# ⚛  L1 Principle — RF Heating — ICRF / LH / ECH wave absorption

**ID:** `L1-351` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Plasma Physics — *Full-wave RF heating of magnetized plasmas*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** rf power deposition profile
> **📡 Carrier:** plasma · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554096

---

## 🧠 1. Introduction

**RF Heating — ICRF / LH / ECH wave absorption** is a **linear inverse problem** whose unknown lives in **rf power deposition profile** space, within the **Full-wave RF heating of magnetized plasmas** sub-domain of **Plasma Physics**.

Measurements consist of plasma particle and field diagnostics via a **rf power diagnostics** sensing mechanism.

The forward operator applies, in order: L · dielectric tensor operator; L · wave propagate operator; L · resonant absorb operator; integration over a band of frequencies.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · dielectric tensor → L · wave propagate → L · resonant absorb → Frequency integration → **y** (detector).

```
y = ∫dω `L.resonant_absorb` `L.wave_propagate` `L.dielectric_tensor` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.dielectric_tensor` | L · dielectric tensor operator |
| `L.wave_propagate` | L · wave propagate operator |
| `L.resonant_absorb` | L · resonant absorb operator |
| `int.frequency` | Integration over a band of frequencies |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Plasma Physics |
| Sub domain | Full-wave RF heating of magnetized plasmas |
| Carrier | plasma |
| Problem class | linear_inverse |
| Solution space | rf_power_deposition_profile |
| Noise model | gaussian |
| Integration axis | frequency |
| Difficulty delta | 5 |
| L dag | 3.5 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `rf_heating` · **Forward operator:** `rf_heating_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N r | — | 128 |
| N z | — | 128 |
| Snr db | dB | 25 |
| N freqs | — | 1 |
| Dielectric error | — | 0 |
| Mode conversion error | — | 0 |
| Antenna coupling error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N r | — | 32 – 1024 |
| N z | — | 32 – 1024 |
| Snr db | dB | 0 – 40 |
| N freqs | — | 1 – 50 |
| Dielectric error | — | 0.0 – 0.2 |
| Mode conversion error | — | 0.0 – 0.3 |
| Antenna coupling error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 22.0

| Metric | Range |
|---|---|
| Psnr db | 10.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `500` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xdee741b0bb268f44f5684e88f88fc8f636e63525d83e3e2b996b8ebfb1291727`
- **Chain tx hash:** `0xe736e902835c65e16a448208e3c5bcf4d0667d1bedeb6b3af0e36b4fe612ee33`
- **Chain block:** `41554096`

---

## File Mapping

This bundle consists of: `L1-351.md`, `L1-351.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-351.md` | Source of truth — edit this | Human or LLM |
| `L1-351.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-351`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._