# ⚛  L1 Principle — Plasma Sheath — Debye-scale boundary layer

**ID:** `L1-350` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Plasma Physics — *Plasma-wall sheath region*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** potential density sheath
> **📡 Carrier:** plasma · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554096

---

## 🧠 1. Introduction

**Plasma Sheath — Debye-scale boundary layer** is a **linear inverse problem** whose unknown lives in **potential density sheath** space, within the **Plasma-wall sheath region** sub-domain of **Plasma Physics**.

Measurements consist of plasma particle and field diagnostics via a **langmuir probe** sensing mechanism.

The forward operator applies, in order: L · poisson operator; L · fluid ion operator; L · boltzmann electron operator; pixel-level spatial averaging on the detector.

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

## ⚙ 2. Forward Model

Physical chain: **x** → L · poisson → L · fluid ion → L · boltzmann electron → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.boltzmann_electron` `L.fluid_ion` `L.poisson` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.poisson` | L · poisson operator |
| `L.fluid_ion` | L · fluid ion operator |
| `L.boltzmann_electron` | L · boltzmann electron operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Plasma Physics |
| Sub domain | Plasma-wall sheath region |
| Carrier | plasma |
| Problem class | linear_inverse |
| Solution space | potential_density_sheath |
| Noise model | gaussian |
| Integration axis | spatial |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 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:** `sheath` · **Forward operator:** `sheath_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N z | — | 128 |
| Snr db | dB | 30 |
| Boundary error | — | 0 |
| Electron temp error | — | 0 |
| Bohm criterion error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N z | — | 32 – 4096 |
| Snr db | dB | 0 – 40 |
| Boundary error | — | 0.0 – 0.2 |
| Electron temp error | — | 0.0 – 0.1 |
| Bohm criterion error | — | 0.0 – 0.2 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 25.0

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

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `240` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x7862b542e53c593030b5c781933863bbaff726966854a3914de1be8a0cc85c4a`
- **Chain tx hash:** `0x63de17a4d2f14d406ff36a593472e98ff744ed300600bfc476602987e7e6061e`
- **Chain block:** `41554096`

---

## File Mapping

This bundle consists of: `L1-350.md`, `L1-350.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-350.md` | Source of truth — edit this | Human or LLM |
| `L1-350.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 `L1-350`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._