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1040 lines
46 KiB
1040 lines
46 KiB
# Tesla Coil Spark Physics - Technical Glossary
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terms:
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- term: "C_mut"
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full_name: "Mutual Capacitance"
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definition: |
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The capacitance between the spark channel and the topload. Represents
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capacitive coupling between these two conductors, measured in FEMM as
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the off-diagonal element of the Maxwell capacitance matrix.
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unit: "pF or F"
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typical_range: "3-15 pF for 1-5 foot sparks"
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related_terms: ["C_sh", "capacitance_matrix", "r"]
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related_topics: ["circuit-topology", "femm-workflow"]
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- term: "C_sh"
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full_name: "Shunt Capacitance"
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definition: |
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The capacitance from the spark channel to ground. Scales approximately
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linearly with spark length at ~2 pF per foot. Extracted from FEMM as
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C_22 - |C_12| from the Maxwell matrix.
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unit: "pF or F"
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typical_range: "2 pF per foot of spark length"
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related_terms: ["C_mut", "capacitance_matrix"]
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related_topics: ["circuit-topology", "femm-workflow"]
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- term: "r"
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full_name: "Capacitance Ratio"
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definition: |
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The ratio C_mut/C_sh. Determines the minimum achievable impedance phase
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angle. When r ≥ 0.207, achieving -45° impedance phase becomes impossible.
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unit: "dimensionless"
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typical_range: "0.1 to 2.0 for typical geometries"
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related_terms: ["C_mut", "C_sh", "phi_Z_min"]
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related_topics: ["circuit-topology"]
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- term: "R_opt_power"
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full_name: "Optimal Resistance for Power Transfer"
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definition: |
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The resistance value that maximizes real power delivered to the spark
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for a fixed topload voltage. Calculated as 1/(ω(C_mut + C_sh)). Plasma
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self-optimizes toward this value (hungry streamer principle).
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unit: "Ω (ohms)"
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typical_range: "20-200 kΩ for typical DRSSTC frequencies"
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related_terms: ["R_opt_phase", "hungry_streamer", "G"]
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related_topics: ["circuit-topology", "lumped-model"]
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- term: "R_opt_phase"
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full_name: "Optimal Resistance for Phase"
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definition: |
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The resistance value that produces the minimum achievable impedance phase
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angle (most resistive-looking). Always larger than R_opt_power.
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Calculated as 1/(ω√(C_mut(C_mut + C_sh))).
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unit: "Ω (ohms)"
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typical_range: "40-400 kΩ for typical DRSSTC frequencies"
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related_terms: ["R_opt_power", "phi_Z_min"]
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related_topics: ["circuit-topology"]
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- term: "phi_Z"
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full_name: "Impedance Phase Angle"
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definition: |
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The phase angle of the spark impedance as seen from the topload port.
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Negative values indicate capacitive loading (typical). Calculated as
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-atan(Im{Y}/Re{Y}).
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unit: "degrees or radians"
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typical_range: "-55° to -75° at R_opt_power"
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related_terms: ["theta_Y", "Y", "phi_Z_min"]
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related_topics: ["circuit-topology"]
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- term: "phi_Z_min"
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full_name: "Minimum Impedance Phase Angle"
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definition: |
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The minimum (most resistive) impedance phase angle achievable for a given
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circuit topology. Determined solely by capacitance ratio r. Calculated as
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-atan(2√(r(1+r))). Represents a fundamental topological constraint.
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unit: "degrees or radians"
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typical_range: "-50° to -70° for typical geometries"
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related_terms: ["r", "phi_Z", "R_opt_phase"]
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related_topics: ["circuit-topology"]
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- term: "theta_Y"
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full_name: "Admittance Phase Angle"
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definition: |
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The phase angle of the spark admittance. Related to impedance phase by
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θ_Y = -φ_Z. Positive values are typical (capacitive susceptance).
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unit: "degrees or radians"
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typical_range: "+55° to +75°"
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related_terms: ["phi_Z", "Y"]
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related_topics: ["circuit-topology"]
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- term: "Y"
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full_name: "Admittance"
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definition: |
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The complex admittance of the spark as seen from the topload port.
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Y = G + jB, where G is conductance and B is susceptance. Calculated
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from circuit topology as ((G+jB₁)·jB₂)/(G+j(B₁+B₂)).
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unit: "S (siemens)"
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typical_range: "10-100 μS for typical sparks"
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related_terms: ["G", "B", "Z", "phi_Z"]
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related_topics: ["circuit-topology"]
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- term: "G"
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full_name: "Conductance"
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definition: |
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The real part of admittance, equal to 1/R. Represents the resistive
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component of the spark load.
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unit: "S (siemens)"
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typical_range: "5-100 μS"
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related_terms: ["Y", "R", "B"]
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related_topics: ["circuit-topology"]
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- term: "B"
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full_name: "Susceptance"
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definition: |
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The imaginary part of admittance. B = ωC for capacitive susceptance.
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B₁ = ωC_mut and B₂ = ωC_sh in the circuit model. Positive for capacitors.
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unit: "S (siemens)"
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typical_range: "10-200 μS"
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related_terms: ["Y", "G", "C_mut", "C_sh"]
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related_topics: ["circuit-topology"]
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- term: "Z_th"
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full_name: "Thévenin Impedance"
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definition: |
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The output impedance of the Tesla coil as seen from the topload port with
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the drive turned off. Measured by applying 1V test source and measuring
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current: Z_th = 1V/I_test. Used for load analysis.
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unit: "Ω (ohms)"
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typical_range: "10-100 kΩ"
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related_terms: ["V_th", "P_load", "Thevenin_equivalent"]
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related_topics: ["thevenin-method", "lumped-model"]
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- term: "V_th"
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full_name: "Thévenin Voltage"
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definition: |
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The open-circuit voltage at the topload port with the drive on and no
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spark load. Complex value including magnitude and phase. Used with Z_th
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for power calculations.
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unit: "V (volts)"
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typical_range: "100-600 kV peak for typical DRSSTCs"
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related_terms: ["Z_th", "P_load", "Thevenin_equivalent"]
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related_topics: ["thevenin-method", "lumped-model"]
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- term: "P_load"
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full_name: "Power to Load"
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definition: |
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Real power delivered to the spark load. Calculated using Thévenin equivalent
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as P = 0.5×|V_th|²×Re{Z_load}/|Z_th+Z_load|². Uses peak phasor values with
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0.5 factor.
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unit: "W (watts)"
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typical_range: "100 W to 5 kW"
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related_terms: ["Z_th", "V_th", "P_max"]
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related_topics: ["thevenin-method", "lumped-model"]
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- term: "P_max"
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full_name: "Maximum Theoretical Power"
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definition: |
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Theoretical maximum power if conjugate match were achievable.
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P_max = 0.5×|V_th|²/(4×Re{Z_th}). Actual spark power is less due to
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topological constraints preventing conjugate match.
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unit: "W (watts)"
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typical_range: "200 W to 10 kW"
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related_terms: ["P_load", "Z_th", "V_th", "conjugate_match"]
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related_topics: ["thevenin-method"]
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- term: "E_inception"
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full_name: "Inception Electric Field"
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definition: |
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The electric field threshold required for initial breakdown and spark
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formation from a smooth electrode. Depends on electrode geometry,
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pressure, and humidity.
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unit: "V/m or MV/m"
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typical_range: "2-3 MV/m at sea level for smooth topload"
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related_terms: ["E_propagation", "E_tip"]
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related_topics: ["field-thresholds"]
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- term: "E_propagation"
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full_name: "Propagation Electric Field"
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definition: |
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The minimum electric field required at the spark tip to sustain leader
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growth. When E_tip falls below this, spark stalls. Varies with altitude
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and humidity by ±20-30%.
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unit: "V/m or MV/m"
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typical_range: "0.4-1.0 MV/m at sea level"
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related_terms: ["E_inception", "E_tip", "dL_dt"]
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related_topics: ["field-thresholds", "distributed-model"]
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- term: "E_tip"
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full_name: "Tip Electric Field"
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definition: |
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The electric field at the tip of the spark. Enhanced above average field
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by geometric factors. Calculated from FEMM simulations. Must exceed
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E_propagation for continued growth.
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unit: "V/m or MV/m"
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typical_range: "0.5-2 MV/m during growth"
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related_terms: ["E_propagation", "kappa", "E_inception"]
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related_topics: ["field-thresholds", "distributed-model"]
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- term: "kappa"
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full_name: "Tip Enhancement Factor"
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definition: |
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Field enhancement factor at spark tip due to geometry. E_tip = κ×E_average.
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Depends on tip sharpness and local geometry.
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unit: "dimensionless"
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typical_range: "2-5 for cylindrical channels"
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related_terms: ["E_tip"]
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related_topics: ["field-thresholds"]
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- term: "epsilon"
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full_name: "Energy per Meter"
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definition: |
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Energy required to grow the spark by one meter. Fundamental parameter
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connecting power to growth rate: dL/dt = P/ε. Depends strongly on
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operating mode (QCW vs burst) and channel type (streamer vs leader).
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unit: "J/m (joules per meter)"
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typical_range: "5-15 J/m (QCW), 20-40 J/m (hybrid), 30-100+ J/m (burst)"
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related_terms: ["dL_dt", "P_stream", "operating_mode"]
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related_topics: ["energy-and-growth", "field-thresholds", "distributed-model"]
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- term: "dL_dt"
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full_name: "Growth Rate"
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definition: |
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Rate of spark length increase over time. Given by dL/dt = P_stream/ε when
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E_tip > E_propagation, otherwise approximately zero (stalled).
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unit: "m/s"
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typical_range: "1-100 m/s for leaders, up to 10⁶ m/s for streamers"
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related_terms: ["epsilon", "P_stream", "E_propagation"]
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related_topics: ["energy-and-growth", "field-thresholds", "distributed-model"]
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- term: "P_stream"
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full_name: "Power to Streamer/Spark"
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definition: |
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Real power delivered to the spark channel. Used in growth rate equation
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dL/dt = P_stream/ε. Measured as P = 0.5×Re{V×I*} at the topload port.
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unit: "W (watts)"
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typical_range: "50 W to 5 kW"
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related_terms: ["dL_dt", "epsilon", "P_load"]
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related_topics: ["energy-and-growth", "power-optimization", "lumped-model"]
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- term: "tau_thermal"
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full_name: "Thermal Time Constant"
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definition: |
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Time constant for thermal diffusion in the spark channel. τ = d²/(4α) where
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α is thermal diffusivity. Determines how quickly channel cools. Actual
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persistence longer due to convection and ionization memory.
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unit: "s (seconds)"
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typical_range: "0.1-0.2 ms (thin streamers), 300-600 ms (thick leaders)"
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related_terms: ["d", "alpha", "thermal_persistence"]
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related_topics: ["thermal-physics"]
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- term: "d"
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full_name: "Channel Diameter"
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definition: |
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Physical diameter of the spark channel. Affects capacitance logarithmically
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and thermal time constant quadratically. Streamers are thin (10-100 μm),
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leaders are thick (mm-cm).
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unit: "m (meters)"
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typical_range: "10-100 μm (streamers), 1-10 mm (leaders)"
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related_terms: ["tau_thermal", "streamer", "leader", "C"]
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related_topics: ["thermal-physics", "streamers-and-leaders", "femm-workflow"]
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- term: "alpha"
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full_name: "Thermal Diffusivity"
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definition: |
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Material property governing heat diffusion. For air, α = k/(ρ×c_p) ≈ 2×10⁻⁵ m²/s.
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Used to calculate thermal time constant.
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unit: "m²/s"
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typical_range: "2×10⁻⁵ m²/s for air"
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related_terms: ["tau_thermal", "k", "rho", "c_p"]
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related_topics: ["thermal-physics"]
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- term: "streamer"
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full_name: "Streamer Discharge"
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definition: |
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Thin (10-100 μm), fast (~10⁶ m/s), low-current (mA) discharge propagating
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via photoionization. Purple/blue appearance, highly branched, short-lived.
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High resistance and high energy per meter (inefficient).
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["leader", "epsilon", "d", "transition"]
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related_topics: ["streamers-and-leaders", "field-thresholds"]
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- term: "leader"
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full_name: "Leader Discharge"
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definition: |
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Thick (mm-cm), slower (~10³ m/s), high-current (A) discharge propagating
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via thermal ionization. White/orange appearance, straighter, persistent.
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Low resistance and low energy per meter (efficient). Temperature 5000-20000 K.
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["streamer", "epsilon", "d", "transition", "thermal_ionization"]
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related_topics: ["streamers-and-leaders", "thermal-physics"]
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- term: "transition"
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full_name: "Streamer-to-Leader Transition"
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definition: |
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Process where initial streamers gain sufficient current to undergo Joule
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heating, leading to thermal ionization and conversion to leader channel.
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Critical for efficient long spark growth. QCW mode optimized for this.
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["streamer", "leader", "Joule_heating", "QCW"]
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related_topics: ["streamers-and-leaders", "thermal-physics"]
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- term: "hungry_streamer"
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full_name: "Hungry Streamer Principle"
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definition: |
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Steve Conner's insight that streamers actively optimize impedance to maximize
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power extraction. Plasma adjusts conductivity, temperature, and geometry to
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approach R_opt_power, creating stable equilibrium at maximum power transfer.
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["R_opt_power", "self_optimization", "plasma_equilibrium"]
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related_topics: ["circuit-topology", "lumped-model"]
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- term: "capacitive_divider"
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full_name: "Capacitive Divider Effect"
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definition: |
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Voltage division between topload and spark tip due to C_mut and C_sh forming
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a divider: V_tip = V_topload×C_mut/(C_mut+C_sh) in open-circuit limit. As
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spark grows, C_sh increases, reducing V_tip and E_tip even if V_topload constant.
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["C_mut", "C_sh", "V_tip", "E_tip"]
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related_topics: ["capacitive-divider", "distributed-model"]
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- term: "V_tip"
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full_name: "Tip Voltage"
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definition: |
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Voltage at the spark tip relative to ground. Lower than topload voltage due
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to capacitive divider effect. Determines E_tip and thus growth capability.
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unit: "V (volts)"
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typical_range: "50-300 kV during growth"
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related_terms: ["capacitive_divider", "V_topload", "E_tip"]
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related_topics: ["capacitive-divider", "distributed-model"]
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- term: "Maxwell_matrix"
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full_name: "Maxwell Capacitance Matrix"
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definition: |
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Symmetric matrix from electrostatic analysis where C_ii > 0 (self-capacitance)
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and C_ij < 0 for i≠j (mutual capacitance). Used to extract C_mut and C_sh
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from FEMM simulations.
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unit: "F (farads)"
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typical_range: "pF scale for Tesla coils"
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related_terms: ["C_mut", "C_sh", "FEMM", "extraction"]
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related_topics: ["femm-workflow"]
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- term: "FEMM"
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full_name: "Finite Element Method Magnetics"
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definition: |
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Open-source finite element analysis software for electromagnetic simulations.
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Used for electrostatic analysis to extract capacitance matrices and field
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distributions for spark modeling.
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["Maxwell_matrix", "C_mut", "C_sh", "E_field"]
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related_topics: ["femm-workflow"]
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- term: "QCW"
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full_name: "Quasi-Continuous Wave"
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definition: |
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Operating mode with long ramp times (5-20 ms) that exploits thermal persistence
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to efficiently grow long sparks. Energy continuously injected maintains hot
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channel, promoting streamer-to-leader transition. Low ε (efficient).
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unit: "N/A"
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typical_range: "5-20 ms ramp times"
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related_terms: ["burst_mode", "epsilon", "leader", "transition"]
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related_topics: ["energy-and-growth", "coupled-resonance"]
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- term: "burst_mode"
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full_name: "Burst Mode"
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definition: |
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Operating mode with short pulses where channel cools between events. Must
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re-ionize repeatedly. High peak current produces bright but short sparks.
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High ε (inefficient for length). Voltage collapse limits growth.
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unit: "N/A"
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typical_range: "50-500 μs pulse widths"
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related_terms: ["QCW", "epsilon", "streamer"]
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related_topics: ["energy-and-growth", "coupled-resonance"]
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- term: "DRSSTC"
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full_name: "Dual Resonant Solid State Tesla Coil"
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definition: |
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Modern Tesla coil design using solid-state switching (IGBTs) with both
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primary and secondary tanks tuned to same frequency. Allows precise control
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of drive waveform and operating mode (burst or QCW).
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unit: "N/A"
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typical_range: "50-400 kHz operating frequency"
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related_terms: ["QCW", "burst_mode", "coupled_resonance"]
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related_topics: ["circuit-topology"]
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- term: "ringdown_method"
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full_name: "Ringdown Measurement Method"
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definition: |
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Technique to measure spark impedance by observing decay of oscillations
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with and without spark. Extracts Q factor and frequency shift to calculate
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equivalent parallel resistance and capacitance change.
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["Q_L", "G_total", "C_eq", "measurement"]
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related_topics: ["thevenin-method", "lumped-model"]
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- term: "Q_L"
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full_name: "Loaded Quality Factor"
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definition: |
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Quality factor of the resonant system with spark load present. Related to
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parallel resistance by Q_L = ω_L×C_eq×R_p. Lower Q indicates more damping
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(higher losses or loading).
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unit: "dimensionless"
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typical_range: "5-50 with spark, 100-500 unloaded"
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related_terms: ["Q_0", "R_p", "G_total", "ringdown_method"]
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related_topics: ["thevenin-method"]
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- term: "Q_0"
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full_name: "Unloaded Quality Factor"
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definition: |
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Quality factor without spark load. Represents intrinsic losses in secondary,
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topload, and environment. Higher is better for efficiency.
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unit: "dimensionless"
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typical_range: "100-500 for typical secondaries"
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related_terms: ["Q_L", "secondary_losses"]
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related_topics: ["thevenin-method"]
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- 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
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power densities.
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unit: "dimensionless (0 to 1)"
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typical_range: "0.1 (300 K) to 1.0 (>2000 K)"
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related_terms: ["thermal_ratcheting", "transition", "vibrational_relaxation"]
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related_topics: ["thermal-physics", "streamers-and-leaders"]
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- term: "Gallimberti_model"
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full_name: "Gallimberti Streamer-to-Leader Model"
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definition: |
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Early (1972) computational model for predicting streamer-to-leader transition.
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Assumes constant stem field, simplified N₂ vibrational-translational (V-T)
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relaxation, and single dominant stem. Qualitatively useful but quantitatively
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unreliable: Liu (2017) showed assumptions do not hold under detailed kinetic
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modeling (45 species, 192 reactions).
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unit: "N/A"
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typical_range: "N/A"
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related_terms: ["transition", "leader", "streamer"]
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related_topics: ["streamers-and-leaders"]
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# --- Terms from Bazelyan & Raizer (2000) ---
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- term: "leader_velocity"
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full_name: "Leader Propagation Velocity"
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definition: |
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Empirical velocity of leader channel advance: v_L = 1500 * sqrt(|Delta_U_t|)
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in cm/s, where Delta_U_t is the tip potential in volts. Derived from extensive
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laboratory spark and lightning data. For TC sparks at 300 kV: ~8.2 km/s.
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Physical basis: conducting streamer length (~1 cm) divided by thermal instability
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contraction time (~1 us) gives ~10 km/s baseline, modulated by tip voltage.
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unit: "cm/s or m/s"
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typical_range: "5-15 km/s for TC voltages (100-600 kV)"
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related_terms: ["dL_dt", "E_propagation", "transition"]
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related_topics: ["streamers-and-leaders", "energy-and-growth"]
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- term: "electron_attachment_time"
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full_name: "Electron Attachment Time in Cool Air"
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definition: |
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Time for free electrons to attach to O2 molecules in cool (non-heated) air
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at atmospheric pressure: ~100 ns (10^-7 s). This is the fundamental timescale
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for plasma decay without heating. At T > 5000 K, attachment becomes negligible.
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At TC frequencies (50-400 kHz), a cold streamer undergoes 12-100 attachment
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times per half-cycle, explaining why heating is essential for persistent channels.
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unit: "s (seconds)"
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typical_range: "~10^-7 s at STP, increases with temperature"
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related_terms: ["streamer", "transition", "tau_thermal", "n_e"]
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related_topics: ["streamers-and-leaders", "thermal-physics"]
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- term: "Bazelyan_VI"
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full_name: "Bazelyan V-I Characteristic"
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definition: |
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Simple relationship between arc/leader current and internal electric field
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in air at atmospheric pressure: i * E = b, where b = 300 V*A/cm. Equivalently,
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R_per_meter = 30,000 / i^2 (ohm/m). Valid for moderate currents (1-100 A).
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Agrees with da Silva's R = A/I^b power law within factor ~2 for TC-relevant
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currents (1-10 A). A quick approximation complementing the more detailed
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three-regime da Silva model.
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unit: "V*A/cm"
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typical_range: "b = 300 V*A/cm (constant)"
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related_terms: ["nonlinear_resistance", "mayr_equation", "hungry_streamer"]
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related_topics: ["streamers-and-leaders", "equations-and-bounds"]
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- term: "energy_ceiling"
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full_name: "Energy Ceiling from Tip Capacitance"
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definition: |
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Maximum energy available per unit length of new channel from the electrostatic
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charge stored at the spark tip: W_max = pi * epsilon_0 * U^2 (J/m), where U
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is the tip potential. For a TC at 300 kV: W_max ~ 25 J/m. The tip (hemisphere)
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stores ln(L/r) times more energy per unit length than the channel body, making
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the tip the primary energy source for initiating each new leader step.
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unit: "J/m"
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typical_range: "3-100 J/m for TC voltages (100-600 kV)"
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related_terms: ["epsilon", "V_tip", "C_mut", "C_sh"]
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related_topics: ["energy-and-growth", "equations-and-bounds"]
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- term: "conductance_relaxation"
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full_name: "Conductance Relaxation Model"
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definition: |
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A dynamic model for time-dependent spark channel conductance:
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dG/dt = [G_st(i) - G(t)] / tau_g, where G_st(i) is the equilibrium conductance
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at current i, and tau_g is an asymmetric time constant: 40 us for heating
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(current rising) and 200 us for cooling (current decreasing). Alternative to
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the Mayr equation; more physical for large transients. The 5:1 heating/cooling
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asymmetry creates a ratcheting effect that favors leader maintenance.
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unit: "S/m (conductance per unit length)"
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typical_range: "tau_g = 40 us (heating), 200 us (cooling)"
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related_terms: ["Mayr_equation", "thermal_ionization", "leader"]
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related_topics: ["thermal-physics", "equations-and-bounds"]
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- term: "corona_shielding"
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full_name: "Corona Shielding Rate Limit"
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definition: |
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The maximum voltage growth rate at which a stable corona can persist on an
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electrode, shielding it from streamer inception: A_u_max ~ 3.6 kV/us. Above
|
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this rate, ions cannot drift fast enough to maintain the space charge cloud
|
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that stabilizes the surface field. TC toploads reach ~300 kV/us (at 200 kHz),
|
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far exceeding this limit, so corona shielding never applies — every cycle
|
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immediately produces streamers.
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unit: "kV/us"
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typical_range: "3.6 kV/us (limit); TC toploads: ~300 kV/us"
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related_terms: ["E_inception", "streamer", "leader"]
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related_topics: ["field-thresholds", "streamers-and-leaders"]
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- term: "stepped_leader"
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full_name: "Stepped Leader Propagation"
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definition: |
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A leader that advances in discrete jumps separated by pauses, characteristic
|
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of negative polarity leaders. Lightning step length: 10-200 m (avg 30 m),
|
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with pauses of 30-90 us. TC sparks on the negative half-cycle could exhibit
|
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stepping, but the fast AC reversal (half-period 1.25-10 us) masks this.
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In contrast, positive leaders propagate continuously. When averaged over
|
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total development time, stepped and continuous leaders have similar velocities
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(10^5-10^6 m/s).
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unit: "dimensionless (mode classification)"
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typical_range: "step length: 10-200 m; pause: 30-90 us"
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related_terms: ["leader", "leader_velocity", "dart_leader"]
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related_topics: ["streamers-and-leaders", "thermal-physics"]
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- term: "dart_leader"
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full_name: "Dart Leader (Re-strike Leader)"
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definition: |
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A leader that re-illuminates an existing hot channel from a previous stroke.
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Always continuous (not stepped), propagating at (1-4)*10^7 m/s — much faster
|
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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
|
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a persistent hot channel from a previous QCW ramp cycle.
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unit: "m/s (velocity)"
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typical_range: "(1-4) * 10^7 m/s"
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related_terms: ["leader", "stepped_leader", "leader_velocity"]
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related_topics: ["streamers-and-leaders", "thermal-physics"]
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- term: "leader_formation_threshold"
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|
full_name: "Minimum Voltage for Leader Formation"
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definition: |
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The minimum potential difference required to excite and develop a leader
|
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in air under normal conditions: Delta_U_min ~ 300-400 kV. Below this,
|
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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.
|
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unit: "kV"
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typical_range: "300-400 kV"
|
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related_terms: ["leader", "leader_velocity", "E_inception"]
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related_topics: ["streamers-and-leaders", "field-thresholds"]
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- term: "driven_leader"
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full_name: "Driven Leader (QCW Growth Mode)"
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definition: |
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The leader propagation mode unique to QCW Tesla coils, where the leader
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|
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
|
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intermediate between free streamers (~10^6 m/s) and natural lightning leaders
|
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(~10^4 m/s averaged). A 10 ms ramp yields ~1.7 m; 20 ms yields ~3.4 m.
|
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unit: "m/s (growth rate)"
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typical_range: "~170 m/s; step time ~60 us"
|
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related_terms: ["leader", "QCW", "conductance_relaxation", "leader_velocity"]
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related_topics: ["streamers-and-leaders", "thermal-physics", "energy-and-growth"]
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|
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- term: "sword_spark"
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|
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.
|
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unit: "N/A"
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typical_range: "1-3.4 m length at 300-600 kHz"
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related_terms: ["QCW", "driven_leader", "leader", "frequency_threshold"]
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related_topics: ["streamers-and-leaders", "thermal-physics"]
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|
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- 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)"
|
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typical_range: "~80 us"
|
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related_terms: ["burst_mode", "tau_thermal", "QCW", "streamer"]
|
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related_topics: ["thermal-physics", "energy-and-growth"]
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- 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"]
|