What this calculator does
An axion haloscope is a resonant dark matter experiment: a strong magnetic field fills a microwave cavity, and if axions make up some of the Milky Way’s dark matter, a tiny fraction can convert into photons at a frequency set by the axion mass. The signal is expected to be extraordinarily small in real experiments, which is why researchers care so much about magnet strength, cavity design, overlap between the field and the resonant mode, and the quality factor that describes how sharply the cavity stores energy near resonance.
This calculator keeps that basic idea but implements it as a compact scaling model. You enter an axion mass, a local dark matter density, an axion-photon coupling, the magnetic field strength, the cavity volume, the mode form factor, and the quality factor. The page then combines them with the built-in formula and reports an estimated signal power in watts. Because the JavaScript model on this page is intentionally simple, the result is most useful for scenario comparison and intuition building: it shows which knobs matter most and how the estimate changes when you strengthen the field, enlarge the cavity, improve overlap, or assume a different mass or coupling.
If you are studying haloscopes for the first time, the most important takeaway is that this is a resonance problem. A haloscope is strongest when the cavity mode, magnetic field geometry, and axion parameters all work together. This page cannot replace a full detector sensitivity study, but it can help you see the scaling clearly before you move on to more detailed analyses.
How to think about each input
Each form field represents a different piece of the haloscope picture, and each one moves the result for a different reason. The labels in the form give the units, but it helps to understand the meaning behind those numbers before you type anything in.
- Axion mass (µeV) sets the resonance scale. In this page’s formula it appears in the denominator, so smaller masses increase the estimated power and larger masses reduce it. In the real physics story, mass also determines the corresponding photon frequency you would tune the cavity to.
- Local density (GeV/cm³) is the assumed dark matter density near Earth. If the local axion density is larger, there is simply more dark matter available to source a signal, so the estimate rises linearly with this input.
- Coupling gₐγ (10⁻¹⁶ GeV⁻¹) measures how strongly axions interact with photons. This term is squared in the page’s model, which means it is a high-leverage assumption. Doubling the coupling raises the estimate by a factor of four.
- Magnetic field B (T) is the static field inside the haloscope magnet. It is also squared. That quadratic dependence is one reason flagship haloscope concepts revolve around large superconducting magnets rather than modest laboratory fields.
- Cavity volume V (m³) tells the model how much resonant space participates in the conversion. All else equal, a larger volume raises the signal linearly because more field-filled cavity region contributes.
- Mode form factor C (0-1) says how well the chosen resonant mode overlaps the magnetic field and the expected signal pattern. A value near 1 means excellent overlap; a value near 0 means the cavity mode is poorly matched and little power is collected.
- Quality factor Q summarizes how narrow and resonant the cavity is. In this simplified calculator, higher Q means greater power because the cavity stores energy more effectively near resonance. In a full experiment you would usually distinguish unloaded and loaded Q, receiver coupling, and scan bandwidth, but the form here keeps the high-level dependency visible.
The defaults in the form are example values chosen to make the page easy to test. They are not claims about the best axion model or the design point of any specific experiment. A good workflow is to begin with a baseline scenario, compute the result, and then change only one input at a time. That isolates sensitivity: you can see whether the output reacts linearly, quadratically, or hardly at all.
Formula and scaling
The calculator preserves the page’s original JavaScript behavior. After converting the mass and density inputs into the internal units used by the script, it computes power with a direct proportional model. Written in symbolic form, the relationship used by the page is:
That expression is the reason some inputs dominate your intuition. Density, volume, form factor, and quality factor are linear multipliers. If you increase any one of them by 10% while holding the others constant, the estimated power also rises by 10%. Coupling and magnetic field are squared, so they act more dramatically. A 10% rise in magnetic field gives roughly a 21% rise in the estimate because B2 changes, not just B. Mass enters inversely, so lighter axions produce a larger estimate in this model.
It is also helpful to keep one caution in mind: the page’s equation is a compact scaling law, not a full experimental forecast. Real haloscope calculations may include additional constants, electromagnetic normalization choices, loaded quality factor, cavity-receiver coupling, scan strategy, bandwidth matching, temperature-dependent noise, and losses in the readout chain. None of those extra ingredients change the basic lesson that stronger magnets, better mode overlap, larger effective volume, and sharper resonance are desirable. They simply matter when you move from “how does it scale?” to “what exact power should an instrument measure?”
The next two MathML blocks are kept exactly as part of the page’s broader sensitivity intuition. They are generic, but they are still useful as reminders that the result is a function of several variables and that some models combine weighted contributions from more than one source.
For this calculator, the important practical question is not whether the notation looks advanced. It is whether your chosen inputs tell a coherent experimental story. If you assume an ambitious magnet and a very high Q, do the cavity volume and form factor still look plausible for that design? If you use a benchmark coupling from one axion model family, does the mass range belong to the same benchmark study? Matching assumptions is just as important as entering the right units.
Worked example using the form defaults
Suppose you use these example inputs: axion mass 5.70 µeV, local density 0.45 GeV/cm³, coupling 1 in units of 10⁻¹⁶ GeV⁻¹, magnetic field 8 T, cavity volume 0.20 m³, form factor 0.50, and quality factor 50,000. When those values are fed into the preserved page formula, the calculator returns an estimated signal power of about 2.53 × 10-4 W. The exact formatting in the result box is scientific notation, so you will see approximately 2.53e-4 W.
Do not read that example as a realistic prediction for a state-of-the-art experiment. Read it as a consistency check on the page’s own model. The result gives you a reference point. If you double the cavity volume while changing nothing else, the output should double. If you move the magnetic field from 8 T to 10 T, the output should rise by the square of the ratio, not merely by 25%. Those are the comparisons this page is best at.
| Scenario | Magnetic field B | Estimated power | What changed |
|---|---|---|---|
| Lower-field check | 6 T | 1.42e-4 W | Only the magnetic field changed, so the estimate fell with the B2 scaling. |
| Baseline example | 8 T | 2.53e-4 W | This matches the defaults loaded into the form. |
| Stronger magnet | 10 T | 3.95e-4 W | The output increased faster than linearly because the field is squared in the formula. |
A simple way to use the calculator well is to repeat that kind of one-variable study for Q, C, or V. If the result does not move the way you expect, check the units and make sure you did not accidentally type a decimal in the wrong place. Scientific notation can hide those mistakes unless you look carefully at the exponent.
How to interpret the result
Once the result appears, ask three questions. First, is the unit what you expected? This page reports watts, so it is giving a power estimate, not a scan time, significance, or temperature. Second, does the direction of change make sense? Lower mass should increase the number in this model, higher density should increase it linearly, and stronger magnetic field should increase it quadratically. Third, is the scenario physically self-consistent enough for a quick comparison? A mathematically valid output can still be misleading if the assumed cavity geometry, field, and Q could not exist together in the same instrument.
The copy button is useful when you are iterating through several scenarios. Run a baseline case, copy the summary, then change just one parameter and copy again. That gives you a lightweight design log you can paste into a notebook, email, or lab chat. Even when the underlying model is simple, a written record of assumptions makes comparisons far more reliable.
Assumptions and limitations
This page is intentionally narrower than a full haloscope analysis package. It assumes the inputs already describe a tuned, resonant situation and that a single compact scaling law is enough for the question you are asking. That makes it fast and transparent, but it also creates limits. The script does not model receiver noise temperature, scan rate, bandwidth matching, form-factor frequency drift, cavity coupling to the receiver chain, magnet engineering limits, or the distinction between loaded and unloaded quality factor. It also does not check whether a chosen mass corresponds to a realistic cavity geometry.
Those limitations do not make the calculator useless. They define its best use case. Use it when you want to see how the signal estimate responds to parameter changes, when you are sanity-checking lecture notes, when you are comparing design directions at a back-of-the-envelope level, or when you want a quick demonstration of why haloscope experiments fight so hard for strong fields and excellent resonance. If you need an experimental forecast suitable for publication, hardware planning, or exclusion-curve work, treat this calculator as the first sketch rather than the final answer.
In short, the page is most trustworthy when you use it as a relative tool. Compare scenario A to scenario B. Look for strong versus weak dependencies. Identify which input dominates your uncertainty. Those are exactly the kinds of decisions a compact web calculator can support well.