgrounds in solar images (Tavabi et al., 2011). The 2011 study applies it mainly to chromospheric structures such as spicules and thin jets in Hinode/SOT Ca II H filtergrams, with the stated aim of tracing bright hair-like features in observations polluted by noise of different origins (Tavabi et al., 2011).

The operator examines each pixel in multiple directions and measures a second-derivative-like convexity in each direction. The final response retains the direction in which the absolute value is maximal. In the notation given in the paper, the image is $100\,\mu\mathrm{eV}$0, and the multiscale operator is written

$100\,\mu\mathrm{eV}$1

with

$100\,\mu\mathrm{eV}$2

Here $100\,\mu\mathrm{eV}$3 denotes averaging every two rows and columns, $100\,\mu\mathrm{eV}$4 and $100\,\mu\mathrm{eV}$5 are expansion operators by bilinear interpolation with scale factors 2 and 4, and $100\,\mu\mathrm{eV}$6 are user-chosen weights (Tavabi et al., 2011).

The paper emphasizes several formal properties. The operator uses the second derivative in the optimally selected direction for which its absolute value has a maximum value; it enhances positive intensity signals superposed on noise; it is shift-invariant and non-idempotent; it is explicitly not a morphological filter; and it is described as less sensitive to additive noise (Tavabi et al., 2011). Directional sampling can use 4, 8, or 16 directions. The cited experiments report that 4 directions are enough to detect major edges but often lose fine structures, 8 directions recover most threads well, and 16 directions improve continuity further while increasing computational cost (Tavabi et al., 2011).

Applied to real Hinode data, Madmax is reported to reveal long parallel threads inside jets, crossing fine threads, the feet of spicules near the limb, and near-limb structures that are weak or nearly invisible in raw filtergrams (Tavabi et al., 2011). In this usage, “MADMAX” is therefore a direction-adaptive, second-derivative-based enhancement operator for curvilinear pattern recognition rather than a dark-matter experiment.

6. Other technical uses of the name

In collider phenomenology, MadMax is a fast, parton-level tool developed as an add-on to MadGraph5 for determining which regions of phase space carry the statistical power of a search (Plehn et al., 2013). The method is based on the Neyman–Pearson lemma and computes the statistically optimal significance from matrix-element information. The paper constructs a likelihood-ratio map over phase-space points $100\,\mu\mathrm{eV}$7,

$100\,\mu\mathrm{eV}$8

then obtains the distributions of $100\,\mu\mathrm{eV}$9 under background and signal-plus-background hypotheses to define the expected Gaussian-equivalent significance (Plehn et al., 2013). Applications to boosted $\beta^2 = \frac{P_{\rm sig}}{P_0},$0 and $\beta^2 = \frac{P_{\rm sig}}{P_0},$1 at 14 TeV showed that the most promising Higgs-boost regime is not the ultra-boosted tail but the moderate window

$\beta^2 = \frac{P_{\rm sig}}{P_0},$2

with top-tagging performance in the $\beta^2 = \frac{P_{\rm sig}}{P_0},$3 GeV range particularly relevant for $\beta^2 = \frac{P_{\rm sig}}{P_0},$4 (Plehn et al., 2013).

A distinct hyphenated acronym, MAD-MAX, was introduced in 2025 for Modular And Diverse Malicious Attack MiXtures in automated LLM red teaming (Schoepf et al., 8 Mar 2025). This method maintains an attack-style library, clusters styles, selects promising clusters for a malicious goal, combines styles across clusters, merges promising attacks across branches, and applies a cosine-similarity filter with threshold 0.95 before expensive target-model queries (Schoepf et al., 8 Mar 2025). On the reported benchmarks against GPT-4o and Gemini-Pro, the abstract states that MAD-MAX jailbreaks 97% of malicious goals compared with 66% for Tree of Attacks with Pruning, while using 10.9 average queries to the target LLM compared with 23.3 for TAP (Schoepf et al., 8 Mar 2025).

These usages are methodologically unrelated. The only commonality is the name: in the literature provided, “MADMAX” labels a dielectric-haloscope axion program, a solar image filter, a collider-significance tool, and, in hyphenated form, an LLM red-teaming framework.