Z-Pinch physics: Axial current Jz →
azimuthal field Bθ → inward Lorentz force
J × B compresses plasma. Sausage (m=0):
symmetric squeezing. Kink (m=1): column bends
sideways. β = 2μ₀nkT / B².
🌀 Z-Pinch
About this simulation
A Z-pinch confines plasma by passing a strong axial electric current
through it: the current generates its own azimuthal magnetic field,
and the resulting Lorentz force squeezes the plasma column inward.
This was one of the earliest approaches to controlled nuclear fusion
and still powers facilities like the Z Machine at Sandia, which
drives radiation experiments and inertial-confinement research. It is
fascinating because the same self-pinching that compresses the plasma
also makes it violently unstable.
How it works
An axial current Jz flows through the plasma column.
It creates an azimuthal magnetic field Bθ wrapping the column.
The inward J × B Lorentz force compresses the plasma toward the axis.
Thermal pressure pushes outward; equilibrium sets the pinch radius — until instabilities (sausage or kink) break it apart.
Key equations
I² = 8π N k T — the Bennett pinch relation, balancing
magnetic compression against thermal pressure (I = current, N = line
density, T = temperature). Plasma beta:
β = 2μ₀ n k T / B² compares plasma pressure to magnetic
pressure.
Current I (MA) — stronger current means tighter, faster compression.
Temperature (keV) — higher thermal pressure widens the equilibrium radius.
Perturbation — sets the seed amplitude that instabilities grow from.
Pause / Reset — freeze the animation or restart the column.
Did you know?
The Z-pinch sausage instability is the same physics that pinches off
a stream of water into droplets — a current-carrying plasma "necks"
wherever it is slightly thinner, because the magnetic field is
stronger there, accelerating the squeeze.
About this simulation
This simulator integrates a simplified magnetohydrodynamic Z-pinch: 180 charged particles orbit inside a cylindrical cross-section while an inward Lorentz-like force −I²·r pulls them toward the axis and an outward thermal-pressure term T/r pushes back, settling at a Bennett-pinch equilibrium radius Req ∝ √T/I (clamped between 0.15 and 1.0). The column is also split into 32 axial segments whose radius or lateral offset is perturbed sinusoidally to seed the two classic ideal-MHD instabilities — the m=0 sausage mode, which periodically necks and bulges the radius along the axis, and the m=1 kink mode, which bends the whole centreline sideways — each growing at a rate proportional to I/(√T·Req).
🔬 What it Shows
Two synchronized views of the same plasma column: the left canvas is a cross-section showing 180 particles and the pinch boundary (with faint magnetic field-line rings), while the right canvas is an axial side profile tracing the column's radius along its length. A growth-percentage readout and colour (amber → red) track how far the selected instability has developed, alongside live Pinch radius, Plasma β, Compression and Time stats.
🎮 How to Use It
Pick Stable, Sausage or Kink from the Mode buttons, then drag Current I (MA) to change the pinch force, Temperature (keV) to change the outward thermal pressure, and Perturbation to set the seed amplitude the instability grows from. Reset reinitializes the 180 particles and 32 segments from scratch; Pause freezes the animation to inspect a moment in detail.
💡 Did You Know?
The Z-pinch's inherent instability is exactly the same physics as the Rayleigh–Plateau instability that breaks a falling stream of water into droplets: a current-carrying column "necks" wherever it happens to be slightly thinner, because the magnetic field is stronger there, accelerating the squeeze — real pulsed-power Z-pinches like Sandia's Z Machine must out-compress this effect within nanoseconds before it destroys the column.
Frequently asked questions
What is a Z-pinch and why is it called that?
A Z-pinch is a plasma-confinement scheme in which a strong current flows along the z-axis of a cylindrical column and generates its own azimuthal magnetic field Bθ. By the Lorentz force law that field pushes back inward on the current-carrying plasma, squeezing — "pinching" — it toward the axis; hence the name. This simulator drives exactly that inward force (∝ −I²·r) against outward thermal pressure (∝ T/r) on 180 particles, settling at a Bennett-like equilibrium radius.
Why does the pinch become unstable instead of just compressing to a steady radius?
A pinched column is only in force balance at one instant; the same feedback that creates the equilibrium also amplifies any small perturbation, because a slightly thinner section still carries the full current through a smaller area, so its magnetic pressure grows faster than thermal pressure can push back. This runaway feedback is what makes an ideal Z-pinch intrinsically unstable, and it is exactly the mechanism the sausage and kink growth-rate formulas in this simulation reproduce.
What is the difference between the sausage (m=0) and kink (m=1) instabilities?
The sausage mode periodically modulates the column's radius along its length — alternating narrow "necks" and bulges — by perturbing each axial segment's radius (segR[]) directly. The kink mode instead displaces the centreline sideways in a snaking pattern without necessarily changing the local radius, by perturbing a lateral offset (segDx[]) per segment. Both grow from the same Perturbation slider, but the simulation gives kink a slightly slower growth-rate factor (0.6) than sausage (0.8).
What is plasma beta (β) and why does the Statistics panel track it?
Plasma beta β = 2μ₀nkT/B² is the ratio of thermal (particle) pressure to magnetic pressure. Low β means the magnetic field dominates and confinement is tight; high β means thermal pressure is comparatively large and the column is looser. The panel recomputes β live from the current Temperature and Current values and the instantaneous equilibrium radius, so raising Temperature or lowering Current visibly pushes β upward.
How do the Current and Temperature sliders change the equilibrium radius and instability growth?
The equilibrium radius follows Req ∝ √T/I: raising Current increases the pinch force (∝ I²), shrinking Req so the Compression stat (R₀/Req) rises; raising Temperature increases outward thermal pressure (∝ T), expanding Req. Both instabilities' growth rates scale as I/(√T·Req), so a hotter, weaker-current column pinches and destabilizes more slowly, while a colder, stronger-current column compresses tightly and grows unstable fast.