# Tesla Coil Spark Physics - Technical Glossary terms: - term: "C_mut" full_name: "Mutual Capacitance" definition: | The capacitance between the spark channel and the topload. Represents capacitive coupling between these two conductors, measured in FEMM as the off-diagonal element of the Maxwell capacitance matrix. unit: "pF or F" typical_range: "3-15 pF for 1-5 foot sparks" related_terms: ["C_sh", "capacitance_matrix", "r"] related_topics: ["circuit-topology", "femm-workflow"] - term: "C_sh" full_name: "Shunt Capacitance" definition: | The capacitance from the spark channel to ground. Scales approximately linearly with spark length at ~2 pF per foot. Extracted from FEMM as C_22 - |C_12| from the Maxwell matrix. unit: "pF or F" typical_range: "2 pF per foot of spark length" related_terms: ["C_mut", "capacitance_matrix"] related_topics: ["circuit-topology", "femm-workflow"] - term: "r" full_name: "Capacitance Ratio" definition: | The ratio C_mut/C_sh. Determines the minimum achievable impedance phase angle. When r ≥ 0.207, achieving -45° impedance phase becomes impossible. unit: "dimensionless" typical_range: "0.1 to 2.0 for typical geometries" related_terms: ["C_mut", "C_sh", "phi_Z_min"] related_topics: ["circuit-topology"] - term: "R_opt_power" full_name: "Optimal Resistance for Power Transfer" definition: | The resistance value that maximizes real power delivered to the spark for a fixed topload voltage. Calculated as 1/(ω(C_mut + C_sh)). Plasma self-optimizes toward this value (hungry streamer principle). unit: "Ω (ohms)" typical_range: "20-200 kΩ for typical DRSSTC frequencies" related_terms: ["R_opt_phase", "hungry_streamer", "G"] related_topics: ["circuit-topology", "lumped-model"] - term: "R_opt_phase" full_name: "Optimal Resistance for Phase" definition: | The resistance value that produces the minimum achievable impedance phase angle (most resistive-looking). Always larger than R_opt_power. Calculated as 1/(ω√(C_mut(C_mut + C_sh))). unit: "Ω (ohms)" typical_range: "40-400 kΩ for typical DRSSTC frequencies" related_terms: ["R_opt_power", "phi_Z_min"] related_topics: ["circuit-topology"] - term: "phi_Z" full_name: "Impedance Phase Angle" definition: | The phase angle of the spark impedance as seen from the topload port. Negative values indicate capacitive loading (typical). Calculated as -atan(Im{Y}/Re{Y}). unit: "degrees or radians" typical_range: "-55° to -75° at R_opt_power" related_terms: ["theta_Y", "Y", "phi_Z_min"] related_topics: ["circuit-topology"] - term: "phi_Z_min" full_name: "Minimum Impedance Phase Angle" definition: | The minimum (most resistive) impedance phase angle achievable for a given circuit topology. Determined solely by capacitance ratio r. Calculated as -atan(2√(r(1+r))). Represents a fundamental topological constraint. unit: "degrees or radians" typical_range: "-50° to -70° for typical geometries" related_terms: ["r", "phi_Z", "R_opt_phase"] related_topics: ["circuit-topology"] - term: "theta_Y" full_name: "Admittance Phase Angle" definition: | The phase angle of the spark admittance. Related to impedance phase by θ_Y = -φ_Z. Positive values are typical (capacitive susceptance). unit: "degrees or radians" typical_range: "+55° to +75°" related_terms: ["phi_Z", "Y"] related_topics: ["circuit-topology"] - term: "Y" full_name: "Admittance" definition: | The complex admittance of the spark as seen from the topload port. Y = G + jB, where G is conductance and B is susceptance. Calculated from circuit topology as ((G+jB₁)·jB₂)/(G+j(B₁+B₂)). unit: "S (siemens)" typical_range: "10-100 μS for typical sparks" related_terms: ["G", "B", "Z", "phi_Z"] related_topics: ["circuit-topology"] - term: "G" full_name: "Conductance" definition: | The real part of admittance, equal to 1/R. Represents the resistive component of the spark load. unit: "S (siemens)" typical_range: "5-100 μS" related_terms: ["Y", "R", "B"] related_topics: ["circuit-topology"] - term: "B" full_name: "Susceptance" definition: | The imaginary part of admittance. B = ωC for capacitive susceptance. B₁ = ωC_mut and B₂ = ωC_sh in the circuit model. Positive for capacitors. unit: "S (siemens)" typical_range: "10-200 μS" related_terms: ["Y", "G", "C_mut", "C_sh"] related_topics: ["circuit-topology"] - term: "Z_th" full_name: "Thévenin Impedance" definition: | The output impedance of the Tesla coil as seen from the topload port with the drive turned off. Measured by applying 1V test source and measuring current: Z_th = 1V/I_test. Used for load analysis. unit: "Ω (ohms)" typical_range: "10-100 kΩ" related_terms: ["V_th", "P_load", "Thevenin_equivalent"] related_topics: ["thevenin-method", "lumped-model"] - term: "V_th" full_name: "Thévenin Voltage" definition: | The open-circuit voltage at the topload port with the drive on and no spark load. Complex value including magnitude and phase. Used with Z_th for power calculations. unit: "V (volts)" typical_range: "100-600 kV peak for typical DRSSTCs" related_terms: ["Z_th", "P_load", "Thevenin_equivalent"] related_topics: ["thevenin-method", "lumped-model"] - term: "P_load" full_name: "Power to Load" definition: | Real power delivered to the spark load. Calculated using Thévenin equivalent as P = 0.5×|V_th|²×Re{Z_load}/|Z_th+Z_load|². Uses peak phasor values with 0.5 factor. unit: "W (watts)" typical_range: "100 W to 5 kW" related_terms: ["Z_th", "V_th", "P_max"] related_topics: ["thevenin-method", "lumped-model"] - term: "P_max" full_name: "Maximum Theoretical Power" definition: | Theoretical maximum power if conjugate match were achievable. P_max = 0.5×|V_th|²/(4×Re{Z_th}). Actual spark power is less due to topological constraints preventing conjugate match. unit: "W (watts)" typical_range: "200 W to 10 kW" related_terms: ["P_load", "Z_th", "V_th", "conjugate_match"] related_topics: ["thevenin-method"] - term: "E_inception" full_name: "Inception Electric Field" definition: | The electric field threshold required for initial breakdown and spark formation from a smooth electrode. Depends on electrode geometry, pressure, and humidity. unit: "V/m or MV/m" typical_range: "2-3 MV/m at sea level for smooth topload" related_terms: ["E_propagation", "E_tip"] related_topics: ["field-thresholds"] - term: "E_propagation" full_name: "Propagation Electric Field" definition: | The minimum electric field required at the spark tip to sustain leader growth. When E_tip falls below this, spark stalls. Varies with altitude and humidity by ±20-30%. unit: "V/m or MV/m" typical_range: "0.4-1.0 MV/m at sea level" related_terms: ["E_inception", "E_tip", "dL_dt"] related_topics: ["field-thresholds", "distributed-model"] - term: "E_tip" full_name: "Tip Electric Field" definition: | The electric field at the tip of the spark. Enhanced above average field by geometric factors. Calculated from FEMM simulations. Must exceed E_propagation for continued growth. unit: "V/m or MV/m" typical_range: "0.5-2 MV/m during growth" related_terms: ["E_propagation", "kappa", "E_inception"] related_topics: ["field-thresholds", "distributed-model"] - term: "kappa" full_name: "Tip Enhancement Factor" definition: | Field enhancement factor at spark tip due to geometry. E_tip = κ×E_average. Depends on tip sharpness and local geometry. unit: "dimensionless" typical_range: "2-5 for cylindrical channels" related_terms: ["E_tip"] related_topics: ["field-thresholds"] - term: "epsilon" full_name: "Energy per Meter" definition: | Energy required to grow the spark by one meter. Fundamental parameter connecting power to growth rate: dL/dt = P/ε. Depends strongly on operating mode (QCW vs burst) and channel type (streamer vs leader). unit: "J/m (joules per meter)" typical_range: "5-15 J/m (QCW), 20-40 J/m (hybrid), 30-100+ J/m (burst)" related_terms: ["dL_dt", "P_stream", "operating_mode"] related_topics: ["energy-and-growth", "field-thresholds", "distributed-model"] - term: "dL_dt" full_name: "Growth Rate" definition: | Rate of spark length increase over time. Given by dL/dt = P_stream/ε when E_tip > E_propagation, otherwise approximately zero (stalled). unit: "m/s" typical_range: "1-100 m/s for leaders, up to 10⁶ m/s for streamers" related_terms: ["epsilon", "P_stream", "E_propagation"] related_topics: ["energy-and-growth", "field-thresholds", "distributed-model"] - term: "P_stream" full_name: "Power to Streamer/Spark" definition: | Real power delivered to the spark channel. Used in growth rate equation dL/dt = P_stream/ε. Measured as P = 0.5×Re{V×I*} at the topload port. unit: "W (watts)" typical_range: "50 W to 5 kW" related_terms: ["dL_dt", "epsilon", "P_load"] related_topics: ["energy-and-growth", "power-optimization", "lumped-model"] - term: "tau_thermal" full_name: "Thermal Time Constant" definition: | Time constant for thermal diffusion in the spark channel. τ = d²/(4α) where α is thermal diffusivity. Determines how quickly channel cools. Actual persistence longer due to convection and ionization memory. unit: "s (seconds)" typical_range: "0.1-0.2 ms (thin streamers), 300-600 ms (thick leaders)" related_terms: ["d", "alpha", "thermal_persistence"] related_topics: ["thermal-physics"] - term: "d" full_name: "Channel Diameter" definition: | Physical diameter of the spark channel. Affects capacitance logarithmically and thermal time constant quadratically. Streamers are thin (10-100 μm), leaders are thick (mm-cm). unit: "m (meters)" typical_range: "10-100 μm (streamers), 1-10 mm (leaders)" related_terms: ["tau_thermal", "streamer", "leader", "C"] related_topics: ["thermal-physics", "streamers-and-leaders", "femm-workflow"] - term: "alpha" full_name: "Thermal Diffusivity" definition: | Material property governing heat diffusion. For air, α = k/(ρ×c_p) ≈ 2×10⁻⁵ m²/s. Used to calculate thermal time constant. unit: "m²/s" typical_range: "2×10⁻⁵ m²/s for air" related_terms: ["tau_thermal", "k", "rho", "c_p"] related_topics: ["thermal-physics"] - term: "streamer" full_name: "Streamer Discharge" definition: | Thin (10-100 μm), fast (~10⁶ m/s), low-current (mA) discharge propagating via photoionization. Purple/blue appearance, highly branched, short-lived. High resistance and high energy per meter (inefficient). unit: "N/A" typical_range: "N/A" related_terms: ["leader", "epsilon", "d", "transition"] related_topics: ["streamers-and-leaders", "field-thresholds"] - term: "leader" full_name: "Leader Discharge" definition: | Thick (mm-cm), slower (~10³ m/s), high-current (A) discharge propagating via thermal ionization. White/orange appearance, straighter, persistent. Low resistance and low energy per meter (efficient). Temperature 5000-20000 K. unit: "N/A" typical_range: "N/A" related_terms: ["streamer", "epsilon", "d", "transition", "thermal_ionization"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "transition" full_name: "Streamer-to-Leader Transition" definition: | Process where initial streamers gain sufficient current to undergo Joule heating, leading to thermal ionization and conversion to leader channel. Critical for efficient long spark growth. QCW mode optimized for this. unit: "N/A" typical_range: "N/A" related_terms: ["streamer", "leader", "Joule_heating", "QCW"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "hungry_streamer" full_name: "Hungry Streamer Principle" definition: | Steve Conner's insight that streamers actively optimize impedance to maximize power extraction. Plasma adjusts conductivity, temperature, and geometry to approach R_opt_power, creating stable equilibrium at maximum power transfer. unit: "N/A" typical_range: "N/A" related_terms: ["R_opt_power", "self_optimization", "plasma_equilibrium"] related_topics: ["circuit-topology", "lumped-model"] - term: "capacitive_divider" full_name: "Capacitive Divider Effect" definition: | Voltage division between topload and spark tip due to C_mut and C_sh forming a divider: V_tip = V_topload×C_mut/(C_mut+C_sh) in open-circuit limit. As spark grows, C_sh increases, reducing V_tip and E_tip even if V_topload constant. unit: "N/A" typical_range: "N/A" related_terms: ["C_mut", "C_sh", "V_tip", "E_tip"] related_topics: ["capacitive-divider", "distributed-model"] - term: "V_tip" full_name: "Tip Voltage" definition: | Voltage at the spark tip relative to ground. Lower than topload voltage due to capacitive divider effect. Determines E_tip and thus growth capability. unit: "V (volts)" typical_range: "50-300 kV during growth" related_terms: ["capacitive_divider", "V_topload", "E_tip"] related_topics: ["capacitive-divider", "distributed-model"] - term: "Maxwell_matrix" full_name: "Maxwell Capacitance Matrix" definition: | Symmetric matrix from electrostatic analysis where C_ii > 0 (self-capacitance) and C_ij < 0 for i≠j (mutual capacitance). Used to extract C_mut and C_sh from FEMM simulations. unit: "F (farads)" typical_range: "pF scale for Tesla coils" related_terms: ["C_mut", "C_sh", "FEMM", "extraction"] related_topics: ["femm-workflow"] - term: "FEMM" full_name: "Finite Element Method Magnetics" definition: | Open-source finite element analysis software for electromagnetic simulations. Used for electrostatic analysis to extract capacitance matrices and field distributions for spark modeling. unit: "N/A" typical_range: "N/A" related_terms: ["Maxwell_matrix", "C_mut", "C_sh", "E_field"] related_topics: ["femm-workflow"] - term: "QCW" full_name: "Quasi-Continuous Wave" definition: | Operating mode with long ramp times (5-20 ms) that exploits thermal persistence to efficiently grow long sparks. Energy continuously injected maintains hot channel, promoting streamer-to-leader transition. Low ε (efficient). unit: "N/A" typical_range: "5-20 ms ramp times" related_terms: ["burst_mode", "epsilon", "leader", "transition"] related_topics: ["energy-and-growth", "coupled-resonance"] - term: "burst_mode" full_name: "Burst Mode" definition: | Operating mode with short pulses where channel cools between events. Must re-ionize repeatedly. High peak current produces bright but short sparks. High ε (inefficient for length). Voltage collapse limits growth. unit: "N/A" typical_range: "50-500 μs pulse widths" related_terms: ["QCW", "epsilon", "streamer"] related_topics: ["energy-and-growth", "coupled-resonance"] - term: "DRSSTC" full_name: "Dual Resonant Solid State Tesla Coil" definition: | Modern Tesla coil design using solid-state switching (IGBTs) with both primary and secondary tanks tuned to same frequency. Allows precise control of drive waveform and operating mode (burst or QCW). unit: "N/A" typical_range: "50-400 kHz operating frequency" related_terms: ["QCW", "burst_mode", "coupled_resonance"] related_topics: ["circuit-topology"] - term: "ringdown_method" full_name: "Ringdown Measurement Method" definition: | Technique to measure spark impedance by observing decay of oscillations with and without spark. Extracts Q factor and frequency shift to calculate equivalent parallel resistance and capacitance change. unit: "N/A" typical_range: "N/A" related_terms: ["Q_L", "G_total", "C_eq", "measurement"] related_topics: ["thevenin-method", "lumped-model"] - term: "Q_L" full_name: "Loaded Quality Factor" definition: | Quality factor of the resonant system with spark load present. Related to parallel resistance by Q_L = ω_L×C_eq×R_p. Lower Q indicates more damping (higher losses or loading). unit: "dimensionless" typical_range: "5-50 with spark, 100-500 unloaded" related_terms: ["Q_0", "R_p", "G_total", "ringdown_method"] related_topics: ["thevenin-method"] - term: "Q_0" full_name: "Unloaded Quality Factor" definition: | Quality factor without spark load. Represents intrinsic losses in secondary, topload, and environment. Higher is better for efficiency. unit: "dimensionless" typical_range: "100-500 for typical secondaries" related_terms: ["Q_L", "secondary_losses"] related_topics: ["thevenin-method"] - term: "C_eq" full_name: "Equivalent Capacitance" definition: | Total equivalent capacitance at topload port when loaded. Calculated from frequency shift: C_eq = C_0×(f_0/f_L)². Includes topload, spark, and all stray capacitances. unit: "pF or F" typical_range: "20-100 pF for typical coils" related_terms: ["Q_L", "frequency_shift", "C_0"] related_topics: ["thevenin-method", "lumped-model"] - term: "R_p" full_name: "Parallel Equivalent Resistance" definition: | Equivalent parallel resistance of the loaded system. Related to Q by R_p = Q_L/(ω_L×C_eq). Represents total losses including spark and secondary. unit: "Ω (ohms)" typical_range: "5-50 kΩ with typical spark" related_terms: ["Q_L", "G_total", "C_eq"] related_topics: ["thevenin-method", "lumped-model"] - term: "G_total" full_name: "Total Conductance" definition: | Total conductance of loaded system, G_total = 1/R_p = ω_L×C_eq/Q_L. Includes spark conductance plus secondary losses. Spark contribution found by subtracting unloaded conductance. unit: "S (siemens)" typical_range: "20-200 μS with spark" related_terms: ["R_p", "Q_L", "G", "G_0"] related_topics: ["thevenin-method"] - term: "omega" full_name: "Angular Frequency" definition: | Angular frequency ω = 2πf. Used in reactance calculations X_C = 1/(ωC), X_L = ωL, and susceptance B = ωC. unit: "rad/s" typical_range: "3×10⁵ to 2×10⁶ rad/s for typical Tesla coils" related_terms: ["f", "B", "X_C", "X_L"] related_topics: ["circuit-topology"] - term: "f" full_name: "Frequency" definition: | Operating frequency of the Tesla coil resonance. Related to angular frequency by f = ω/(2π). Shifts lower when loaded by spark. unit: "Hz" typical_range: "50-400 kHz for typical Tesla coils" related_terms: ["omega", "f_0", "f_L", "frequency_shift"] related_topics: ["circuit-topology"] - term: "f_0" full_name: "Unloaded Frequency" definition: | Resonant frequency without spark load. Natural frequency of secondary LC circuit with topload and stray capacitance. unit: "Hz" typical_range: "50-400 kHz" related_terms: ["f_L", "C_0", "L"] related_topics: ["circuit-topology", "thevenin-method"] - term: "f_L" full_name: "Loaded Frequency" definition: | Resonant frequency with spark load present. Lower than f_0 due to added capacitance from spark. Used to calculate C_eq and track operating point. unit: "Hz" typical_range: "5-20% lower than f_0" related_terms: ["f_0", "C_eq", "frequency_shift"] related_topics: ["thevenin-method", "lumped-model"] - term: "frequency_shift" full_name: "Frequency Shift with Loading" definition: | Change in resonant frequency when spark loads the system. Indicates added capacitance: C_eq = C_0×(f_0/f_L)². Important for tracking and matching. unit: "Hz or %" typical_range: "5-20% decrease typical" related_terms: ["f_0", "f_L", "C_eq"] related_topics: ["thevenin-method", "lumped-model"] - term: "conjugate_match" full_name: "Conjugate Match" definition: | Theoretical condition where load impedance equals complex conjugate of source impedance (Z_load = Z_source*). Maximizes power transfer. Often unachievable for Tesla coils due to topological constraints. unit: "N/A" typical_range: "N/A" related_terms: ["P_max", "phi_Z_min", "matching"] related_topics: ["thevenin-method"] - term: "nth_order_model" full_name: "nth-Order Distributed Spark Model" definition: | Advanced model dividing spark into n segments, each with own capacitances and resistance. Captures current distribution and tip/base differences. Typically n=10 for good accuracy. unit: "N/A" typical_range: "n=5 to 20 segments" related_terms: ["lumped_model", "distributed_model", "Maxwell_matrix"] related_topics: ["femm-workflow"] - term: "lumped_model" full_name: "Lumped Spark Model" definition: | Simplified model treating entire spark as single R, C_mut, C_sh network. Fast simulation, good for impedance matching studies. Cannot capture distributed effects or tip/base differences. unit: "N/A" typical_range: "N/A" related_terms: ["nth_order_model", "C_mut", "C_sh", "R_opt_power"] related_topics: ["lumped-model", "femm-workflow"] - term: "Joule_heating" full_name: "Joule Heating" definition: | Resistive heating in the spark channel proportional to I²R. Increases temperature, promoting thermal ionization and streamer-to-leader transition. Key mechanism in hungry streamer self-optimization. unit: "W (watts)" typical_range: "10-1000 W/m in channel" related_terms: ["transition", "leader", "thermal_ionization", "P_stream"] related_topics: ["thermal-physics", "streamers-and-leaders"] - term: "thermal_ionization" full_name: "Thermal Ionization" definition: | Ionization of gas molecules due to high temperature (5000-20000 K). Dominant mechanism in leader channels. Maintains high conductivity and low resistance. Contrast with photoionization in streamers. unit: "N/A" typical_range: "Significant above ~5000 K" related_terms: ["leader", "Joule_heating", "transition", "conductivity"] related_topics: ["thermal-physics", "streamers-and-leaders"] - term: "photoionization" full_name: "Photoionization" definition: | Ionization caused by UV photons from discharge. Dominant propagation mechanism in streamers. Allows very fast propagation (~10⁶ m/s) ahead of thermal effects. unit: "N/A" typical_range: "N/A" related_terms: ["streamer", "thermal_ionization"] related_topics: ["streamers-and-leaders", "field-thresholds"] - term: "position" full_name: "Position Parameter" definition: | Normalized position along spark in nth-order model. position = i/(n-1), where 0 is base (topload) and 1 is tip. Used for position-dependent resistance bounds and initialization. unit: "dimensionless" typical_range: "0 (base) to 1 (tip)" related_terms: ["nth_order_model", "R_min", "R_max"] related_topics: ["femm-workflow"] - term: "damping" full_name: "Damping Factor" definition: | Factor α in iterative resistance optimization that controls update rate: R_new = α×R_optimal + (1-α)×R_old. Prevents oscillations and ensures convergence. Typical α = 0.3-0.5. unit: "dimensionless" typical_range: "0.3-0.5 for stability" related_terms: ["nth_order_model", "iterative_optimization", "convergence"] related_topics: ["femm-workflow"] - term: "Freau_scaling" full_name: "Freau's Empirical Scaling" definition: | Empirical relationships for spark length vs energy. Single-shot: L ∝ √E. Repetitive: L ∝ P^0.3-0.5. QCW: L ∝ E^0.6-0.8. Based on community observations and voltage-limited growth physics. unit: "N/A" typical_range: "N/A" related_terms: ["epsilon", "bang_energy", "scaling_laws"] related_topics: ["empirical-scaling", "energy-and-growth"] - term: "bang_energy" full_name: "Bang Energy" definition: | Total energy delivered in a single pulse or burst. Used in single-shot scaling laws: L ∝ √E_bang. Typical range 1-100 J for DRSSTC bursts. unit: "J (joules)" typical_range: "1-100 J for typical DRSSTC bursts" related_terms: ["Freau_scaling", "epsilon", "burst_mode"] related_topics: ["empirical-scaling", "energy-and-growth"] - term: "pole_frequency" full_name: "Pole Frequency" definition: | Eigenfrequency of the coupled Tesla coil system. Two poles exist (upper and lower) even without spark. Spark loading shifts both poles lower and increases damping. Should track to loaded pole for accurate measurements. unit: "Hz" typical_range: "Within ±10% of design frequency" related_terms: ["f_L", "coupled_resonance", "frequency_shift"] related_topics: ["circuit-topology", "lumped-model"] - term: "coupled_resonance" full_name: "Coupled Resonance" definition: | Resonant behavior of magnetically coupled primary and secondary tanks. Creates two poles (eigenfrequencies) and complex energy transfer dynamics. Spark loading modifies both pole frequencies and damping. unit: "N/A" typical_range: "N/A" related_terms: ["pole_frequency", "k", "DRSSTC"] related_topics: ["circuit-topology"] - term: "k" full_name: "Coupling Coefficient" definition: | Magnetic coupling coefficient between primary and secondary coils. k = M/√(L_p×L_s) where M is mutual inductance. Affects pole spacing and energy transfer rate. unit: "dimensionless" typical_range: "0.05-0.25 for typical Tesla coils" related_terms: ["coupled_resonance", "M", "L_p", "L_s"] related_topics: ["circuit-topology"] - term: "topload" full_name: "Topload" definition: | Metallic terminal at top of secondary coil (toroid, sphere, etc.). Provides capacitance to ground, serves as voltage reference point, and is where spark connects. Determines C_mut with spark. unit: "N/A" typical_range: "10-100 pF capacitance typical" related_terms: ["C_mut", "C_0", "V_topload"] related_topics: ["circuit-topology", "femm-workflow"] - term: "secondary_losses" full_name: "Secondary Losses" definition: | Power dissipated in secondary coil resistance, topload surface resistance, and dielectric losses. Reduces Q and limits efficiency. Represented by parallel conductance G_0 in unloaded system. unit: "W (watts)" typical_range: "10-30% of input power" related_terms: ["Q_0", "G_0", "efficiency"] related_topics: ["thevenin-method"] - term: "efficiency" full_name: "Power Transfer Efficiency" definition: | Ratio of spark power to primary input power: η = P_spark/P_input. Accounts for secondary losses, corona, radiation. Typical 15-50% depending on design and operating mode. unit: "dimensionless or %" typical_range: "15-50% typical, up to 70% for well-optimized QCW" related_terms: ["P_spark", "P_load", "secondary_losses"] related_topics: ["thevenin-method", "lumped-model"] - term: "corona" full_name: "Corona Discharge" definition: | Partial breakdown in high-field regions without full arc formation. Occurs at sharp points, wire surfaces, etc. Represents power loss without contributing to spark. Increases with voltage. unit: "N/A" typical_range: "5-15% power loss typical" related_terms: ["E_inception", "losses"] related_topics: ["field-thresholds"] # --- Plasma Physics Terms (from Becker et al. 2005) --- - term: "reduced_field" full_name: "Reduced Electric Field (E/N)" definition: | Electric field divided by gas number density, measured in Townsend (Td). 1 Td = 10^-21 V*m^2. At STP, 100 Td corresponds to approximately 25 kV/cm. Governs ionization and attachment rates in gases; breakdown in air occurs at E/N ~ 100 Td. unit: "Td (Townsend)" typical_range: "100 Td at breakdown, 10-150 Td in discharge modeling" related_terms: ["E_inception", "ionization_coefficient", "E_propagation"] related_topics: ["field-thresholds"] - term: "ionization_coefficient" full_name: "Townsend Ionization Coefficient (alpha)" definition: | Number of ionization events per unit length of electron drift in an applied field. In air: alpha/N = A*exp(-B*N/E) with A = 1.4e-20 m^2, B = 660 Td. Determines avalanche growth rate and breakdown conditions. unit: "m^-1 or cm^-1" typical_range: "0-1000 cm^-1 depending on field strength" related_terms: ["reduced_field", "streamer_criterion", "E_inception"] related_topics: ["field-thresholds"] - term: "streamer_criterion" full_name: "Streamer Criterion (Meek Criterion)" definition: | Condition for transition from Townsend avalanche to self-propagating streamer: N_critical ~ 10^8 electrons (alpha*d ~ 18-20). When the space charge field of the avalanche head equals the applied field, the avalanche becomes a self-propagating streamer. unit: "dimensionless" typical_range: "alpha*d ~ 18-20" related_terms: ["ionization_coefficient", "streamer", "E_inception"] related_topics: ["field-thresholds", "streamers-and-leaders"] - term: "n_e" full_name: "Electron Number Density" definition: | Number of free electrons per unit volume in the plasma. Determines electrical conductivity via sigma = n_e*e^2/(m_e*nu_e). Ranges from 10^11 cm^-3 at the streamer boundary to 10^16 cm^-3 in a fully developed spark channel. unit: "cm^-3 or m^-3" typical_range: "10^11-10^13 (streamers), 10^14-10^16 (sparks/arcs)" related_terms: ["conductivity", "recombination_rate", "ionization_coefficient"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "recombination_rate" full_name: "Electron-Ion Recombination Rate Coefficient" definition: | Rate coefficient for electron capture by positive ions, governing plasma decay when the driving field is removed. For major atmospheric ions (O2+, N2+, NO+), approximately 2e-7 cm^3/s at 300 K electron temperature. Determines plasma decay time: tau_recomb = 1/(alpha_recomb * n_e). unit: "cm^3/s" typical_range: "2e-7 cm^3/s (binary at 300 K), up to 1e-4 cm^3/s (three-body at high pressure)" related_terms: ["n_e", "tau_thermal", "ionization_memory"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "ionization_energy_cost" full_name: "Average Ionization Energy Cost in Air" definition: | Average energy expended per electron-ion pair created in air, including all loss channels (excitation, dissociation, vibrational modes). Approximately 14 eV, which is higher than the bare ionization potentials of N2 (15.6 eV) or O2 (12.1 eV) because of energy diverted to non-ionizing collisions. unit: "eV" typical_range: "~14 eV in air" related_terms: ["n_e", "epsilon", "P_stream"] related_topics: ["thermal-physics", "energy-and-growth"] # --- Terms from Liu (2017) and Yang et al. (2022) --- - term: "dark_period" full_name: "Dark Period (Streamer Inception)" definition: | The interval between successive streamer bursts during leader inception. After a streamer burst, positive space charge near the electrode shields the field below inception threshold. Ion drift (~2×10⁻⁴ m²/(V·s)) slowly restores the field over ~1-5 ms, triggering the next burst. Multiple dark period cycles typically precede stable leader inception (thermal ratcheting). unit: "s (seconds)" typical_range: "1-5 ms between bursts" related_terms: ["aborted_leader", "streamer", "leader", "transition"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "aborted_leader" full_name: "Aborted Leader" definition: | A failed leader inception attempt where the streamer stem heats to near-critical temperature but fails to sustain it through gas expansion and convection losses. Multiple aborted leaders typically precede stable leader inception, with each attempt pre-heating the gas (thermal ratcheting). Gas temperature must significantly exceed 2000 K to survive expansion cooling. unit: "N/A" typical_range: "N/A" related_terms: ["dark_period", "transition", "leader", "thermal_ratcheting"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "mayr_equation" full_name: "Mayr Arc Equation" definition: | Differential equation for time evolution of arc conductance: dG/dt = (1/τ_m) × (P/P₀ - 1) × G, where G is conductance, τ_m is the thermal time constant, P is instantaneous dissipated power, and P₀ is the cooling power. Appropriate for low-current discharges (TC sparks). Naturally produces hungry streamer self-optimization toward R_opt_power. unit: "N/A" typical_range: "τ_m: 0.1-500 ms; P₀: 1 W/m to 1 kW/m" related_terms: ["hungry_streamer", "R_opt_power", "transition"] related_topics: ["streamers-and-leaders", "thermal-physics", "power-optimization"] - term: "thermal_ratcheting" full_name: "Thermal Ratcheting" definition: | Progressive pre-heating of the streamer stem through successive aborted leader attempts. Each streamer burst deposits energy; the stem cools during the dark period but retains residual warmth. After several cycles, cumulative heating pushes the stem past the critical temperature for stable leader inception. unit: "N/A" typical_range: "N/A" related_terms: ["aborted_leader", "dark_period", "transition"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "nonlinear_resistance" full_name: "Nonlinear Resistance Power Law" definition: | Equilibrium resistance per unit length of a spark channel follows R = A/I^b (Ohm/m) where I is current in Amps. Three regimes: Region I (1-10 A, A=12400, b=1.84) for TC streamers; Region II (10-1000 A, A=2820, b=1.16) for DRSSTC burst; Region III (>1000 A, A=180, b=0.75) for arcs. The steep b=1.84 in Region I quantifies the positive feedback driving streamer-to-leader transition. Channel "forgets" initial conditions at ~10 ms timescale. unit: "Ω/m (ohms per meter)" typical_range: "179-12,400 Ω/m for 1-10 A (Region I)" related_terms: ["mayr_equation", "hungry_streamer", "R_opt_power", "transition"] related_topics: ["streamers-and-leaders", "thermal-physics", "power-optimization"] - term: "heating_efficiency" full_name: "Air Heating Efficiency (eta_T)" definition: | Fraction of electrical energy deposited in a discharge channel that actually heats the neutral gas. At ambient temperature, eta_T ~ 0.1 (only 10% heats gas; 90% excites N₂ vibrational modes). Above 2000 K, eta_T ~ 1.0 (full thermalization). Formula: eta_T = 0.1 + 0.9*[tanh(T/T_amb - 4) + 1]/2. Explains why streamer-to-leader transition takes milliseconds despite MW/m power densities. unit: "dimensionless (0 to 1)" typical_range: "0.1 (300 K) to 1.0 (>2000 K)" related_terms: ["thermal_ratcheting", "transition", "vibrational_relaxation"] related_topics: ["thermal-physics", "streamers-and-leaders"] - term: "Gallimberti_model" full_name: "Gallimberti Streamer-to-Leader Model" definition: | Early (1972) computational model for predicting streamer-to-leader transition. Assumes constant stem field, simplified N₂ vibrational-translational (V-T) relaxation, and single dominant stem. Qualitatively useful but quantitatively unreliable: Liu (2017) showed assumptions do not hold under detailed kinetic modeling (45 species, 192 reactions). unit: "N/A" typical_range: "N/A" related_terms: ["transition", "leader", "streamer"] related_topics: ["streamers-and-leaders"] # --- Terms from Bazelyan & Raizer (2000) --- - term: "leader_velocity" full_name: "Leader Propagation Velocity" definition: | Empirical velocity of leader channel advance: v_L = 1500 * sqrt(|Delta_U_t|) in cm/s, where Delta_U_t is the tip potential in volts. Derived from extensive laboratory spark and lightning data. For TC sparks at 300 kV: ~8.2 km/s. Physical basis: conducting streamer length (~1 cm) divided by thermal instability contraction time (~1 us) gives ~10 km/s baseline, modulated by tip voltage. unit: "cm/s or m/s" typical_range: "5-15 km/s for TC voltages (100-600 kV)" related_terms: ["dL_dt", "E_propagation", "transition"] related_topics: ["streamers-and-leaders", "energy-and-growth"] - term: "electron_attachment_time" full_name: "Electron Attachment Time in Cool Air" definition: | Time for free electrons to attach to O2 molecules in cool (non-heated) air at atmospheric pressure: ~100 ns (10^-7 s). This is the fundamental timescale for plasma decay without heating. At T > 5000 K, attachment becomes negligible. At TC frequencies (50-400 kHz), a cold streamer undergoes 12-100 attachment times per half-cycle, explaining why heating is essential for persistent channels. unit: "s (seconds)" typical_range: "~10^-7 s at STP, increases with temperature" related_terms: ["streamer", "transition", "tau_thermal", "n_e"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "Bazelyan_VI" full_name: "Bazelyan V-I Characteristic" definition: | Simple relationship between arc/leader current and internal electric field in air at atmospheric pressure: i * E = b, where b = 300 V*A/cm. Equivalently, R_per_meter = 30,000 / i^2 (ohm/m). Valid for moderate currents (1-100 A). Agrees with da Silva's R = A/I^b power law within factor ~2 for TC-relevant currents (1-10 A). A quick approximation complementing the more detailed three-regime da Silva model. unit: "V*A/cm" typical_range: "b = 300 V*A/cm (constant)" related_terms: ["nonlinear_resistance", "mayr_equation", "hungry_streamer"] related_topics: ["streamers-and-leaders", "equations-and-bounds"] - term: "energy_ceiling" full_name: "Energy Ceiling from Tip Capacitance" definition: | Maximum energy available per unit length of new channel from the electrostatic charge stored at the spark tip: W_max = pi * epsilon_0 * U^2 (J/m), where U is the tip potential. For a TC at 300 kV: W_max ~ 25 J/m. The tip (hemisphere) stores ln(L/r) times more energy per unit length than the channel body, making the tip the primary energy source for initiating each new leader step. unit: "J/m" typical_range: "3-100 J/m for TC voltages (100-600 kV)" related_terms: ["epsilon", "V_tip", "C_mut", "C_sh"] related_topics: ["energy-and-growth", "equations-and-bounds"] - term: "conductance_relaxation" full_name: "Conductance Relaxation Model" definition: | A dynamic model for time-dependent spark channel conductance: dG/dt = [G_st(i) - G(t)] / tau_g, where G_st(i) is the equilibrium conductance at current i, and tau_g is an asymmetric time constant: 40 us for heating (current rising) and 200 us for cooling (current decreasing). Alternative to the Mayr equation; more physical for large transients. The 5:1 heating/cooling asymmetry creates a ratcheting effect that favors leader maintenance. unit: "S/m (conductance per unit length)" typical_range: "tau_g = 40 us (heating), 200 us (cooling)" related_terms: ["Mayr_equation", "thermal_ionization", "leader"] related_topics: ["thermal-physics", "equations-and-bounds"] - term: "corona_shielding" full_name: "Corona Shielding Rate Limit" definition: | The maximum voltage growth rate at which a stable corona can persist on an electrode, shielding it from streamer inception: A_u_max ~ 3.6 kV/us. Above this rate, ions cannot drift fast enough to maintain the space charge cloud that stabilizes the surface field. TC toploads reach ~300 kV/us (at 200 kHz), far exceeding this limit, so corona shielding never applies — every cycle immediately produces streamers. unit: "kV/us" typical_range: "3.6 kV/us (limit); TC toploads: ~300 kV/us" related_terms: ["E_inception", "streamer", "leader"] related_topics: ["field-thresholds", "streamers-and-leaders"] - term: "stepped_leader" full_name: "Stepped Leader Propagation" definition: | A leader that advances in discrete jumps separated by pauses, characteristic of negative polarity leaders. Lightning step length: 10-200 m (avg 30 m), with pauses of 30-90 us. TC sparks on the negative half-cycle could exhibit stepping, but the fast AC reversal (half-period 1.25-10 us) masks this. In contrast, positive leaders propagate continuously. When averaged over total development time, stepped and continuous leaders have similar velocities (10^5-10^6 m/s). unit: "dimensionless (mode classification)" typical_range: "step length: 10-200 m; pause: 30-90 us" related_terms: ["leader", "leader_velocity", "dart_leader"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "dart_leader" full_name: "Dart Leader (Re-strike Leader)" definition: | A leader that re-illuminates an existing hot channel from a previous stroke. Always continuous (not stepped), propagating at (1-4)*10^7 m/s — much faster than initial leaders (10^5-10^6 m/s) because the pre-heated, pre-ionized channel requires minimal fresh ionization. Analogous to a TC spark re-using a persistent hot channel from a previous QCW ramp cycle. unit: "m/s (velocity)" typical_range: "(1-4) * 10^7 m/s" related_terms: ["leader", "stepped_leader", "leader_velocity"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "leader_formation_threshold" full_name: "Minimum Voltage for Leader Formation" definition: | The minimum potential difference required to excite and develop a leader in air under normal conditions: Delta_U_min ~ 300-400 kV. Below this, only streamers form. Most DRSSTCs operate at 100-600 kV topload voltage; the 300 kV threshold explains the disproportionate improvement in spark length efficiency observed when coils cross this voltage level. unit: "kV" typical_range: "300-400 kV" related_terms: ["leader", "leader_velocity", "E_inception"] related_topics: ["streamers-and-leaders", "field-thresholds"] - term: "driven_leader" full_name: "Driven Leader (QCW Growth Mode)" definition: | The leader propagation mode unique to QCW Tesla coils, where the leader advances continuously at ~170 m/s (half the speed of sound), fed by sustained current from the resonant circuit. Each step involves: (1) streamer launch from leader tip, (2) thermal conversion of streamer to leader segment in ~60 us (close to tau_g = 40 us), (3) repeat. The net growth rate (~170 m/s) is intermediate between free streamers (~10^6 m/s) and natural lightning leaders (~10^4 m/s averaged). A 10 ms ramp yields ~1.7 m; 20 ms yields ~3.4 m. unit: "m/s (growth rate)" typical_range: "~170 m/s; step time ~60 us" related_terms: ["leader", "QCW", "conductance_relaxation", "leader_velocity"] related_topics: ["streamers-and-leaders", "thermal-physics", "energy-and-growth"] - term: "sword_spark" full_name: "Sword Spark (Straight QCW Discharge)" definition: | The distinctive straight, bright, sword-like spark produced by QCW Tesla coils operating at 300-600 kHz. Characterized by a single dominant leader channel with minimal branching, white/yellow appearance, and lengths of 7-16x the secondary coil length. Requires: (1) operating frequency >300 kHz for continuous heating, (2) coupling k >= 0.3, (3) smooth continuous power ramp of 10-20 ms, (4) no pulse-skip modulation. Below 300 kHz, sparks are "chaotic and less straight"; above 600 kHz, they become "curvy." The physical basis is that the RF half-period at >300 kHz (< 1.7 us) is much shorter than the thermal diffusion time of even thin streamers (~125 us for 100 um), enabling effectively continuous heating that maintains a single dominant conductive path. unit: "N/A" typical_range: "1-3.4 m length at 300-600 kHz" related_terms: ["QCW", "driven_leader", "leader", "frequency_threshold"] related_topics: ["streamers-and-leaders", "thermal-physics"] - term: "burst_ceiling" full_name: "Burst Mode Growth Ceiling" definition: | The maximum spark growth time in burst-mode DRSSTC operation, beyond which additional ON time produces no further spark length. Measured by Steve Ward at ~80 us on DRSSTC-0.5. Consistent with the thermal time constant for 100 um streamers (tau_thermal ~ 125 us): after approximately one thermal time constant, streamer channels cool as fast as they heat, saturating growth. Additional energy goes into re-heating decayed channels rather than forward propagation. This is the fundamental wall that QCW overcomes by sustaining drive beyond this timescale. unit: "us (microseconds)" typical_range: "~80 us" related_terms: ["burst_mode", "tau_thermal", "QCW", "streamer"] related_topics: ["thermal-physics", "energy-and-growth"] - term: "wave_impedance" full_name: "Channel Wave Impedance" definition: | The characteristic impedance of a spark/leader channel treated as a lossy transmission line: Z = sqrt(L_1/C_1). For lightning leaders: Z ~ 500 ohm (with C_1 ~ 10 pF/m, L_1 ~ 2.5 uH/m). For TC sparks: estimated 700-1200 ohm (higher due to smaller corona envelope and thinner channels). Relevant for strike events and return stroke analogy. unit: "ohm" typical_range: "500-1200 ohm" related_terms: ["C_sh", "leader"] related_topics: ["equations-and-bounds", "streamers-and-leaders"]