Plasma is the fourth state of matter—an ionised gas in which electrons have been stripped from atoms, leaving a mixture of free electrons and positive ions that respond collectively to electromagnetic fields. It constitutes over 99% of visible matter in the universe, from stellar interiors and solar wind to lightning bolts and fluorescent lamps. Particle-in-cell (PIC) simulations track macroparticles (each representing many real particles) moving under self-consistently computed E and B fields.
This PIC simulation lets you observe charge separation, collective Langmuir oscillations at the plasma frequency ωp, and the transition from neutral gas to plasma as ionisation degree increases. Adjust particle density, temperature, and background magnetic field to see how these parameters shape plasma behaviour.
What defines a plasma and how is it different from a gas?
A plasma is an ionised gas in which enough electrons have been freed from atoms that the mixture exhibits collective electromagnetic behaviour. Unlike a neutral gas, a plasma is quasi-neutral overall but responds to fields: it screens electrostatic charges over the Debye length, supports wave modes absent in neutral gases, and is strongly affected by magnetic fields. The key criteria are that the Debye length is much smaller than the system size, and there are many particles per Debye sphere.
What is charge separation in a plasma?
If electrons are displaced from their equilibrium positions relative to the heavier ions (which are effectively stationary on electron timescales), a restoring electric field builds up. This field pulls the electrons back, but their inertia causes them to overshoot, setting up oscillations at the plasma frequency ωp = √(ne²/ε₀me). For a solar wind density of 5 × 10⁶ m⁻³, ωp corresponds to about 20 kHz.
What is the particle-in-cell (PIC) method?
PIC is a computational technique where macroparticles (each representing 10⁶–10¹² real particles) are tracked in continuous position-velocity space, while fields are computed on a fixed grid. Particle positions are used to deposit charge/current onto the grid; field equations are solved on the grid; then fields are interpolated back to particle positions to update velocities (via the Lorentz force). PIC is the gold standard for kinetic plasma simulations.
Ionisation occurs when the thermal energy of atoms (or photons illuminating them) exceeds the ionisation potential. For hydrogen this is 13.6 eV, corresponding to temperatures above about 10,000 K. At solar core temperatures (15 MK) all matter is fully ionised. In laboratory discharges, electric fields accelerate electrons to ionise gas at much lower bulk temperatures. The Saha equation gives the ionisation fraction as a function of T and n.
Charged particles in a magnetic field undergo circular motion (cyclotron motion) perpendicular to B, with radius r = mv⊥/(qB). Ions gyrate at the ion cyclotron frequency Ωi = qB/mi; electrons at Ωe = eB/me (much faster). Magnetic fields can confine plasma (as in tokamaks), support additional wave modes (Alfvén waves, whistler waves), and cause plasma to drift when field gradients or curvatures are present.
On scales larger than the Debye length λD = √(ε₀kBTe/ne²), a plasma is quasi-neutral: the electron and ion charge densities are approximately equal (ne ≈ Zni). Any local charge imbalance is screened out exponentially over λD. For a warm laboratory plasma with Te = 10 eV and n = 10¹⁶ m⁻³, λD ≈ 0.7 mm—far smaller than a typical plasma vessel.
Plasma physics underpins nuclear fusion energy research (tokamaks, stellarators, inertial confinement), plasma-based semiconductor etching (reactive ion etching in chip fabrication), plasma thrusters for spacecraft, neon and fluorescent lighting, plasma sterilisation of medical equipment, and plasma-assisted combustion. The Sun's energy production depends entirely on high-temperature plasma enabling nuclear fusion.
Debye shielding is the process by which free charges in a plasma rearrange to neutralise any external electric field beyond the Debye length. This means a single ion placed in a plasma is surrounded by a slight excess of electrons within λD, effectively reducing its apparent charge to zero at larger distances. This collective screening is what distinguishes a plasma from an ionised gas of independent particles.
As energy is added (thermal, electromagnetic, or collisional), ionisation events create electron-ion pairs. If the ionisation rate exceeds the recombination rate (which depends on density and temperature), the ionisation degree rises. In a gas discharge, a critical electric field causes avalanche ionisation (Townsend breakdown), rapidly transforming the neutral gas into a conducting plasma. The breakdown voltage for air at atmospheric pressure is about 3 MV/m.
The solar wind is a continuous stream of plasma (mostly protons and electrons at 400–800 km/s) expelled from the Sun's corona. It is supersonic and super-Alfvénic by the time it passes 10 solar radii. Its interaction with Earth's magnetosphere—itself a magnetised plasma—drives geomagnetic storms, auroras, and can induce currents in power grids. Understanding solar wind PIC dynamics is essential for space weather forecasting.
This sandbox runs a direct, particle-by-particle N-body Coulomb solver: every charge pulls or pushes on every other charge with F = k·q₁q₂/r², summed pairwise each frame with a small softening term so particles never fling apart at zero distance. Switch on the magnetic field slider and each particle also feels the Lorentz force q(v × B), bending its path into circular gyration rather than a straight line. Three confinement modes — Free, Z-Pinch and Torus — add extra inward forces that mimic how real magnetic bottles squeeze a plasma column.
Positive ions (larger, purple) and lighter, faster electrons (cyan) drift and collide electrostatically inside a circular confinement wall. Trails trace each particle's recent path, and an optional arrow grid renders the instantaneous electric field these charges create.
Sliders set particle count (40–300), temperature (0.1–5.0 kK, which sets initial speed), magnetic field B (0–2.0 T, which adds circular gyration), and the ion/electron ratio (0.1–0.9). Mode buttons switch between Free, Z-Pinch and Torus confinement; Reset, Pause, Trails and E-Field buttons control playback and overlays.
Real Z-pinch devices confine plasma using the magnetic field generated by the plasma's own current — the same self-squeezing principle this mode approximates by pulling every particle toward the central axis.
Every frame it loops over all unique pairs of particles and computes the Coulomb force F = k times q1 times q2 divided by r squared, where k is a scaled constant and r is the distance between the pair. A small softening value is added to r squared so the force never blows up when two particles get very close. The resulting force is split into x and y components and applied as acceleration to both particles in the pair, scaled by each particle's mass.
Raising the magnetic field B slider adds a Lorentz force term to every charged particle equal to q times v cross B. In this two dimensional view that works out to an extra acceleration proportional to the particle's velocity, perpendicular to its direction of travel, which curves its path into circular or spiral gyration instead of a straight line. Ions and electrons carry opposite charge sign, so they gyrate in opposite senses.
Free mode applies no extra confinement beyond the outer circular wall, so particles interact only through Coulomb repulsion and any magnetic field. Z-Pinch mode adds a steady inward force pulling every particle toward a central vertical axis, approximating how current-generated magnetic fields compress a real plasma column. Torus mode instead pulls particles toward a target radius around the centre, so they settle into a ring shape similar to confinement in a doughnut-shaped magnetic bottle.
Ions are created with four times the mass of electrons and a positive charge, while electrons are lighter and negatively charged and are given roughly twice the initial speed. Because acceleration from a given force is inversely proportional to mass, the lighter electrons respond much more quickly to both the Coulomb forces and the magnetic field, while the heavier ions drift more slowly, similar to the mass disparity in real plasmas.
Particles is simply the current count of simulated charges. Avg KE is the average kinetic energy per particle, computed from each particle's mass and speed squared and displayed in scaled electron volt units. Temp converts that same kinetic energy into a rough temperature in thousands of kelvin. Ionisation percent is the fraction of particles that are positive ions rather than electrons, set directly by the ion or electron ratio slider.