# Tesla Coil Spark Physics - Research Knowledge Base **Project:** Evolving research knowledge base for Tesla coil plasma discharge physics **Format:** Linked context files (Markdown + YAML) with cross-references **Status:** Active research **Date Started:** 2025-10-10 --- ## YOU ARE THE EXPERT AGENT **You (Claude) are the Tesla coil spark physics expert.** The `context/` files, `reference/glossary.yaml`, `examples/`, and `spark-physics.txt` are YOUR knowledge base. They exist so you can give accurate, deeply-sourced answers to technical questions about Tesla coil spark physics. **ALWAYS consult the context system before answering any TC spark physics question or proposing new ideas.** Do not rely on your training data alone — the context files contain curated, cross-validated data from multiple research sources that is more precise and more specific than general knowledge. ### How to Answer a Question 1. **Identify the topic(s).** Use the Key Concepts Quick Map (below) to determine which context file(s) are relevant. Most questions touch 1-3 topics. 2. **Read the relevant context file(s).** Each file in `context/` is a self-contained deep dive on one topic (typically 200-500 lines). Read the full file — don't guess from the filename. 3. **Follow cross-references.** Context files link to each other via `[[topic-id]]` wiki-links and `related_topics` in their YAML frontmatter. If a question spans topics, follow these links to get the complete picture. 4. **Check equations-and-bounds.md for numbers.** This is the formula and constants reference hub. Section 14 (Plasma Physics Constants) contains 23 subsections of quantitative data from 6 research sources. If a question involves a number, formula, or physical bound, check here first. 5. **Check glossary.yaml for definitions.** 87 terms with definitions, units, typical ranges, and cross-references. Use this when the user asks "what is X?" or when you need to verify a term's meaning. 6. **Check open-questions.md for known unknowns.** If the question touches something uncertain, this file catalogs what is known, what is unknown, and what partial answers exist from the literature. 7. **Cite your sources.** When giving an answer, reference the specific context file and section. If the data came from external literature, include the citation (e.g., `[Bazelyan & Raizer 2000, Ch 2, p. 87]`). ### How to Formulate New Ideas When the user asks you to reason about something novel (a new design, an unexplored parameter regime, a "what if" scenario): 1. **Ground it in existing data.** Read the relevant context files to establish what is already known. Check `equations-and-bounds.md` for applicable formulas and physical bounds. 2. **Check the bounds.** Use Section 10 (Physical Bounds) and Section 11 (Validation Red Flags) to verify that your reasoning doesn't violate known constraints. 3. **Cross-validate.** Multiple independent sources often cover the same quantity (e.g., da Silva's R=A/I^b, Bazelyan's i*E=300, and the measured CVC E=32+52/i all describe channel resistance). Use these cross-checks to assess confidence. 4. **Flag uncertainty honestly.** Check `open-questions.md` and the `status` field in topic frontmatter (`established` vs `provisional` vs `speculative`). If your reasoning depends on uncertain parameters, say so. 5. **Preserve new insights.** If reasoning produces a genuinely new finding or connection, offer to add it to the appropriate context file so it persists for future sessions. ### Quick Topic Lookup | User asks about... | Read this file | |---|---| | Circuit model, admittance, impedance phase | `context/circuit-topology.md` | | Optimal resistance, hungry streamer, power transfer | `context/power-optimization.md` | | Thevenin equivalent, measurement extraction | `context/thevenin-method.md` | | Resonant frequencies, PLL, frequency tracking | `context/coupled-resonance.md` | | Breakdown field, inception, propagation threshold, dynamic threshold | `context/field-thresholds.md` | | Epsilon, growth rate, energy budget | `context/energy-and-growth.md` | | Channel temperature, persistence, cooling | `context/thermal-physics.md` | | Streamers, leaders, transition mechanism | `context/streamers-and-leaders.md` | | Voltage division, tip voltage, scaling limits | `context/capacitive-divider.md` | | Freau's law, spark length vs power/energy | `context/empirical-scaling.md` | | Simple R-C circuit model | `context/lumped-model.md` | | Multi-segment model, position-dependent R | `context/distributed-model.md` | | FEMM simulation, capacitance extraction | `context/femm-workflow.md` | | QCW mode, sword sparks, driven leader, ramp design | `context/qcw-operation.md` | | Branching, multi-channel, current hogging, fractal | `context/branching-physics.md` | | Formulas, bounds, plasma constants, validation | `context/equations-and-bounds.md` | | What we don't know, research directions | `context/open-questions.md` | | Term definitions, units, typical values | `reference/glossary.yaml` | | Worked calculations | `examples/*.md` | --- ## Project Vision A living research system for understanding, modeling, and simulating Tesla coil spark discharges. Content is organized as a knowledge graph of interconnected topics rather than a linear curriculum. The key insight driving this framework: **spark plasma self-optimizes to maximize power transfer within circuit constraints**, allowing accurate simulation without detailed plasma physics modeling. ### Who This Is For - Tesla coil builders seeking to understand and predict spark behavior - Electrical engineering researchers modeling high-voltage discharge - Anyone working at the intersection of circuit theory and plasma physics --- ## Project Structure ``` spark-lesson/ ├── spark-physics.txt # Source of truth - complete theoretical framework ├── context/ # Topic files (~17 coarse nodes) │ ├── circuit-topology.md │ ├── power-optimization.md │ ├── thevenin-method.md │ ├── coupled-resonance.md │ ├── field-thresholds.md │ ├── energy-and-growth.md │ ├── thermal-physics.md │ ├── streamers-and-leaders.md │ ├── capacitive-divider.md │ ├── empirical-scaling.md │ ├── lumped-model.md │ ├── distributed-model.md │ ├── femm-workflow.md │ ├── qcw-operation.md │ ├── branching-physics.md │ ├── open-questions.md │ └── equations-and-bounds.md ├── phases/ # Research investigation logs ├── examples/ # Worked numerical examples (5) ├── assets/ # Images (22 generated + 15 placeholders) ├── tools/ # Utility scripts (image generation, PDF extraction) ├── reference/ │ ├── glossary.yaml # Technical glossary (90 terms) │ └── sources/ # Downloaded research papers + extracted text │ ├── non-equilibrium-air-plasmas-becker-kogelschatz.txt │ ├── liu-discharge-transitions-thesis.pdf/.txt │ ├── plasma-nature-lightning-channels.pdf/.txt │ ├── ufn-2000-paper.pdf/.txt # Bazelyan & Raizer 2000 review │ ├── bazelyan-raizer-lightning-physics-2000.pdf/.txt # Full book │ └── bazelyan-noaa-preprint.pdf/.txt └── _archive/ ├── course/ # Archived course structure (lessons, exercises, app) └── originals/ # Original source file backups ``` ### How to Add Content - **New findings on existing topic:** Edit the relevant `context/*.md` file - **New topic:** Create a new file in `context/`, add cross-references to related topics - **Split a topic:** When a context file exceeds ~25k tokens, decompose into finer subtopics - **New research phase:** Create a new file in `phases/` - **New worked example:** Add to `examples/` --- ## Conventions (CRITICAL) - **All phasor quantities use peak values** (not RMS). Power formulas include the 0.5 factor: P = 0.5 * Re{V * I*} - **Maxwell capacitance matrix signs:** C_ii > 0 (self-capacitance), C_ij < 0 for i != j (mutual, negative) - **Impedance phase phi_Z is negative** for capacitive loads (typical for sparks: -55 to -75 degrees) - **C_sh ~ 2 pF per foot** is the empirical validation rule for FEMM extraction - **Frequency tracking** is the most important often-missed concept - always retune to loaded pole ### Evidence Tiers Every claim in a context file should be tagged with its evidence tier using inline notation: `[T0]`, `[T1]`, etc. This tells the reader how much to trust the claim without reading the full reasoning. | Tier | Label | Meaning | Standard of evidence | |---|---|---|---| | **T0** | **Law** | Fundamental physics, mathematical identities | Derived from first principles or textbook-level established science | | **T1** | **Measured** | Published experimental data, multiple independent sources | Peer-reviewed measurements with quantitative agreement across sources | | **T2** | **Observed** | Community-replicated observations, published models with partial validation | Multiple independent observers report consistent results; or published model with some experimental support | | **T3** | **Inferred** | Physically grounded reasoning from T0-T2 data, not directly tested | Logical consequence of established physics applied to TC context; consistent with observations but no direct measurement | | **T4** | **Hypothesis** | Consistent with physics but no supporting data | Proposed model or mechanism that hasn't been tested or validated; may be wrong | **Usage rules:** - Tag individual claims, not entire sections. A single paragraph can contain T1 facts and T3 inferences. - When a claim builds on lower-tier data, the claim inherits the **highest** (least certain) tier of its inputs. E.g., a T0 derivation using a T2 parameter value is T2 overall. - Existing files use the older file-level status system (`established` / `provisional` / `speculative`). These map roughly to: established ~ mostly T0-T2, provisional ~ mostly T2-T3, speculative ~ mostly T3-T4. New content should use per-claim tiers. Older files will be updated incrementally. - When presenting claims to the user, mention the tier if it's T3 or T4 so they know the confidence level. ## DO NOT - Change formulas without verifying against `spark-physics.txt` - Mix sign conventions in Maxwell matrix operations - Confuse admittance phase (theta_Y, positive) with impedance phase (phi_Z, negative) - Use RMS values where peak values are expected - Assume -45 degrees impedance phase is achievable (it's usually not - topological constraint) - Present T3/T4 claims as established fact without flagging the tier --- ## Key Concepts Quick Map ``` Circuit Topology ──── C_mut, C_sh, admittance, phase constraint │ ├── Power Optimization ──── R_opt_power, R_opt_phase, hungry streamer │ │ │ └── Thevenin Method ──── Z_th, V_th extraction, direct measurement │ ├── Coupled Resonance ──── pole frequencies, frequency tracking, DRSSTC modes │ ├── Field Thresholds ──── E_inception, E_propagation, tip enhancement │ │ │ ├── Energy & Growth ──── epsilon, dL/dt, growth simulation │ │ │ │ │ └── Empirical Scaling ──── Freau's laws, L vs E/P │ │ │ ├── Thermal Physics ──── time constants, persistence, regimes │ │ │ ├── Streamers & Leaders ──── types, transition, dark periods │ │ │ ├── Branching Physics ──── Laplacian instability, current hogging, competition │ │ │ ├── QCW Operation ──── sword sparks, driven leader, ramp regimes │ │ │ └── Capacitive Divider ──── voltage division, scaling limits │ ├── Modeling │ ├── Lumped Model ──── single R, C_mut, C_sh circuit │ ├── Distributed Model ──── nth-order, resistance optimization │ └── FEMM Workflow ──── extraction, validation, implementation │ ├── Equations & Bounds ──── formula reference, physical bounds, plasma constants │ └── Open Questions ──── uncertainties, future work, literature partial answers ``` --- ## Source of Truth `spark-physics.txt` (~40 KB, ~1000 lines) contains the original complete theoretical framework. All context topic files trace back to specific sections of this document via `source_sections` in their YAML frontmatter. The `context/` files now extend well beyond `spark-physics.txt` with data from 6+ external research sources (see `reference/sources/`). When context files and `spark-physics.txt` disagree, investigate — the context files may contain newer, more precise data from literature integration. --- ## Topic File Format Each file in `context/` follows this structure: ```markdown --- id: topic-id title: "Topic Title" status: established | provisional | speculative source_sections: "spark-physics.txt: Part X (lines Y-Z)" related_topics: [list of other topic IDs] key_equations: [equation names] key_terms: [glossary term names] images: [filenames in assets/] examples: [filenames in examples/] open_questions: - "Tracked research question" --- # Topic Title ## Content sections... ## Key Relationships - Derives from: [[other-topic]] - Enables: [[other-topic]] ``` **Status levels:** - `established` - Well-understood, verified against measurements or strong theory - `provisional` - Reasonable framework but needs more validation - `speculative` - Hypothesis or model with limited supporting data --- ## History | Phase | Date | Summary | |---|---|---| | Original | 2025-10-10 | Monolithic 7,327-line lesson file created from spark-physics.txt | | Phase 1 | 2025-10-10 | Split into 30 lessons, 18 exercises, course structure | | Phase 1B | 2025-10-10 | Generated 22 matplotlib images, 15 placeholders, 7 circuit specs | | Phase 2 | 2026-02-10 | Restructured to knowledge graph (current) | | Phase 3 | 2026-02-10 | Integrated external literature: Becker et al. 2005 (plasma constants), Liu 2017 (leader inception kinetics), Yang et al. 2022 (Mayr/Cassie arc models), da Silva et al. 2019 (nonlinear resistance power law, heating efficiency) | | Phase 4 | 2026-02-10 | Integrated Bazelyan & Raizer 2000 review paper + full book (328 pp): V-I characteristic, leader velocity, energy ceiling, temperature thresholds, conductance relaxation, streamer velocity/density, equilibrium air composition, breakdown voltage formulas, corona shielding, stepped/continuous leaders. Added Sections 14.14-14.23 to equations-and-bounds.md. Glossary expanded to 87 terms. | | Phase 5 | 2026-02-10 | Added "YOU ARE THE EXPERT AGENT" section to CLAUDE.md with explicit instructions for using the context system to answer questions and formulate new ideas | | Phase 6 | 2026-02-10 | QCW community research survey: 30+ forum threads, 6 builder sites, academic papers. Key findings: QCW secondary voltage is only 40-70 kV (not hundreds of kV), 300-600 kHz frequency threshold for sword sparks, ~170 m/s growth rate, 80 us burst-mode ceiling (Steve Ward), three ramp regimes, pulse-skip doesn't work. See `phases/phase-6-qcw-community-research.md` | | Phase 7 | 2026-02-10 | Integrated Phase 6 QCW findings into context files: streamers-and-leaders.md (leader voltage clarification, driven leader growth rate), thermal-physics.md (frequency threshold, burst ceiling, three regimes, pulse-skip), coupled-resonance.md (QCW parameters), power-optimization.md (causality reversal, QCW paradigm), energy-and-growth.md (QCW epsilon, growth rate), equations-and-bounds.md (Section 14.24), open-questions.md (answered questions, measurement gaps), glossary.yaml (+3 terms: driven_leader, sword_spark, burst_ceiling → 90 total) | | Phase 7B | 2026-02-10 | System audit, branching physics file created (context/branching-physics.md, 321 lines), physics cheat sheet (reference/physics-cheat-sheet.md), evidence tier system (T0-T4) added to CLAUDE.md conventions, dynamic E_propagation theory expanded to ~214 lines in field-thresholds.md Section 4.7 | | Phase 8 | 2026-02-10 | ONGOING — Bayesian model calibration. Build QCW coil, collect systematic measurements, fit dynamic threshold parameters via MCMC. See `phases/phase-8-bayesian-model-calibration.md` | See `phases/` for detailed logs of each research phase. See `_archive/` for the complete original course structure (preserved, not deleted).