The Coilgun: Launching a Slug With Pure Magnetism

The Machine: A Capacitor, a Coil, and a Slug

Strip a coilgun to its essentials and you find three parts. A capacitor bank stores the energy — often a few hundred volts across thousands of microfarads, holding anywhere from a few joules to a few hundred. A short, fat coil of heavy magnet wire, wound around a non-magnetic barrel, is the electromagnet. And a small ferromagnetic projectile — a slug of soft, low-carbon iron or steel — sits just behind the coil's mouth, free to slide down the barrel.

Pull the trigger and a switch — a thyristor (SCR), an IGBT, or on hobby rigs sometimes a beefy relay — connects the charged capacitor to the coil. Current explodes from near zero to hundreds or thousands of amps in well under a millisecond. The coil becomes a solenoid with a field of a tesla or more concentrated in its throat, and the iron slug is hauled bodily toward the center of the coil.

• No propellant, no expanding gas. Unlike a gun or a light-gas launcher, nothing burns and nothing pushes from behind — the projectile is pulled from the front by a field.
• No sliding electrical contact. The slug never has to conduct the coil current, which is exactly what sets a coilgun apart from a railgun.
• The whole event is over in milliseconds. The interesting physics happens in the time it takes the capacitor to ring down through the coil.

Why the Iron Gets Pulled In: The Reluctance Force

A ferromagnetic slug is drawn toward the strongest part of a magnetic field. The cleanest way to see the force is through energy. A coil carrying current I stores magnetic energy set by its inductance L; sliding a high-permeability iron slug into the coil raises that inductance, because the iron concentrates the flux. The mechanical force on the slug is the rate at which magnetic co-energy changes with position:

F = ½·I²·(dL/dx)

As the slug moves from outside the coil toward the middle, L is climbing, so dL/dx is positive and F points inward — the slug is sucked toward the coil's throat. Equivalently, in field language the force per unit volume on soft magnetic material scales as the gradient of B², always pointing toward the region of strongest field. The projectile is a piece of iron trying to lower the system's magnetic reluctance by parking itself where the flux is densest, exactly as a compass needle tries to align with a field.

Two hard limits cap this force. First, saturation: once the iron is fully magnetized — around B_s ≈ 1.5–2.1 T for iron and steel — pouring in more current no longer increases its magnetization, and the force stops scaling with B². Second, the force depends on I², so it does not care about the current's direction — reversing the polarity of the coil does nothing. That indifference is precisely why the coilgun cannot simply flip its field to fix the problem it is about to run into.

The Suck-Back Problem and the Tyranny of Timing

Here is the trap that defines coilgun design. The reluctance force is attractive toward the coil center — from either side. While the slug approaches the middle, dL/dx > 0 and the field accelerates it forward. At the exact center the inductance is maximal, dL/dx = 0, and the force vanishes. Once the slug passes the center, dL/dx flips negative and the same field now decelerates it, trying to drag it back into the throat. This is the notorious suck-back.

If the current were left on for the whole transit, the pull-in and the pull-back would nearly cancel and the slug would barely leave, oscillating around the coil like a mass on a magnetic spring. The only way to net a launch is to make sure the coil is de-energized by the time the slug reaches center, so it coasts out the far side carrying the momentum it gained on the way in. Practical designs achieve this several ways:

• Ring the capacitor down fast. Size L and C so the current pulse has largely decayed by the moment the slug hits the middle — the discharge is essentially finished before suck-back can bite.
• Freewheel diode. A diode across the coil lets the stored magnetic energy circulate and die away smoothly after the capacitor empties, instead of reversing.
• Active switching. An optical gate or Hall sensor detects the slug's position and commands an IGBT to cut the current at the optimum instant — the closest thing to "perfect" timing.

Because the force depends on I² and the ideal cut-off is a knife-edge in time, a coilgun's performance is dominated far more by when the current turns off than by how much energy you dumped in.

One Shot, Step by Step

Follow a single-stage discharge. The capacitor and coil form an RLC circuit: the capacitance C, the coil inductance L, and the resistance R of the wire and switch. The stored energy is

E = ½·C·V²

so a modest 4,000 µF bank at 400 V holds ½·(4×10⁻³)·(400)² ≈ 320 J. When the switch closes, current rises like a damped sinusoid, peaking at roughly I_peak ≈ V·√(C/L). For C = 1 mF and L = 100 µH that is about 400·√(10⁻³/10⁻⁴) ≈ 1,300 A, reached in a quarter-period of order (π/2)·√(LC) ≈ 0.5 ms. The current pulse, the slug's transit, and the switch-off all have to interlock on this sub-millisecond stage.

Two loss channels bleed the shot even before suck-back:

• Resistive heating. Hundreds of amps through milliohms of wire dissipate real power as I²R; the coil audibly buzzes and warms with every shot.
• Eddy currents and field diffusion. The slug is a conductor, so the rising field induces circulating currents in it (Lenz's law) that oppose field penetration. If the pulse is too fast, the field cannot soak into the iron within the magnetic-diffusion time and the interior is shielded — the reluctance force drops, and the induced currents even push outward. This is why coilgun slugs are soft iron rather than good conductors, and why the pulse must not be arbitrarily brief.

Velocity is measured the way ballisticians measure any projectile — a pair of light gates times the slug over a known gap, or a ballistic pendulum catches it and reports the momentum — while coil current is read with a Rogowski coil or a low-inductance shunt.

Stacking Stages: The Multi-Stage Gauss Gun

A single coil can only do so much: it must switch off at its own center, so it gives the slug one clean kick and no more. To go faster you chain coils in series down the barrel and fire each in turn, precisely as the slug arrives. Each stage catches the projectile already moving, adds another increment of speed, and shuts off before its own suck-back region — a linear accelerator built from reluctance kicks.

The catch compounds with success. Because the slug is faster at every successive stage, the time it spends inside each coil shrinks, so the timing windows get tighter and tighter down the line. Later stages demand faster switching and often shorter, snappier current pulses. Designers instrument the barrel with a photodiode gate or Hall sensor at each stage and let a microcontroller fire the next capacitor bank the instant the slug breaks the beam.

Well-tuned multi-stage reluctance coilguns push projectiles past 100 m/s, and the more stages you add — with enough capacitor energy and clean timing — the higher you climb. But every stage is still an inefficient reluctance kick, so the gains come at a steep cost in stored energy, switching hardware, and heat.

Coilgun vs. Railgun: Two Ways to Push With Magnetism

The coilgun's famous rival, the railgun, works on an entirely different force. Two parallel conducting rails carry a colossal current up one side, across a sliding conductive armature (or a plasma), and back down the other. The rails' own magnetic field crosses the armature current, and the Lorentz force F = I L × B drives the armature — and the payload riding it — forward. In terms of the rails' inductance gradient L′ (typically ~0.5 µH/m), the thrust is F = ½·L′·I², and it always points down the barrel, so there is no suck-back. The price is that the armature must conduct millions of amps through a sliding contact: railguns suffer violent rail erosion and need staggering pulsed-power supplies. The US Navy's electromagnetic railgun reached about 2,500 m/s (Mach 7) and muzzle energies above 30 MJ before the program wound down around 2021.

There is also a middle device — the induction coilgun. Here the projectile is not iron but a conductive ring or sleeve. A fast coil pulse induces eddy currents in it, and by Lenz's law the two opposing fields repel, flinging the armature away — the same physics as Thomson's jumping-ring lecture demo scaled up. Because the force is repulsive and forward, the induction coilgun sidesteps suck-back entirely. Sandia National Laboratories built induction ("reconnection") coilguns in the 1980s for hypervelocity-launch research, reaching far higher speeds than reluctance guns manage, though at the cost of intense heating in the armature.

Why Efficiency Is So Low — and What It's Good For

Coilguns are famously wasteful. A simple single-stage reluctance gun typically converts only ~1–5% of its stored capacitor energy into projectile kinetic energy; even carefully optimized multi-stage machines struggle to reach the tens of percent. The losses are everywhere: I²R heating in the windings, eddy currents and hysteresis in the iron, magnetic energy left circulating in the coil at cut-off, and — worst of all — any residual suck-back from imperfect timing.

The projectile itself is chosen to fight these losses. It is soft magnetic iron — high permeability so it is grabbed hard, but low remanence and coercivity (little magnetic hysteresis) so it does not stay magnetized and stick to the coil after the shot. A slug of hard magnetic steel would cling to the field it was supposed to escape.

The idea is old. The Norwegian physicist Kristian Birkeland — better known for explaining the aurora — patented an "electromagnetic cannon" in 1901 and built several coilguns; a 1903 public demonstration ended when a short circuit threw a spectacular arc across the hall, and his gun reached only about 50 m/s, far short of the supersonic speeds he had promised investors. That gap between promise and physics has haunted coilguns ever since. Today they thrive mainly as a maker's proving ground for pulsed power and timing, but the concept persists in serious proposals for electromagnetic space launch — NASA's studied Maglifter launch-assist track and the superconducting StarTram concept both imagine accelerating vehicles with staged coils, trading the coilgun's low efficiency for the priceless advantage of leaving the propellant on the ground.

Three ways to push a projectile with magnetism — the reluctance coilgun, its induction cousin, and the railgun.

Property	Reluctance coilgun	Induction coilgun	Railgun
Projectile	Ferromagnetic (soft iron) slug	Conductive ring/sleeve armature	Conductive armature bridging two rails
Force mechanism	Reluctance pull, F = ½I²·dL/dx toward peak field	Induced eddy currents repelled (Lenz's law)	Lorentz force F = ½·L′·I² on the armature
Sliding contact?	None — projectile never touches the coil	None	Yes — armature slides on the rails (erosion)
The suck-back problem	Severe — must kill current at coil center	Absent — force is purely repulsive	Absent — force is always forward
Typical muzzle speed	Tens of m/s (single stage); >100 m/s multi-stage	Hundreds of m/s to km/s (research)	~2,500 m/s (Mach 7) demonstrated
Main limit	Timing, iron saturation, resistive loss	Skin-depth heating, low coupling	Megaampere currents, rail erosion