Exploding Wire: A Copper Thread Becomes Plasma in Ten Microseconds

A hundred joules into half a milligram

Take a copper wire 50 µm across — about half the width of a human hair — and 30 mm long. Its cross-section is 2.0×10⁻⁹ m² and at copper's density of 8,960 kg·m⁻³ it weighs 0.53 mg. Clamp it between two low-inductance electrodes, connect a 2 µF capacitor bank charged to 10 kV — about 100 J, the kinetic energy of a professionally served tennis ball — and close the switch.

Current rises at roughly V/L ≈ 3×10⁹ A·s⁻¹ in a 3 µH loop and reaches several kiloamps within microseconds, a current density near 4×10¹² A·m⁻². What follows is repeatable enough to serve as a laboratory clock:

• 0–2 µs — solid heating. The wire glows, then whitens. Resistivity climbs with temperature, so the heating accelerates.
• ~2–3 µs — melt and superheat. Copper melts at 1,358 K, but inertia and its own magnetic pressure hold the liquid column together. It sails past the 2,835 K boiling point without boiling.
• ~3–5 µs — burst. At roughly 0.8–0.9 of the critical temperature the metastable liquid nucleates bubbles everywhere at once and blows itself apart.
• +50–500 ns — the dwell. Resistance leaps by three to four orders of magnitude, current collapses, and the inductive kick L·dI/dt drives tens of kilovolts across the gap.
• Restrike. The field exceeds the vapour's breakdown strength; a second current pulse burns as an arc through the wire's own atoms.
• 10 µs onward. Debris streams outward at 1–5 km·s⁻¹ and a cylindrical shock reaches a few centimetres, arriving as a sharp crack.

Volumetric heating: the governing relation and the numbers

Everything rests on one expression for ohmic power per unit volume, p = ρ_e j². With cold copper (ρ_e = 1.7×10⁻⁸ Ω·m) at j = 4×10¹² A·m⁻², p = 2.7×10¹⁷ W·m⁻³, or about 3×10¹³ W per kilogram. Copper needs roughly 6 MJ·kg⁻¹ to reach full vapour: ~0.4 MJ·kg⁻¹ of sensible heat to the melt at 385 J·kg⁻¹K⁻¹, 0.21 MJ·kg⁻¹ of latent heat of fusion, ~0.7 MJ·kg⁻¹ through the liquid, then the dominant term — 4.73 MJ·kg⁻¹ of latent heat of vaporisation. At 3×10¹³ W·kg⁻¹ that budget is delivered in about 200 ns; because a real bank ramps its current rather than switching it on flat, the burst lands at 1–10 µs. For our 0.53 mg wire the whole vaporisation bill is just 3.2 J of the 100 J stored.

Engineers compress this into the action integral ∫j²dt, which for copper reaches vaporisation at of order 10¹⁷ A²·s·m⁻⁴. So long as the heating stays adiabatic and the current fills the cross-section, it depends only on the material and not on wire size — which is why the same figure of merit turns up in fuse short-circuit ratings and in wire-array design. The caveat is real: on millisecond overloads conduction to the leads bleeds heat away, and on nanosecond drivers the current crowds into a skin, so at both extremes the constant stops holding.

Two length scales explain why the heating is genuinely volumetric rather than skin-deep. The skin depth δ = √(ρ_e/πfµ₀) at ~500 kHz is about 90 µm in copper, comfortably larger than the wire's 25 µm radius, so current fills the cross-section uniformly. And the thermal diffusion length √(αt), with α = 1.1×10⁻⁴ m²·s⁻¹, is only ~10 µm in 1 µs — heat cannot escape down 30 mm of wire to the electrodes in the time available. The wire is heated everywhere at once, and adiabatically.

The phase explosion: why the liquid never boils

Ordinary boiling is heterogeneous: bubbles nucleate on surfaces, impurities and container walls, and the liquid stays near its equilibrium boiling point while latent heat is consumed. That needs time, and a free surface. An exploding wire denies it both. Energy arrives faster than bubbles can grow and faster than the column can expand, so the liquid copper is driven into a metastable superheated state, following an essentially isochoric path on the phase diagram rather than the equilibrium vapour curve.

Metastability has a hard limit. As the temperature approaches roughly 0.8–0.9 T_c, the rate of homogeneous nucleation — bubbles forming spontaneously in the bulk from thermal fluctuations, no wall required — rises by tens of orders of magnitude over a narrow temperature interval, and the liquid disintegrates in bulk into droplets and vapour. This is a phase explosion, the same mechanism that limits nanosecond laser ablation of metals, and it is why exploding-wire debris is largely nanometre-scale droplets rather than free atoms.

The governing limit is copper's critical point, and here the physics is genuinely unsettled. Estimates cluster near T_c ≈ 7,000–9,000 K with P_c of order 0.5–1 GPa, but they come from extrapolated equations of state, not direct measurement: no container survives those conditions. Exploding wires are among the few tools that get close.

Dwell and restrike: the signature no fuse has

When the column fragments, its resistivity jumps from ~10⁻⁷ Ω·m in the hot liquid — copper is 1.7×10⁻⁸ Ω·m cold, but climbs more than tenfold on the way to vaporisation — to ~10⁻⁴–10⁻³ Ω·m in the expanded two-phase debris, a factor of 10³–10⁴ within tens of nanoseconds. The circuit sees a switch opening and reacts as any inductive circuit does: the current cannot collapse without the inductance opposing it, and the energy ½LI² stored in the loop's field is driven into the opening gap as a steep voltage. With L = 3 µH and current falling from 8 kA in 100 ns, L·dI/dt is of order 10⁵ V — an upper bound, since in practice the current sags rather than switching off, which is why measured dwell voltages are usually tens of kilovolts. That interval — low current, enormous voltage, dim emission — is the dwell (or current pause), and it is the unambiguous fingerprint of a true wire explosion.

The dwell ends when the field across the expanding, partly ionised copper vapour exceeds its breakdown strength. The vapour ionises and the discharge restrikes: a second current pulse flows through a plasma made entirely of the wire's own atoms, reaching brightness temperatures of 20,000–40,000 K, far above the Sun's 5,772 K photosphere. That is precisely why John A. Anderson at Mount Wilson Observatory pressed exploding wires into service around 1920 as a calibrated high-temperature flash source and opacity standard.

Whether restrike happens at all depends on the ratio of energy deposited before burst to the vaporisation enthalpy. A fast, low-inductance bank can deposit several times that enthalpy and give a bright, essentially complete explosion; a sluggish bank deposits less than one and yields a long, ordinary-looking arc. In vacuum, restrike is near-universal, and the wire develops a dense, poorly conducting core wrapped in a hot low-density corona that carries most of the current.

The magnetic squeeze and the striations

A wire carrying a large current sits inside its own azimuthal magnetic field, and the resulting J×B force points inward all the way around — the conductor squeezes itself. At the surface of a 50 µm wire carrying 10 kA, B = µ₀I/2πr ≈ 80 T, and the magnetic pressure B²/2µ₀ ≈ 2.5 GPa. That is far above copper's yield strength (~70 MPa) and comparable to the vapour pressure near the critical point, so the pinch genuinely helps confine the superheating liquid — part of why the metastable state survives long enough to explode rather than boil.

It also seeds instability. A cylindrical current channel is unstable to the m = 0 sausage mode: where the column necks in, r falls, B ∝ 1/r rises, the inward pressure grows, and the neck pinches harder. Photographs of exploded wires show a ladder of bright bands and dark gaps — striations — with wavelengths from ~0.1 to a few millimetres, often strikingly regular.

Their origin is still argued. Some striations are clearly magnetohydrodynamic necking; others appear too early, or in geometries carrying too little current, and are better explained by a purely thermal overheating instability in the two-phase region, where a locally hotter slice becomes more resistive, absorbs more power and runs away. Both mechanisms are real; which dominates depends on current, rise time, wire diameter and ambient pressure, and no single predictive criterion spans the range.

How it is measured — and what it is used to measure

The core electrical diagnostics are a Rogowski coil (a toroidal winding whose output is proportional to dI/dt, integrated to give current) and a resistive or capacitive voltage divider. The subtlety is that the measured voltage is not the resistive voltage: one must subtract the inductive term, V_res = V_meas − L·dI/dt, before the deposited energy ∫I·V_res·dt means anything. Getting L right to a few percent separates a credible energy-deposition curve from nonsense.

Optically, the toolkit is nanosecond-gated framing and streak cameras, laser shadowgraphy and schlieren to track the expansion front and shock, and Mach–Zehnder interferometry at 532 nm to map density. Emission spectroscopy gives brightness temperature and, via Stark broadening of Cu I lines, electron densities of 10²⁴–10²⁶ m⁻³. For the opaque dense core, laboratories such as Cornell use an X-pinch — two crossed 10–25 µm wires that collapse to a micron-sized, nanosecond keV X-ray source — as a backlighter.

The scientific payoff is that a wire explosion sweeps a metal through the warm dense matter regime, thousands to tens of thousands of kelvin at near-solid density, which no static apparatus can hold. Alan DeSilva and John Katsouros used exploding wires in water to measure the conductivity of dense copper and aluminium plasmas (Physical Review E, 1998), producing benchmark data still used to test Lee–More and quantum-molecular-dynamics models. Yakov Krasik's group at the Technion drives strong converging shocks with underwater wire explosions for equation-of-state work.

From Nairne to the Z machine — and what it is not

Edward Nairne reported wires exploded by Leyden-jar discharges to the Royal Society in 1774. Michael Faraday deflagrated gold wires in his 1857 Bakerian Lecture, using the vapour to deposit the thin gold films whose colours he could not otherwise explain. Anderson turned the flash into an astrophysical instrument in 1920, and W. G. Chace's four Exploding Wires conference volumes (Plenum, 1959–1968) mark the field's post-war maturity.

The consequential application came from Luis Alvarez and Lawrence Johnston at Los Alamos in 1944: the exploding-bridgewire detonator, in which a fast capacitor discharge bursts a fine gold or gold–platinum bridge and the shock initiates PETN directly. Because only a genuine high-current burst will do it, an EBW is insensitive to static discharge and stray currents while firing with sub-0.1 µs jitter — exactly what an implosion lens needs. EBWs fired the Trinity device on 16 July 1945. Today Sandia's Z machine bursts arrays of ~300 tungsten wires 7.5 µm in diameter at ~20 MA in ~100 ns, converting the imploding plasma into ~1.8 MJ of soft X-rays, and groups at Tomsk make 20–100 nm metal nanopowders by exploding wire in inert gas.

Two confusions recur. The first is a fuse simply melting: a fuse works at ~10⁷–10⁸ A·m⁻² over milliseconds, heat has time to conduct to the leads, so the wire fails at one hot spot and the arc is quenched. The tell is dwell-and-restrike on the current trace — a fuse has neither. The second is combustion. Nothing burns: the wire explodes identically in vacuum, argon or water, and the arithmetic rules chemistry out — fully oxidising 0.53 mg of copper releases about 1.3 J, less than half the 3.2 J needed merely to vaporise it. Aluminium is the honest exception, its ~31 MJ·kg⁻¹ oxidation enthalpy giving a real afterburn in air.

Open questions remain substantial. Copper's critical point is still an extrapolation; conductivity models of warm dense metals near the metal–nonmetal transition disagree by factors of several; the breakdown criterion setting dwell duration is empirical rather than predictive; and how much current the dense core carries versus the surrounding corona is a live issue for wire-array pinch design.

One wire, four current regimes — and four completely different outcomes

Regime	Current density	Timescale	Outcome and diagnostic tell
Household fuse blowing	~10⁷–10⁸ A·m⁻²	10 ms – 1 s	Melts at the single hottest spot; the brief arc is quenched by the enclosure — quartz sand in HRC types, the gap alone in a glass cartridge. No dwell, no shock.
Slow overload burn-out	~10⁸–10⁹ A·m⁻²	0.1–10 ms	Wire melts and beads up into droplets by the Plateau–Rayleigh instability; no restrike.
Exploding wire (µs capacitor bank)	~10¹¹–10¹² A·m⁻²	1–10 µs	Uniform superheat to ~0.9 T_c, phase explosion, current dwell, restrike arc at 20,000–40,000 K, cylindrical blast wave.
Exploding bridgewire (EBW) detonator	~10¹¹–10¹² A·m⁻²	1–3 µs	Burst shock initiates PETN directly; firing jitter below ~0.1 µs; insensitive to static and stray currents.
Wire-array Z-pinch (Sandia Z)	≳10¹² A·m⁻² in the ablated corona	~100 ns	~300 tungsten wires at 20 MA ablate and implode; ~1.8 MJ of soft X-rays at ~200 TW.