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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

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.
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.
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.
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.
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.
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.
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):

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.
Check the bounds. Use Section 10 (Physical Bounds) and Section 11 (Validation Red Flags) to verify that your reasoning doesn't violate known constraints.
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.
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.
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:

---
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).

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