Corona Discharge: The Glow at the Edge of High Voltage

The threshold: where air stops being an insulator

Dry air is an excellent insulator until the electric field reaches the dielectric strength of air, E₀ ≈ 3.0 MV/m (equivalently 30 kV/cm, or 3 kV/mm) at standard temperature and pressure. Below this field a stray free electron — always present from cosmic rays and background radioactivity at roughly 10 ion pairs per cm³ per second — drifts along without much consequence. Above it, the electron gains enough kinetic energy between collisions to knock an outer electron off an N₂ or O₂ molecule (ionization energies ≈ 15.6 eV and 12.1 eV respectively), producing a second free electron.

The crucial point about corona is that the field is non-uniform. Around a thin wire or a sharp point, the field falls off steeply with distance, so the 3 MV/m threshold is exceeded only in a thin shell right at the conductor. Ionization is confined there — a partial discharge — while the bulk of the gap stays below breakdown. For a cylindrical conductor of radius r at potential V surrounded by a coaxial ground at radius R, the surface field is:

• E(r) = V / [r · ln(R/r)]

Halve the wire radius and, for the same voltage, the surface field roughly doubles. This is exactly why corona haunts thin conductors, frayed strands, sharp burrs, and pointed lightning rods — small r means enormous local E even at modest voltage.

The Townsend avalanche: exponential multiplication

The engine of corona is the electron avalanche described by John Townsend (c. 1900). Each electron, drifting through the high-field shell, produces on average α new ionizing collisions per metre — the first Townsend ionization coefficient. Over a distance dx the electron population grows as:

• dn/n = α dx ⟹ n(x) = n₀ eᵅˣ

So a single seed electron becomes eᵅˣ electrons after distance x — an exponential cascade. The coefficient α depends steeply on the field: α/p is a function of E/p (the reduced field), because what matters is the energy gained per mean free path. In air near threshold α reaches ~10³–10⁴ m⁻¹, so an avalanche over a millimetre-scale shell multiplies by factors of e¹⁰ or more.

An avalanche alone would fizzle out — the electrons sweep to the anode and the ions drift away. For a self-sustaining discharge you need a feedback loop that regenerates seed electrons. This is captured by the second Townsend coefficient γ: positive ions striking the cathode (or UV photons from excited molecules) liberate fresh electrons with probability ~γ. The self-sustaining (Townsend) criterion is:

• γ (eᵅᵈ − 1) = 1

where d is the gap. When this equality is met, each avalanche exactly replaces its own seed and the discharge burns steadily. In point-to-plane geometry, photoionization ahead of the avalanche head often dominates the feedback, launching streamers — thin, fast-propagating ionization fingers — in the more energetic corona modes.

Peek's law: predicting the onset voltage

The engineering workhorse is Peek's law, an empirical relation Frank W. Peek Jr. of General Electric fit to thousands of measurements between 1911 and the 1920s. It gives the surface field at which visible corona ignites on a smooth cylindrical conductor:

• Eᵥ = E₀ · δ · (1 + K/√(δ·r))

with E₀ ≈ 3.0 MV/m the intrinsic disruptive gradient, r the conductor radius in metres, K ≈ 0.0301 √m a surface/geometry constant, and δ the relative air density:

• δ = (p/p₀)·(T₀/T) — pressure and temperature corrected to reference (≈ 1 at 25 °C, 101.3 kPa)

Two lessons fall out immediately. First, the √(δr) term means smaller conductors need a higher surface field to spark corona but reach that field at much lower voltage — so thin wires corona easily. Second, corona onset tracks air density: at altitude (lower p and δ), or on hot days, Eᵥ drops and corona worsens, which is why high-voltage lines through mountain passes are engineered with fatter bundled conductors. The multiplicative δ factor is why a spark gap that holds off 30 kV at sea level breaks down at a lower voltage on Denver's mile-high plateau.

A worked estimate: corona on a transmission line

Take a single conductor of radius r = 1.5 cm at δ = 1. Peek's law gives the onset surface gradient:

• Eᵥ = 3.0 × 10⁶ × 1 × (1 + 0.0301/√0.015) = 3.0 × 10⁶ × (1 + 0.246) ≈ 3.74 MV/m

For a conductor of that radius suspended h = 10 m above ground, the surface field is approximately E ≈ V / [r · ln(2h/r)]. Setting E = Eᵥ and solving for the onset line-to-ground voltage:

• ln(2·10 / 0.015) = ln(1333) ≈ 7.20
• V ≈ Eᵥ · r · ln(2h/r) = 3.74 × 10⁶ × 0.015 × 7.20 ≈ 404 kV

So a bare 1.5-cm conductor stays quiet up to a few hundred kilovolts — which is exactly why extra-high-voltage lines use bundled conductors (two, three, or four sub-conductors per phase). Bundling raises the effective radius seen by the field, lowering the surface gradient below Eᵥ and killing the corona. The power lost to corona scales roughly as the square of the voltage excess, P ∝ (V − Vₒₙₛₑₜ)² in Peek's loss formula, and in foul weather (rain drips form sharp micro-points) it can climb from a few kW/km to tens of kW/km — a serious, weather-dependent efficiency penalty summed over thousands of line-kilometres.

Polarity, modes, and the ion wind

Corona is not one thing — its character flips with the electrode's polarity, because electrons and positive ions have wildly different mobilities. Near a sharp electrode the two behave differently:

• Negative corona (Trichel pulses): electrons are repelled outward into weakening field, attach to O₂ to form negative ions, and the discharge self-quenches and reignites in regular current pulses at ~kHz. It produces more ozone and is used in ozone generators and precipitators.
• Positive corona: electrons are drawn into the intense field near the point; propagation relies on photoionization ahead of the front, giving smoother, glow-like or burst/streamer behavior and, at higher voltage, long luminous streamers.

A signature byproduct is the ion wind (electrohydrodynamic or 'corona wind'). Ions created at the point drift toward the far electrode, colliding with ~10¹⁰ neutral molecules each along the way and dragging a net airflow of order 1 m/s. This momentum transfer is the basis of silent, moving-part-free 'ionic' air movers and of experimental EHD thrusters ('lifters'). The thrust per watt is modest — a few newtons per kilowatt — but it is genuinely solid-state propulsion. The same wind is a nuisance in precision electronics, where it stirs dust into a fine deposit.

Where corona shows up: from the power grid to the mast

Corona is ubiquitous wherever high voltage meets sharp geometry:

• St. Elmo's fire: the blue-violet corona glow seen on ship masts, aircraft wingtips, and church spires when a thunderstorm charges the atmosphere to ~10⁴–10⁵ V/m near pointed conductors. Pilots report it as a shimmering discharge on the windscreen.
• Electrostatic precipitators: negative corona charges soot and fly-ash particles, which then migrate to grounded collector plates — removing >99% of particulate mass from coal-plant flue gas.
• Ozone generation and surface treatment: corona in air/oxygen cracks O₂ into atomic O, which recombines as O₃; corona-treating raises the surface energy of plastic films so ink and glue will bond.
• Nuisance and hazard: corona is the leading source of radio and TV interference from power lines (broadband RF from ~0.1 MHz to hundreds of MHz), an audible 'sizzle,' and slow insulation damage — the ozone and UV embrittle polymers and the discharge erodes cable dielectrics, a classic partial-discharge failure mode utilities monitor with acoustic and UV cameras.

The corona's characteristic 120 Hz hum (twice the 60 Hz line frequency, since the field peaks in magnitude twice per cycle) is the acoustic fingerprint of the discharge pulsing on and off with the AC waveform.

Subtleties and common misconceptions

Corona is not a spark, and not an arc. A spark is a complete conducting bridge across the gap; corona is a partial, self-limited discharge that never bridges. This distinction matters: corona draws microamps to milliamps and dissipates watts, whereas an arc draws amperes and dissipates kilowatts as a thermal plasma at thousands of kelvin. Corona is a non-thermal (cold) plasma — the electrons are hot (a few eV, ~10⁴–10⁵ K equivalent) but the gas stays near room temperature because the ions and neutrals barely heat up.

'30 kV/cm is the breakdown voltage of air' is only half true. That figure is the dielectric strength for a uniform field over a modest gap; it also depends on gap length through Paschen's law, which shows breakdown voltage has a minimum (~327 V for air near pd ≈ 0.75 kPa·mm) and rises again for very small gaps. Corona lives specifically in the non-uniform, sharp-electrode regime where the threshold is a local surface condition, not a gap average.

Sharper is not always better. Lightning rods are pointed to encourage corona and bleed off charge quietly — but blunt-tipped rods can be more reliable at initiating an upward leader because the sharp point's dense space charge shields the tip and stalls the streamer. And more corona means more loss: for transmission engineers the goal is to suppress it, using corona rings, grading toroids, and bundled conductors to smooth the field and keep the surface gradient safely below Peek's Eᵥ.

Corona discharge versus a fully developed spark/arc in air

Property	Corona discharge	Spark / arc breakdown
Extent	Thin luminous shell (~mm) around electrode	Full conducting channel bridges the gap
Field geometry	Highly non-uniform (small r, sharp point)	Approx. uniform or fully bridged
Current	μA–mA (self-limited)	A to kA (limited by external circuit)
Onset field (air, STP)	≈ 3 MV/m at the surface	≈ 3 MV/m averaged over whole gap
Gas temperature	Near ambient (non-thermal, ~300 K)	Thermal plasma, 6,000–20,000 K in arc
Energy fate	Ionization, light, ozone, ion wind, RF	Ohmic heating, channel expansion, thunder