Plasma State

Examples of plasma

JavaScript — plasma calculations

const k_B = 1.38e-23;
const e_charge = 1.602e-19;
const epsilon_0 = 8.854e-12;
const m_e = 9.11e-31;

// Debye length
function debyeLength(n_density, T_K) {
  return Math.sqrt(epsilon_0 * k_B * T_K / (n_density * e_charge * e_charge));
}

// Fusion plasma: n = 10²⁰ /m³, T = 10⁸ K
console.log(`Fusion λ_D: ${(debyeLength(1e20, 1e8) * 1000).toFixed(2)} mm`);
// ~0.2 mm — much smaller than reactor size (good)

// Solar wind: n = 5e6 /m³, T = 10⁵ K
console.log(`Solar wind λ_D: ${debyeLength(5e6, 1e5).toFixed(2)} m`);

// Plasma frequency
function plasmaFrequency(n_density) {
  return Math.sqrt(n_density * e_charge * e_charge / (epsilon_0 * m_e));
}

console.log(`Fusion plasma frequency: ${(plasmaFrequency(1e20) / (2 * Math.PI) / 1e9).toFixed(0)} GHz`);
console.log(`Ionosphere frequency: ${(plasmaFrequency(1e12) / (2 * Math.PI) / 1e6).toFixed(1)} MHz`);
// ~9 MHz — explains AM radio reflection from ionosphere

// Plasma parameter Λ (must be >> 1 for ideal plasma)
function plasmaParameter(n_density, T_K) {
  const lambda_D = debyeLength(n_density, T_K);
  return (4/3) * Math.PI * n_density * Math.pow(lambda_D, 3);
}

console.log(`Lab plasma Λ: ${plasmaParameter(1e15, 1e4).toExponential(2)}`);
console.log(`Solar wind Λ: ${plasmaParameter(5e6, 1e5).toExponential(2)}`);
// Both >> 1 — valid plasmas

// Magnetic confinement: gyroradius
function gyroradius(velocity, B, mass = m_e, charge = e_charge) {
  return mass * velocity / (charge * B);
}

// Electron in tokamak: 1 keV at 5 T
const v_e = Math.sqrt(2 * 1000 * e_charge / m_e);
console.log(`Electron gyroradius (1 keV, 5T): ${(gyroradius(v_e, 5) * 1e6).toFixed(1)} µm`);

// Ion gyroradius (deuterium): much larger
const m_d = 3.34e-27;
const v_d = Math.sqrt(2 * 1000 * e_charge / m_d);
console.log(`Deuteron gyroradius (1 keV, 5T): ${(gyroradius(v_d, 5, m_d) * 1000).toFixed(2)} mm`);

// Ionization energy of hydrogen
const E_H_ionize = 13.6;  // eV
const T_H_ionize = E_H_ionize * e_charge / k_B;
console.log(`H ionization T: ${T_H_ionize.toExponential(2)} K`);
// ~158,000 K — but Saha equation shows ionization significant at lower T due to entropy

Where plasma matters

• Astrophysics. Stars, galactic dynamos, accretion disks, intergalactic medium.
• Fusion energy. All approaches involve hot plasma. ITER, NIF, private startups.
• Industrial processing. Plasma etching/deposition for semiconductors; plasma cutting/welding.
• Lighting. Fluorescent, neon, plasma display panels.
• Medical. Plasma sterilization, surgical scalpels.
• Spacecraft. Ion thrusters; ionospheric communication; reentry plasma sheath.
• Atmospheric/space weather. Auroras, solar flares affect ionosphere → comm disruption.

Common mistakes

• Confusing "plasma TV" with regular plasma. Plasma TVs use small gas-discharge plasmas (real plasma). Most modern displays are LCD/OLED (not plasma).
• Treating plasma as just hot gas. Crucial difference — collective behavior. Charged particles interact via long-range Coulomb forces, creating plasma-specific phenomena.
• Forgetting electromagnetic interaction. Plasmas conduct electricity and respond to magnetic fields. MHD is essential at appropriate scales.
• Confusing plasma frequency with cyclotron frequency. Plasma f = √(n·e²/ε₀·m) — collective oscillation. Cyclotron f = qB/m — single particle in magnetic field. Different physics.
• Underestimating plasma's prevalence. 99% of visible universe! Most "matter" we see is plasma (stars). Solid Earth-like objects rare.
• Treating cold plasma like hot. Cold plasma (room T, partial ionization) very different from fusion plasma (millions K, full ionization). Different physics; different applications.