# Superconducting magnet A superconducting magnet is an electromagnet whose winding is held cold enough to lose its resistance entirely, so that the [[Electric_current|current]] once established in it does not decay. The [[Electric_power_transmission|electricity]] saved is the least interesting consequence. The interesting one is that a resistanceless winding can be closed on itself and left carrying hundreds of amperes for years, which means it holds megajoules of magnetic [[Energy|energy]] with no slow way to give them back. The critical surface the conductor must stay inside, the quench that follows when it strays out, and the boiling of an entire bath of [[Liquid_helium|liquid helium]] in seconds all descend from that one fact — and that is why [[Helium|helium]] is an industrial necessity here rather than a laboratory convenience. ## Microsims — three.js <iframe src="https://wikitube-3d-microsims.netlify.app/Superconducting_magnet.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Superconducting magnet — three.js microsim"></iframe> **`Superconducting_magnet` (three.js).** The scene sets the two subjects of this article side by side: at left the [[Superconductivity|superconducting]] winding drawn as its real turn stack, at right the conductor's critical surface Jc(T, B) rendered as an actual three-dimensional sheet, with the magnet's operating point inside it, a line dropped to each axis, and the straight load line the point travels along as the [[Electric_current|current]] is ramped. Pick a conductor, then drag *Bath temperature* upward and watch the operating point climb toward the sheet while the HUD names which of the three axes is binding — that naming is the lesson, because a magnet never quenches merely "because it warmed up", it quenches because one of T, B or J crossed a face. Set *Protection* to None and press *Trigger quench*: the normal zone runs along the wire at the physical propagation [[Velocity|velocity]] and sideways at one to three per cent of it, the hot spot sails past the 200 K design limit and on toward the melting point of [[Copper|copper]], and the magnet is scrap. Switch to *Quench heaters* and repeat — the hot spot now barely reaches 100 K and the magnet survives, but the live litres-of-helium counter lands on the same number either way, which is the whole argument: protection saves the magnet, not the helium. ## Microsim ### Live player <div class="microsim-player"> <iframe src="https://editor.p5js.org/sciencenibber/full/Xu7mG4Yo_" width="100%" height="620" frameborder="0" sandbox="allow-scripts allow-same-origin"></iframe> </div> <div class="microsim-fallback"> <img src="Microsims/thumbs/Superconducting_magnet.png" alt="Superconducting_magnet microsim poster" style="width:100%;border:1px solid #4445;border-radius:6px;"> <p><em>Live microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/Xu7mG4Yo_">open sketch in the p5.js editor</a></em></p> </div> **Editor URL:** https://editor.p5js.org/sciencenibber/sketches/Xu7mG4Yo_ **Description (100 words):** A block-diagram microsim of a wet-helium superconducting magnet. The reader sees the power supply, persistent switch, NbTi coil, quench-protection diodes, field probe, and liquid helium bath laid out inside a dashed cryostat envelope, with animated green tokens tracing the active current path. Three sliders drive the current setpoint, ramp rate, and parasitic heat load on the bath. A button toggles between ramp mode (supply drives the coil through the open switch) and persistent mode (switch closes, supply isolated, current circulates losslessly). A second button forces a quench: tokens turn red, current dumps through the diode bank, the bath temperature spikes, and helium boils away. Gauges read current, stored [[Energy|energy]], field, and bath state in real time. ```js // ===================================================================== // Superconducting_magnet.js -- Wikitube microsim // Article: Superconducting_magnet en.wikitube.io/wiki/Superconducting_magnet // Room: Helium Pattern: G (block diagram, system flow, // process chain) // --------------------------------------------------------------------- // Idea: an animated block diagram of a wet-helium superconducting magnet, // showing the closed current loop and the cryogenic envelope around it. // // The reader drives three sliders and two buttons: // // * I_set (0 - 600 A) the magnet current setpoint // * dI/dt (0 - 4 A/s) the ramp rate from supply to coil // * Q_leak (0 - 4 W) parasitic heat load on the He bath // * "persistent / ramp" closes the superconducting switch and isolates // the supply, putting the magnet into persistent // mode where I circulates with zero dissipation // * "trigger quench" forces a small section of NbTi normal, which // cascades, dumps stored energy into the bath, // and boils helium // // Visual layout (720 x 520 canvas): // // [ He cryostat envelope - dashed box ] // [ Power supply ]--leads-->[ Switch ]--->[ Superconducting coil ] // | | | // | | +--> [ Field B at probe ] // +--------------+ // (persistent loop) // // [ Quench-protection diodes ] // parallel to coil // // [ LHe bath gauge ] // [ Boil-off vent ] // // Animated tokens (small dots) travel along the active current path // at a speed proportional to I; the path itself depends on the state // of the persistent switch. Color-coded: // // * green : current flowing in superconducting state (lossless) // * red : current flowing through resistive / normal section // (during a quench) // * grey : idle (no current) // // Gauges on the right read: // // * I (A) magnet current // * B (T) central field, B = mu_0 * n * I (solenoid approx) // * E (kJ) stored magnetic energy, E = (1/2) L I^2 // * T_He (K) bath temperature (rises during quench) // * He (%) liquid level (drops during quench as latent heat // boils off helium) // // Canonical equation (bottom-right): // // E = (1/2) L I^2 [stored magnetic energy in the coil] // // Physics constants used: // * L = 5 H inductance (lab-scale magnet) // * mu_0 * n = 0.012 T/A field per amp (so 600 A -> 7.2 T) // * He_lat = 20.7 J/g latent heat of vaporization of LHe // * He_density = 125 g/L liquid helium density // * V_bath = 100 L nominal bath volume // // Conventions (Wikitube Betterfire Standard v0): // * single ARTICLE constant at the top, single quotes // * p5.disableFriendlyErrors = true to keep the editor console clean // * non-ASCII (Greek mu, arrows, lambda) lives in COMMENTS ONLY; // every text() string literal is ASCII // * Energy-room palette (P5_JS_EDITOR section 4): dark BG, HOT/COLD // tones, STRUCT grey, TRAJ accent // * sliders are placed with .position(x, y).size(w) (never floating) // // Reference: P5_JS_EDITOR.md section 4 (Energy room) is the closest // analog for this room; Pattern G is consumed here as a block diagram // whose nodes have running state variables and animated flow tokens. // ===================================================================== const ARTICLE = 'Superconducting_magnet'; const TITLE = ARTICLE.replace(/_/g, ' '); p5.disableFriendlyErrors = true; // ----- Energy room palette (P5_JS_EDITOR section 4, line 165) -------- const BG = 18; const FG = 240; const DIM = [240, 240, 240, 140]; const HOT = [220, 110, 60]; // resistive / quench / boil-off const COLD = [60, 130, 220]; // LHe / cold side const COLDER = [40, 80, 180]; // superfluid / cryostat fill const STRUCT = [120, 130, 150]; // block outlines, structure const TRAJ = [240, 220, 80]; // probe / accent const SC_GREEN = [80, 220, 130]; // lossless superconducting current const GREY_IDLE = [110, 110, 110]; // idle wires const SCRATCH = [120, 120, 120, 90]; // grid / scratch lines // ----- Physics constants -------------------------------------------- const L_COIL = 5.0; // H, magnet inductance const FIELD_PER_A = 0.012; // T/A, central-field-per-amp (mu_0 * n) const HE_LAT = 20.7; // J/g, latent heat of LHe vaporization const HE_RHO = 125; // g/L, liquid helium density const V_BATH = 100; // L, nominal bath volume const T_BATH_NOM = 4.222; // K, normal boiling point of He at 1 atm const T_QUENCH_PK = 60.0; // K, transient peak after a full dump // ----- Slider / button handles -------------------------------------- let iSetSlider, dIdtSlider, qLeakSlider; let modeButton, quenchButton, resetButton; // ----- Live state ---------------------------------------------------- let I = 0.0; // A, present coil current let mode = 'ramp'; // 'ramp' | 'persistent' | 'quench' let quenchT = 0.0; // seconds since quench started let tBath = T_BATH_NOM; // K let hePct = 100.0; // %, liquid level remaining let flowPhase = 0; // animation phase for current tokens (0..1) // ----- Layout (set in setup; named constants make draw() readable) --- let cryo; // {x, y, w, h} of dashed cryostat envelope let supplyBox; // power supply block let switchBox; // persistent switch block let coilBox; // superconducting coil block let diodeBox; // quench-protection diode block let probeBox; // field probe block let bathBox; // LHe bath gauge block function setup() { createCanvas(720, 520); pixelDensity(2); textFont('system-ui'); // ---- Layout. All boxes are {x, y, w, h} in canvas pixels. ---------- // Cryostat dashed envelope encloses everything cold (switch, coil, // diodes, bath) but NOT the power supply (warm). supplyBox = { x: 30, y: 110, w: 110, h: 60 }; switchBox = { x: 230, y: 110, w: 110, h: 60 }; coilBox = { x: 410, y: 110, w: 150, h: 130 }; diodeBox = { x: 410, y: 270, w: 150, h: 50 }; probeBox = { x: 600, y: 145, w: 80, h: 60 }; bathBox = { x: 230, y: 270, w: 150, h: 50 }; // Cryostat envelope wraps switch + coil + diodes + bath + probe. cryo = { x: 200, y: 80, w: 500, h: 280 }; // ---- Controls. .position(x, y).size(w) per Betterfire Standard. ---- const ctrlY = 410; iSetSlider = createSlider(0, 600, 0, 1 ).position(20, ctrlY + 0).size(180); dIdtSlider = createSlider(0.1, 4, 1, 0.1 ).position(20, ctrlY + 30).size(180); qLeakSlider = createSlider(0, 4, 0.2, 0.05).position(20, ctrlY + 60).size(180); modeButton = createButton('persistent mode (closes switch)'); modeButton.position(260, ctrlY + 0); modeButton.mousePressed(onMode); quenchButton = createButton('trigger quench'); quenchButton.position(260, ctrlY + 30); quenchButton.mousePressed(onQuench); resetButton = createButton('reset (refill bath)'); resetButton.position(260, ctrlY + 60); resetButton.mousePressed(onReset); } // ===================================================================== // Main draw loop // ===================================================================== function draw() { background(BG); const dt = Math.min(deltaTime / 1000, 0.05); // s, clamped per editor stepPhysics(dt); drawCryostatEnvelope(); drawWires(); drawCurrentTokens(); drawBlock(supplyBox, 'POWER SUPPLY', supplyDetail()); drawBlock(switchBox, 'PERSISTENT SWITCH', switchDetail()); drawCoilBlock(); drawBlock(diodeBox, 'QUENCH-PROT. DIODES', diodeDetail()); drawBlock(probeBox, 'FIELD PROBE', probeDetail()); drawBlock(bathBox, 'LIQUID He BATH', bathDetail()); drawGauges(); drawSliderLabels(); drawHUD(); } // ===================================================================== // Physics update -- one forward-Euler step per draw frame // ===================================================================== function stepPhysics(dt) { const iSet = iSetSlider.value(); const dIdt = dIdtSlider.value(); const qLeak = qLeakSlider.value(); if (mode === 'quench') { // ---- Quench dynamics: coil current decays exponentially through // the diode bank. Stored magnetic energy boils LHe. const tauQ = 8.0; // s, dump time constant const dI = -I / tauQ; const dE = -L_COIL * I * dI; // W, into bath const dHe = (dE * dt) / HE_LAT / HE_RHO; // L of LHe boiled this step hePct = Math.max(0, hePct - (dHe / V_BATH) * 100); I = Math.max(0, I + dI * dt); // Bath temperature transient: ramps to peak, decays toward 4.222 K // as residual liquid recovers; floor at NBP. quenchT += dt; const tau = 6.0; const peakFactor = Math.exp(-quenchT / tau); tBath = T_BATH_NOM + (T_QUENCH_PK - T_BATH_NOM) * peakFactor * (I / 0.1 + 0.05); tBath = Math.max(T_BATH_NOM, Math.min(T_QUENCH_PK, tBath)); if (I < 1.0 && quenchT > 12) { // Quench complete; magnet is at zero, bath partially gone. mode = 'ramp'; I = 0; tBath = T_BATH_NOM; } } else if (mode === 'persistent') { // ---- Persistent mode: switch is closed, supply isolated. // I stays constant in the ideal superconducting loop. // Parasitic heat slowly boils helium. const dHe = (qLeak * dt) / HE_LAT / HE_RHO; hePct = Math.max(0, hePct - (dHe / V_BATH) * 100); if (hePct <= 0.01) { // Bath exhausted -> coil warms -> quench follows. mode = 'quench'; quenchT = 0; } } else { // ---- Ramp mode: supply drives I toward I_set at rate dI/dt. const err = iSet - I; const step = Math.sign(err) * Math.min(Math.abs(err), dIdt * dt); I += step; // Parasitic heat load still boils helium (lead conduction, etc.) const dHe = ((qLeak + 0.5) * dt) / HE_LAT / HE_RHO; hePct = Math.max(0, hePct - (dHe / V_BATH) * 100); if (hePct <= 0.01) { mode = 'quench'; quenchT = 0; } } // ---- Advance animation phase for current tokens ------------------- flowPhase = (flowPhase + dt * (0.05 + I / 600 * 0.8)) % 1.0; } // ===================================================================== // Button handlers // ===================================================================== function onMode() { // Toggle between ramp and persistent. Disabled during a quench. if (mode === 'quench') return; if (mode === 'ramp') { mode = 'persistent'; modeButton.html('ramp mode (opens switch)'); } else { mode = 'ramp'; modeButton.html('persistent mode (closes switch)'); } } function onQuench() { // Force a quench. Only meaningful if there is current to dump. if (mode === 'quench' || I < 1.0) return; mode = 'quench'; quenchT = 0; } function onReset() { // Cold restart: refill bath, zero current, switch open. I = 0; mode = 'ramp'; quenchT = 0; tBath = T_BATH_NOM; hePct = 100.0; iSetSlider.value(0); modeButton.html('persistent mode (closes switch)'); } // ===================================================================== // Diagram drawing -- one section per visual region // ===================================================================== function drawCryostatEnvelope() { // Dashed rectangle marks the cold boundary. Helps the reader see // which components are inside the helium space and which are not. push(); noFill(); stroke(...COLDER, 200); strokeWeight(1.5); drawingContext.setLineDash([6, 5]); rect(cryo.x, cryo.y, cryo.w, cryo.h, 8); drawingContext.setLineDash([]); // Label noStroke(); fill(...COLDER); textSize(11); textAlign(LEFT, BOTTOM); text('cryostat (4 K)', cryo.x + 8, cryo.y - 4); pop(); } function drawWires() { // ---- Power supply -> persistent switch (warm-to-cold lead) -------- push(); stroke(GREY_IDLE); strokeWeight(2); line(supplyBox.x + supplyBox.w, supplyBox.y + 30, switchBox.x, switchBox.y + 30); // ---- Switch -> coil (always present, in the persistent loop) ----- line(switchBox.x + switchBox.w, switchBox.y + 30, coilBox.x, coilBox.y + 50); // ---- Coil return -> switch (closes the loop) --------------------- // Down the right of the coil, across, up to switch bottom. line(coilBox.x + coilBox.w / 2, coilBox.y + coilBox.h, coilBox.x + coilBox.w / 2, coilBox.y + coilBox.h + 30); line(coilBox.x + coilBox.w / 2, coilBox.y + coilBox.h + 30, switchBox.x + switchBox.w / 2, coilBox.y + coilBox.h + 30); line(switchBox.x + switchBox.w / 2, coilBox.y + coilBox.h + 30, switchBox.x + switchBox.w / 2, switchBox.y + switchBox.h); // ---- Diode bank parallels the coil -------------------------------- line(coilBox.x + 20, coilBox.y + coilBox.h, diodeBox.x + 20, diodeBox.y); line(coilBox.x + coilBox.w - 20, coilBox.y + coilBox.h, diodeBox.x + diodeBox.w - 20, diodeBox.y); pop(); } function drawCurrentTokens() { // Animated dots travel along the active conduction path. The path // depends on mode; color depends on whether the conductor is // superconducting (green) or normal/resistive (red). const tokenColor = (mode === 'quench') ? HOT : SC_GREEN; if (I < 0.5 && mode !== 'quench') return; // idle -> no tokens // Build the path as a list of segment endpoints. The token's // position is parameterized by phase in [0, 1]. const path = (mode === 'persistent') ? persistentPath() : rampPath(); const tokens = 8; for (let k = 0; k < tokens; k++) { const phase = (flowPhase + k / tokens) % 1.0; const p = pointAlongPath(path, phase); push(); noStroke(); fill(...tokenColor); circle(p.x, p.y, 6); pop(); } // Quench path: dump through diodes (parallel branch) if (mode === 'quench') { const dPath = diodePath(); for (let k = 0; k < 5; k++) { const phase = (flowPhase + k / 5) % 1.0; const p = pointAlongPath(dPath, phase); push(); noStroke(); fill(...HOT); circle(p.x, p.y, 5); pop(); } } } function rampPath() { // Supply -> switch -> coil -> back to switch -> back to supply. // The reader sees a complete external loop. return [ { x: supplyBox.x + supplyBox.w, y: supplyBox.y + 30 }, { x: switchBox.x, y: switchBox.y + 30 }, { x: switchBox.x + switchBox.w, y: switchBox.y + 30 }, { x: coilBox.x, y: coilBox.y + 50 }, { x: coilBox.x + coilBox.w / 2, y: coilBox.y + 50 }, { x: coilBox.x + coilBox.w / 2, y: coilBox.y + coilBox.h }, { x: coilBox.x + coilBox.w / 2, y: coilBox.y + coilBox.h + 30 }, { x: switchBox.x + switchBox.w / 2, y: coilBox.y + coilBox.h + 30 }, { x: switchBox.x + switchBox.w / 2, y: switchBox.y + switchBox.h } ]; } function persistentPath() { // Closed loop entirely inside the cryostat: switch <-> coil only. return [ { x: switchBox.x + switchBox.w, y: switchBox.y + 30 }, { x: coilBox.x, y: coilBox.y + 50 }, { x: coilBox.x + coilBox.w / 2, y: coilBox.y + 50 }, { x: coilBox.x + coilBox.w / 2, y: coilBox.y + coilBox.h }, { x: coilBox.x + coilBox.w / 2, y: coilBox.y + coilBox.h + 30 }, { x: switchBox.x + switchBox.w / 2, y: coilBox.y + coilBox.h + 30 }, { x: switchBox.x + switchBox.w / 2, y: switchBox.y + switchBox.h } ]; } function diodePath() { // Through the protection-diode bank: coil top -> diodes -> coil bottom. return [ { x: coilBox.x + 20, y: coilBox.y + coilBox.h }, { x: diodeBox.x + 20, y: diodeBox.y }, { x: diodeBox.x + diodeBox.w - 20, y: diodeBox.y }, { x: coilBox.x + coilBox.w - 20, y: coilBox.y + coilBox.h } ]; } function pointAlongPath(path, phase) { // Walk segment lengths until we land at `phase` of total length. const lens = []; let total = 0; for (let i = 0; i < path.length - 1; i++) { const dx = path[i + 1].x - path[i].x; const dy = path[i + 1].y - path[i].y; const d = Math.sqrt(dx * dx + dy * dy); lens.push(d); total += d; } const target = phase * total; let walked = 0; for (let i = 0; i < lens.length; i++) { if (walked + lens[i] >= target) { const frac = (target - walked) / lens[i]; return { x: path[i].x + frac * (path[i + 1].x - path[i].x), y: path[i].y + frac * (path[i + 1].y - path[i].y) }; } walked += lens[i]; } return path[path.length - 1]; } function drawBlock(box, title, lines) { // Standard rounded-rectangle block with a title and a small set of // detail lines. Used for all Pattern G nodes except the coil (which // has its own custom render with the field-coil glyph). push(); noFill(); stroke(...STRUCT); strokeWeight(2); rect(box.x, box.y, box.w, box.h, 6); noStroke(); fill(FG); textAlign(LEFT, TOP); textSize(11); text(title, box.x + 8, box.y + 6); fill(...DIM); textSize(10); for (let i = 0; i < lines.length; i++) { text(lines[i], box.x + 8, box.y + 22 + i * 12); } pop(); } function drawCoilBlock() { // The coil is a stack of horizontal turns. Brightness encodes // current; warm tint encodes resistive (quench) state. push(); noFill(); stroke(...STRUCT); strokeWeight(2); rect(coilBox.x, coilBox.y, coilBox.w, coilBox.h, 6); // Title noStroke(); fill(FG); textAlign(LEFT, TOP); textSize(11); text('SUPERCONDUCTING COIL (NbTi)', coilBox.x + 8, coilBox.y + 6); // Turn stack const turns = 6; const x0 = coilBox.x + 14; const x1 = coilBox.x + coilBox.w - 14; const yTop = coilBox.y + 28; const yBot = coilBox.y + coilBox.h - 14; const dy = (yBot - yTop) / (turns - 1); const frac = Math.min(1, I / 600); const col = (mode === 'quench') ? [HOT[0], HOT[1], HOT[2]] : [SC_GREEN[0], SC_GREEN[1], SC_GREEN[2]]; for (let i = 0; i < turns; i++) { const y = yTop + i * dy; stroke(col[0], col[1], col[2], 80 + frac * 175); strokeWeight(3); line(x0, y, x1, y); // Connect adjacent turns at alternating ends (helical hint) stroke(...STRUCT); strokeWeight(1.5); if (i < turns - 1) { const xConnect = (i % 2 === 0) ? x1 + 4 : x0 - 4; line(xConnect, y, xConnect, y + dy); } } // Field readout on the coil block const B = FIELD_PER_A * I; noStroke(); fill(...DIM); textSize(10); text('I = ' + nf(I, 1, 1) + ' A', coilBox.x + 8, coilBox.y + coilBox.h - 26); text('B0 = ' + nf(B, 1, 2) + ' T', coilBox.x + 8, coilBox.y + coilBox.h - 14); pop(); } // ===================================================================== // Per-block detail lines // ===================================================================== function supplyDetail() { if (mode === 'persistent') { return ['isolated', 'switch closed']; } if (mode === 'quench') { return ['tripped', 'breakers open']; } const iSet = iSetSlider.value(); return ['I_set = ' + nf(iSet, 1, 0) + ' A', 'dI/dt = ' + nf(dIdtSlider.value(), 1, 1) + ' A/s']; } function switchDetail() { if (mode === 'persistent') { return ['closed', 'lossless link']; } if (mode === 'quench') { return ['open', 'heater off']; } return ['open', 'heater on']; } function diodeDetail() { if (mode === 'quench') { return ['CONDUCTING', 'dumping E_mag']; } return ['reverse-biased', 'idle']; } function probeDetail() { const B = FIELD_PER_A * I; return ['Hall probe', 'B = ' + nf(B, 1, 2) + ' T']; } function bathDetail() { return ['T = ' + nf(tBath, 1, 2) + ' K', 'He = ' + nf(hePct, 1, 1) + ' %']; } // ===================================================================== // Gauges (right-side energy / state column) // ===================================================================== function drawGauges() { const E = 0.5 * L_COIL * I * I / 1000; // kJ stored // Background panel push(); noFill(); stroke(...SCRATCH); strokeWeight(1); rect(530, 320, 170, 75, 6); noStroke(); fill(FG); textAlign(LEFT, TOP); textSize(11); text('STATE', 540, 326); fill(...DIM); textSize(10); text('mode = ' + mode, 540, 342); text('I = ' + nf(I, 1, 1) + ' A', 540, 354); text('E = ' + nf(E, 1, 2) + ' kJ', 540, 366); text('T_He = ' + nf(tBath, 1, 2) + ' K', 540, 378); pop(); } // ===================================================================== // Slider labels (text drawn next to each createSlider, since p5 // sliders have no built-in label) // ===================================================================== function drawSliderLabels() { push(); noStroke(); fill(...DIM); textAlign(LEFT, CENTER); textSize(11); const x = 210; text('I_set ' + nf(iSetSlider.value(), 1, 0) + ' A', x, 422); text('dI/dt ' + nf(dIdtSlider.value(), 1, 1) + ' A/s', x, 452); text('Q_leak ' + nf(qLeakSlider.value(), 1, 2) + ' W', x, 482); pop(); } // ===================================================================== // HUD (Betterfire Standard top-left + bottom-right equation) // ===================================================================== function drawHUD() { // Top-left: title + Wikitube URL (Betterfire Standard rule 2) noStroke(); fill(FG); textAlign(LEFT, TOP); textSize(20); text(TITLE, 14, 12); fill(...DIM); textSize(12); text('Wikitube microsim . en.wikitube.io/wiki/Superconducting_magnet', 14, 36); // Top-right: pattern label textAlign(RIGHT, TOP); textSize(10); text('Pattern G - block diagram / process chain', width - 14, 12); text('drive: I_set, dI/dt, Q_leak, mode, quench', width - 14, 24); // Bottom-right: canonical equation (Betterfire Standard rule 4) textAlign(RIGHT, BOTTOM); fill(FG); textSize(13); text('E = (1/2) L I^2 [stored magnetic energy]', width - 14, height - 6); } ``` ## Links (Wikipedia order) <!-- injected from _registry/childlinks/Superconducting_magnet.json (2026-07-30T02:09:12Z) --> `Abrikosov_vortex` · `Andreev_reflection` · `BCS_theory` · `Bean's_critical_state_model` · `Bilayer_graphene` · `Bitter_electromagnet` · `CERN` · `Conventional_superconductor` · `Cooper_pair` · [[Copper]] · `Covalent_superconductor` · `Critical_field` · `Cryocooler` · [[Cryogenics]] · `Cryostat` · `Cryotron` · `Crystallographic_defect` · `Cuprate_superconductor` · `Direct_current` · `Eddy_current` · [[Electric_current]] · `Electromagnet` · `Fault_current_limiter` · `Ferromagnetic_superconductor` · `Flux_pinning` · `Flux_pumping` · `Fusion_power` · `Georg_Bednorz` · `Ginzburg–Landau_theory` · `Heat_pump` · `Heavy_fermion_superconductor` · `Heike_Kamerlingh_Onnes` · `High-temperature_superconductivity` · `Homes's_law` · `ITER` · `Inductor` · `Iron-based_superconductor` · `Japan` · `John_Eugene_Kunzler` · `Josephson_effect` · `Joule_heating` · `Kelvin` · `Kohn–Luttinger_superconductivity` · `Lanthanum_barium_copper_oxide` · `Large_Hadron_Collider` · [[Liquid_helium]] · `Liquid_nitrogen` · `List_of_superconductors` · `Little–Parks_effect` · `London_equations` · `London_penetration_depth` · `Lorentz_force` · `Magnesium_diboride` · `Magnet` · `Magnetic_field` · [[Magnetic_resonance_imaging]] · `Matthias_rules` · `Mattis–Bardeen_theory` · `Meissner_effect` · `Micrometre` · `National_High_Magnetic_Field_Laboratory` · [[Niobium]] · `Niobium–tin` · `Niobium–titanium` · [[Nuclear_magnetic_resonance]] · `Organic_superconductor` · `Oxypnictide` · `Particle_accelerator` · `Persistent_current` · `Power_supply` · `Proximity_effect_(superconductivity)` · `Pulse_tube_refrigerator` · `Reentrant_superconductivity` · `Resonating_valence_bond_theory` · `Room-temperature_superconductor` · `Rutherford_cable` · `SCMaglev` · `SQUID` · `SU(2)_color_superconductivity` · `Silsbee_effect` · `Skin_effect` · `Superconducting_coherence_length` · `Superconducting_quantum_computing` · `Superconducting_wire` · [[Superconductivity]] · `Superconductor_classification` · `Supercurrent` · `Superdiamagnetism` · `Superstripes` · `Technological_applications_of_superconductivity` · `Temperature` · `Tesla_(unit)` · `Thallium_barium_calcium_copper_oxide` · `Topological_superconductor` · `Type-1.5_superconductor` · `Type-II_superconductor` · `Type-I_superconductor` · `Unconventional_superconductor` · `Watt` · `Werthamer–Helfand–Hohenberg_theory` ## From the vault media library !Superconducting magnet thumb.png *Superconducting Magnet — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.* <!-- LOCAL-MEDIA-PASS:END --> > **Room:** [[Helium]] · **Status:** ✅ shipped ## Overview The governing quantity is stored magnetic [[Energy|energy]], **E = (1/2) L I²**, and the governing fact is that a [[Superconductivity|superconducting]] winding has no gradual way to give it back. A resistive electromagnet dissipates continuously, so switching it off costs nothing: the [[Energy_transformation|energy]] was being replaced from the [[Electrical_grid|supply]] every second and simply stops arriving. A superconducting winding is different in kind. It is charged once, closed on itself, and thereafter holds its [[Electric_current|current]] — and its megajoules — for as long as it stays cold. The whole [[Engineering|engineering]] discipline, from the [[Metallurgy|metallurgy]] of the [[Alloy|alloy]] to the [[Safety_engineering|safety]] pipe on the roof, is the business of keeping that state and of surviving the moment it ends. The design point worth memorising is a clinical 3 T [[Magnetic_resonance_imaging|magnetic resonance imaging]] magnet: **inductance 100 H, operating current 400 A, stored energy 8 MJ.** That is the ISMRM figure verbatim — "A 3T MRI magnet typically has an inductance of 100 H for a magnet current of 400 A. The magnetic stored energy of this inductor is 0.5 L I^2, which yields 8 megajoule" — and the arithmetic checks, (1/2)(100)(400)² = 8.0 × 10⁶ J, about 2.2 kWh. Two conditions travel with it. It is one design point and not a constant: a review of [[Materials_science|magnet design]] tabulates 2–4 MJ at 1.5 T, **10–15 MJ at 3 T** and 50–90 MJ at 7 T, so 8 MJ sits at the floor of the 3 T band. And the same source fixes the geometry behind it — roughly 10 000 turns per tesla at 300 A, at a winding-pack [[Density|current density]] near 200 A/mm². For scale outside [[Medicine|medicine]]: an LHC dipole holds a comparable 7.8 MJ at L = 0.12 H and I = 11.5 kA, the same [[Energy|energy]] in a magnet with a thousandth of the inductance. Around the winding sits the cryostat: a [[Liquid_helium|liquid helium]] vessel, a vacuum space, one or more radiation shields intercepting room-temperature [[Heat_transfer|heat]], demountable current leads, and cold protection diodes across the coil sections. Outside [[Medicine|clinical]] [[Magnetic_resonance_imaging|MRI]] at 1.5 T and 3 T, the same architecture carries high-field [[Nuclear_magnetic_resonance|NMR]] spectroscopy, the dipoles and quadrupoles of accelerator rings, the confinement coils of [[Nuclear_fusion|fusion]] [[Plasma_(physics)|plasma]] machines, magnetic levitation transport, and laboratory high-field [[Physics|physics]]. What follows is common to all of them, because all of them live under the same surface. ## Persistent mode: a current with nowhere to go The device that makes the [[Energy|energy]] permanent is the **superconducting switch** — a short length of [[Superconductivity|superconductor]] wrapped with a small heater and wired across the coil terminals. Energise the heater and that length goes normal, developing "a resistance of the order of 100 Ohm" (Overweg); the [[Voltage|supply]] then drives [[Electric_current|current]] into the coil through the [[Copper|copper]] leads and the magnet ramps. Cut the heater, let the switch cool back through its [[Phase_transition|transition]], and the coil is shorted by a [[Superconductivity|superconductor]]. The [[Electrical_engineering|power supply]] can be disconnected and the leads withdrawn. Nothing pushes the [[Electric_current|current]] any more; nothing needs to. What is left is an L/R decay against the only resistance still in the loop, which lives in the joints. Commercial magnets demand "nearly-perfect superconducting joints with guaranteed resistance of <10-11 ohm", and Overweg gives the consequence for a 40 H magnet: a decay time constant of 4 × 10¹⁰ s, "equivalent to a relative field loss of less than 0.1 ppm/hour" — under 0.09 per cent a year. That is what "held for years" means quantitatively, and it is why [[Nuclear_magnetic_resonance|nuclear magnetic resonance]] spectroscopy and [[Magnetic_resonance_imaging|MRI]] can build on a field whose [[Accuracy_and_precision|absolute value]] is never re-measured against a standard during a scan; the [[Control_system|control system]] has nothing to regulate, because there is no [[Feedback|feedback]] loop and no drive. It also means the magnet is connected to nothing. There is no external circuit standing by, no breaker, no [[Electric_power_transmission|cable]] to open. Hold that thought: it is where the protection section below ends. ## The critical surface A conductor is not "superconducting below Tc". It is superconducting inside a **surface in three variables at once** — temperature T, magnetic field B, and [[Density|current density]] J — and the [[Cryogenics|cryogenic]] plant, the [[Materials_science|conductor]] choice and the winding geometry all exist to keep one moving point underneath it. The sheet Jc(T, B) meets the floor along the curve Bc2(T) and pinches to a point at (Tc, 0, 0). Cross any face — warm it, raise the field on it, push more [[Electric_current|current]] through it — and the material goes normal. This is why the [[Mathematical_model|model]] in the sim above is three-dimensional: the object genuinely is, and every [[Failure_mode_and_effects_analysis|failure mode]] in this article is a crossing of one of its faces. - **[[Niobium|Niobium]]–[[Titanium|titanium]] (NbTi)**, the ductile [[Alloy|alloy]] that carries essentially all of [[Medicine|clinical]] [[Magnetic_resonance_imaging|MRI]]: Tc ≈ 9.2 K, Bc2 ≈ 15 T extrapolated to 0 K and **≈ 10 T at 4.2 K**. A second review gives 9.3 K and "relatively low critical field of about 10.5 tesla at 4.2 K", with Jc "> 3,000 Amp/mm2 at 4 T, 4.2 K". Note what those numbers do to the [[Helium|helium]] budget: a magnet bathed at 4.2 K in [[Liquid_helium|liquid helium]] sits barely five kelvin below Tc, which sounds generous and is not, because warming the [[Thermodynamic_system|winding]] collapses Bc2 and Jc at the same time as it eats the [[Thermodynamics|thermal]] margin. NbTi is the reason [[Helium_cryogenics|helium cryogenics]] is a hospital technology. - **[[Niobium|Niobium]]–[[Tin|tin]] (Nb3Sn)**, brittle, reacted after winding, the [[Materials_science|conductor]] of high-field [[Nuclear_magnetic_resonance|NMR]] and of accelerator and [[Nuclear_fusion|fusion]] magnets: Tc up to 18.3 K, Bc2 around 30 T at 0 K and ≈ 23 T at 4.2 K, with state-of-the-art restacked-rod strand measured at 25–27 T at 4.2 K, and whole-wire Jc near 1000 A/mm² at 4.2 K and 15 T. It roughly doubles the accessible field; it does not free anyone from [[Helium|helium]], because the magnets that need it run colder still, often in [[Superfluid_helium-4|superfluid helium II]] near 1.8 K, below the [[Lambda_point|lambda point]], where [[Superfluidity|superfluid]] [[Heat_transfer|heat transport]] rather than ordinary [[Diffusion|conduction]] is what cools the coil. - **REBCO** (rare-earth [[Barium|barium]] [[Copper|copper]] oxide; the [[Yttrium|yttrium]] member is YBCO) changes the shape of the argument rather than its terms. Tc ≈ 92 K; Bc2 "exceeds 100 T at low temperature", and in YBCO it is strongly anisotropic — about 120 T with the field perpendicular to the CuO₂ planes and 250 T parallel to them, so a single Bc2 for a [[Crystal_structure|layered]] [[Superconductivity|superconductor]] is an incomplete statement in exactly the way a [[Boiling_point|boiling point]] without a pressure is. Jc exceeds 3 MA/cm² at 77 K in self-field. What REBCO really changes is that the operating point can sit at 20 K and still be buried deep inside the surface — which means it can be reached by a closed-cycle cryocooler with **no [[Liquid_helium|liquid helium]] in the machine at all.** That, and not the liquid-[[Nitrogen|nitrogen]] headline, is the industrially decisive property of high-Tc [[Materials_science|conductors]]. ## The quench, in causal order A **quench** is the loss of the [[Superconductivity|superconducting]] state in a magnet that is carrying [[Electric_current|current]]. It is not a fault in the sense of a broken part. It is a runaway, and the order of the chain is the entire explanation. 1. **A small volume crosses the surface.** Almost nothing is required. The minimum quench energy of NbTi is tabulated at **1–10 mJ** — a wire moving a micrometre under magnetic [[Force|load]], a [[Fracture_mechanics|crack]] in the epoxy, a flux jump in a [[Crystal_structure|filament]]. Millijoules, against the magnet's eight million joules. [[Vibration|Mechanical]] [[Fatigue_(material)|movement]] of the winding is the commonest trigger, which is why coils are potted and pre-stressed. 2. **That volume now has resistance,** and it is still carrying the full transport [[Electric_current|current]], now through the [[Copper|copper]] matrix. A typical [[Magnetic_resonance_imaging|MRI]] conductor is "80 to 90 volume percent of copper, and only 10% to 20% NbTi" precisely so that there is somewhere for the [[Electric_current|current]] to go. 3. **Ohmic heating, into almost no heat capacity.** P = I²R is modest; the [[Thermodynamics|thermal]] mass it acts on is not. [[Copper|Copper]]'s volumetric heat capacity near 4.2 K is about 900 J m⁻³ K⁻¹ — computed from the standard Sommerfeld constant 0.695 mJ mol⁻¹ K⁻² and Debye temperature 343 K — against roughly 3.5 × 10⁶ J m⁻³ K⁻¹ at room temperature. It is **nearly four thousand times smaller.** A trickle of power is a violent [[Thermodynamics|temperature]] rise, and this single fact is why [[Cryogenics|cryogenic]] systems are unforgiving in a way room-temperature [[Electrical_engineering|electrical engineering]] is not. 4. **The neighbours are driven normal,** and the boundary moves. The **normal zone propagation velocity** for adiabatic NbTi is "5 - 20 ms-1" longitudinally along the wire. Transversely, turn to turn, it is far slower: the ratio of transverse to longitudinal [[Velocity|velocity]] is **0.01 to 0.03**, one to three per cent, because it scales as the square root of the ratio of the two [[Heat_transfer|thermal conductivities]]. Both numbers matter, and the second matters more than it looks — in a solenoid the transverse direction crosses thousands of tightly stacked turns, so a front creeping sideways at a few per cent of the axial [[Velocity|speed]] still consumes whole turns faster than the axial front can wrap them. The propagating boundary is a [[Percolation|front]], not a [[Diffusion|diffusion]]. 5. **The growing normal zone is a growing resistance in series with the magnet's own inductance,** so the [[Closed_system|persistent loop]] stops being a short circuit and the [[Electric_current|current]] decays: L dI/dt = −(R_n + R_d) I, an [[Ordinary_differential_equation|ordinary differential equation]] whose coefficient is itself growing. Notice the [[Positive_feedback|positive feedback]] — more normal volume, more resistance, more heating, more normal volume — which makes the process a [[Nonlinear_system|nonlinear]] runaway rather than a decay. 6. **Every joule the field was holding is converted to heat.** All 8 MJ, in seconds, inside a [[Thermodynamic_system|winding]] that was at 4 K a moment earlier. 7. **That heat reaches the [[Liquid_helium|liquid helium]] bath, which boils violently,** and the gas has nowhere to go but the quench pipe. ## The arithmetic that matters Everything above stays qualitative until numbers are put on the [[Helium|helium]], and the numbers are brutal. **[[Liquid_helium|Liquid helium]]'s latent heat is almost nothing.** At its normal [[Boiling_point|boiling point]] the [[Fluid_dynamics|liquid]] has [[Density|density]] 124.98 kg/m³ and a latent heat of vaporisation of 20.28 kJ/kg. Multiply: **2.53 kJ per litre.** The independent cross-check is a [[Cryogenics|cryogenics]] guide quoting "only about 2.6 kJ/l" for [[Helium|helium]] against "about 160 kJ/l" for liquid [[Nitrogen|nitrogen]] — a factor of sixty-three, and the reason [[Helium_cryogenics|helium]] and [[Nitrogen|nitrogen]] are not interchangeable [[Stock_and_flow|inventories]]. The same guide notes that "a heat input of only 1 watt will boil away 1.4 l of LHe in an hour", which reproduces exactly from 3600 J ÷ 2.53 kJ/L = 1.42 L. **The expansion ratio is enormous — and it cannot be quoted without its reference temperature.** [[Helium|Helium]] is very nearly ideal at one atmosphere, so the gas [[Density|density]] follows from the [[Kinetic_theory_of_gases|ideal-gas law]] and a molar mass of 4.002602: - at **0 °C** (273.15 K), 101.325 kPa: 0.17858 kg/m³, giving 124.98 / 0.17858 = **1 : 700** - at **21.1 °C** (70 °F), 101.325 kPa: 0.16577 kg/m³, giving **1 : 754** Those are the two figures in circulation and they are not a disagreement — they are one [[Accuracy_and_precision|measurement]] referred to two different gas temperatures. The industrial [[Safety_engineering|safety]] table that is the usual source prints "Expansion Ratio, Liquid to Gas, B.P. to 32°F (0°C) 1 to 754", but 754 does **not** reproduce from a 0 °C reference — which gives 700 — and does reproduce, to three figures, from that same table's own 70 °F gas-[[Density|density]] row. Wikipedia's expansion-ratio table gives 1 : 745 for [[Helium|helium]] "boiling point to ambient", the same room-temperature family. The clinical [[Magnetic_resonance_imaging|MRI]] literature splits the difference at "approximately 700–760:1", honest about the spread without explaining it. The rule: **1 : 700 is the 0 °C reference, 1 : 745–757 is the ~21 °C reference, and a figure printed without one is incomplete.** **Now do the sum, and the conclusion falls out of it.** A conventional whole-body magnet holds "approximately 1500-2000 liters of liquid Helium". Take 1700 L. Its entire latent-heat capacity is 1700 × 2.53 kJ = **4.3 MJ** — against a magnet storing **8 MJ**. Absorbing 8 MJ as latent heat would take 3 160 L, nearly twice the [[Stock_and_flow|inventory]]. So a full quench does not partly boil the bath. **It boils all of it,** and vents roughly 1 190 m³ of gas at 0 °C (1 280 m³ at room temperature) up a pipe. That is what a quench pipe is for; it is why its burst disc is specified to open at a scanner-specific pressure; and it is why the [[Safety_engineering|safety]] procedure is immediate evacuation, because [[Helium|helium]] is chemically an [[Inert_gas|inert gas]] and physiologically an [[Oxygen|oxygen]] displacer. It is also why an [[Magnetic_resonance_imaging|MRI]] suite is a [[Helium|helium]] consumer and not a [[Helium|helium]] borrower. ## Quench protection saves the magnet, not the helium Protection does not stop the [[Energy|energy]] release. It only decides where the [[Energy_transformation|energy]] goes, and the design target is the peak conductor temperature — "as a general guideline, the peak temperature inside the magnet should not exceed 200 K." **Quench heaters** are the method that dominates [[Magnetic_resonance_imaging|MRI]]. A [[Sensor|detector]] watches for resistive [[Voltage|voltage]] across the winding, and on [[Detection_theory|detection]] the [[Real-time_computing|protection circuit]] deliberately fires heaters that drive much more of the coil normal at once. This is counterintuitive and correct: many normal zones mean higher total resistance, a shorter decay time and a far lower hot-spot temperature, because the same joules are spread over kilometres of [[Materials_science|conductor]] instead of centimetres. Overweg puts the objective plainly — "it must be avoided that all of the magnet's energy is dissipated at or near the spot where the quench started... this is done by rapidly activating a system of heaters, with the objective to initiate many additional normal zones." The microsim's model winding, built from the ISMRM ampere-turns and [[Density|current density]] with a 1.15 m mean turn, comes to about 81 km of [[Materials_science|conductor]]; spreading 8 MJ across all of it rather than into one hot turn is the difference between a 100 K hot spot and melted [[Copper|copper]]. **External dump resistors** are the other classic method, and the reason they are weak here is two lines of algebra. Open a breaker and force the [[Electric_current|current]] through an external resistance R_d: the [[Electric_current|current]] decays with time constant τ = L/R_d, while the [[Voltage|terminal voltage]] the magnet develops is V = I·R_d. Multiply, and R_d cancels: **τ·V = L·I,** a number fixed by the magnet and not by the [[Electrical_engineering|circuit designer]]. For the 3 T [[Magnetic_resonance_imaging|MRI]] magnet L·I = 40 000 V·s, so a 1 kV insulation limit forces a dump lasting at least 40 s — during which the winding is absorbing most of the [[Energy|energy]] anyway. For an LHC dipole, L·I = 1 380 V·s and the same kilovolt empties it twenty-nine times faster. That is the structural reason high-inductance, moderate-[[Electric_current|current]] magnets protect themselves internally while low-inductance, high-current accelerator strings can afford external dumps. And [[Magnetic_resonance_imaging|MRI]] magnets carry a second, harder reason: in persistent mode there is no external circuit at all — the switch is closed, the [[Voltage|supply]] is gone, the leads are withdrawn. There is nothing to open a breaker into. The [[Energy|energy]] is going into the winding and the bath whatever anyone does; the only free variable is how evenly it is shared. Which is the previous section's conclusion restated as [[Reliability_engineering|reliability engineering]]. [[Redundancy_(engineering)|Redundant]] heaters, subdivided coils and cold diodes change the [[Availability|survivability]] of the magnet by orders of magnitude and change the [[Helium|helium]] outcome not at all. Every joule still arrives at the [[Liquid_helium|helium]]. **Protection saves the magnet. It never saves the helium.** ## Why this dominates helium demand Because there is no substitute at the cold end. A balloon can be flown on hydrogen and a weld shielded with argon, but nothing except [[Helium|helium]] is a [[Fluid_dynamics|liquid]] at 4.2 K, so NbTi magnets are a demand that price cannot reallocate — the [[Limiting_factor|limiting factor]] is [[Physics|physics]], not cost. The magnet industry consumes "about 60% of all superconducting wire (including copper), and about 40% of the NbTi alloy", and every one of those magnets has a pipe pointed at the sky. The [[Helium_production_in_the_United_States|US]] end-use split, from the USGS *Mineral Commodity Summaries*, shows both the scale and a trend worth reading carefully: - **2023 edition:** end uses listed "in descending order by estimated quantity, magnetic resonance imaging, lifting gas, analytical and laboratory applications..." — [[Magnetic_resonance_imaging|MRI]] **first**. - **2025 edition:** [[Magnetic_resonance_imaging|MRI]] **17 %**, behind analytical/engineering/lab/specialty gases at 22 % and [[Lifting_gas|lifting gas]] at 18 %. - **2026 edition (the current figure, reporting calendar 2025):** [[Magnetic_resonance_imaging|MRI]] **15 %**, behind analytical and specialty gases (22 %), controlled atmospheres, fibre optics and [[Semiconductor_device_fabrication|semiconductors]] (17 %) and [[Lifting_gas|lifting gas]] (17 %). Two honest readings of that. [[Magnetic_resonance_imaging|MRI]] is no longer the largest single US end use, and any article still claiming it is has stopped checking. But it remains the largest *named single application* with no substitute, and the decline is at least partly the industry engineering its own demand away. **Zero-boil-off** magnets close the [[Closed_system|loop]]: a cryocooler recondenses the evaporating gas, "eliminating the need for any refill except after a quench event". Beyond that come sealed, low-[[Stock_and_flow|inventory]] magnets that abandon the bath altogether — a 1.5 T system at **7 L**, a 0.55 T system at **0.7 L**, a compact conduction-cooled 3 T head magnet at **12 L**, against 1500–2000 L for a conventional design. A well-built conventional magnet already leaks very little: a two-shield [[Cryogenics|cryostat]] carrying a 30 mW heat load loses "about a litre per day". The [[Stock_and_flow|inventory]] is not there because the magnet consumes it steadily. **It is there to survive the quench** — and, as the arithmetic above shows, it does not. Which closes the loop back to the lede. Cutting the bath from 1700 L to 7 L does not make the magnet quench-proof; it makes the quench cheap. That is the same design move as [[Helium_storage_and_conservation|conservation]] everywhere else in the [[Helium|helium]] economy, and it rests on the same [[Second_law_of_thermodynamics|thermodynamic]] fact that governs the [[National_Helium_Reserve|reserve]] and the [[Natural_gas|gas field]]: the [[Thermodynamics|thermodynamics]] cannot be made kinder, so the exposure is made smaller. ## See also - Room hub: [[Helium]] - p5.js Editor conventions: P5 JS EDITOR - Wiki root: MAIN - three.js conventions: [[WT!Three_js_Microsim_Master_Class|three.js Master Class]] --- *Scaffolded by `generative-microsim` from row 88 of the Helium sheet on 2026-05-12T09:57:46Z.* <!-- LOCAL-MEDIA-PASS:START --> <!-- CRAFT-LINK:START g12 --> *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].* <!-- CRAFT-LINK:END --> ## Sources Annotated; one clause each on what the source establishes. Bibliography lines are link-light by house rule (§4). **Magnet parameters and persistent mode** - ISMRM 2017 Proceedings, abstract 7979, "MRI magnet design". [cds.ismrm.org](https://cds.ismrm.org/protected/17MProceedings/PDFfiles/7979.html) — the load-bearing design point, verbatim: "A 3T MRI magnet typically has an inductance of 100 H for a magnet current of 400 A. The magnetic stored energy of this inductor is 0.5 L I^2, which yields 8 megajoule"; also "For each tesla of central field one needs approximately 10 000 turns at a current of 300 amperes" and "Typical current densities in an MRI magnet are of the order of 200 A/mm2". - Overweg, J. "MRI main field magnets." ISMRM 2006 educational course, Philips Research Hamburg. [mri-q.com](https://mri-q.com/uploads/3/4/5/7/34572113/main_field_magnets_ismrm2006.pdf) — the persistent-mode switch, verbatim: "With the heater on, this so-called persistent mode switch has a resistance of the order of 100 Ohm"; the drift figure "For a magnet with an inductance of 40 Henry, the decay time-constant L/Rd then becomes 4 10^10 seconds, equivalent to a relative field loss of less than 0.1 ppm/hour"; the quench-heater rationale; and the 30 mW / "about a litre per day" boil-off figure. - "Advances in magnet design" (MRI main-magnet review), hosted at mriquestions. [s.mriquestions.com](https://s.mriquestions.com/uploads/3/4/5/7/34572113/advances_in_magnet_design.pdf) — stored-energy table (1.5 T 2–4 MJ, 3 T 10–15 MJ, 7 T 50–90 MJ); NbTi "low critical temperature of 9.3 K and relatively low critical field of about 10.5 tesla at 4.2 K", Jc "> 3,000 Amp/mm2 at 4 T, 4.2 K"; conductor composition "80 to 90 volume percent of copper, and only 10% to 20% NbTi"; joints of "<10-11 ohm"; and the demand figures "MRI magnets use about 60% of all superconducting wire (including copper), and about 40% of the NbTi alloy". **The critical surface** - Alliance for Superconducting Technologies, superconductor documentation. [superconductingalliance.org/docs](https://superconductingalliance.org/docs) — the three-conductor comparison used above, verbatim: NbTi "Tc ~9.2 K and Bc2 ~15 T at 0 K (~10 T at 4.2 K)"; Nb3Sn "Tc ~18.3 K and Bc2 ~30 T at 0 K (~23 T at 4.2 K)"; REBCO "Tc ~92 K", "upper critical fields exceeding 100 T at low temperature", "Jc > 3 MA/cm² at 77 K self-field". - Xu, X. (2017). "A review and prospects for Nb3Sn superconductor development." *Superconductor Science and Technology* **30**, 093001. doi:[10.1088/1361-6668/aa7a20](https://doi.org/10.1088/1361-6668/aa7a20) · [arXiv:1706.10253](https://arxiv.org/abs/1706.10253) — Tc "up to 18.3 K", Bc2 "around 30 T" with state-of-the-art RRP strand at "25-27 T" at 4.2 K, and whole-wire Jc "1000 A/mm² at 4.2 K, 15 T". The primary source for the Nb3Sn numbers; the AST page above agrees with it. - Wikipedia, "Yttrium barium copper oxide" — the anisotropic upper critical field, "120 T for B perpendicular and 250 T for B parallel to the CuO2 planes". Tertiary, used only for the anisotropy statement, which is the point that a single Bc2 for a layered superconductor is incomplete. **The quench and its protection** - Wilson, M. N. (2016). "Quench and protection", Lecture 4, Joint Universities Accelerator School, CERN. [indico.cern.ch](https://indico.cern.ch/event/471931/contributions/1149667/attachments/1222206/1787378/JUAS_16_lect_4_quench_and_protection.pdf) — the propagation numbers this article turns on: adiabatic longitudinal "Typical values vad = 5 - 20 ms-1", and the transverse-to-longitudinal velocity ratio "0.01 to 0.03" arising from v_trans/v_long = sqrt(k_trans/k_long). Also the dump-resistor circuit ("circuit breaker must be able to open at full current against a voltage V = I.Rp (expensive)"), quench-back heaters, coil subdivision, and the LHC dipole "L = 0.12H I = 11.5kA E = 7.8 x 10^6 Joules". The tau·V = L·I identity in the body is this article's own two-line rearrangement of Wilson's tau = L/Rd and V = I·Rd, not a quoted result. - "Superconducting magnet designs and MRI accessibility: a review." [arXiv:2205.08918](https://arxiv.org/abs/2205.08918) — the helium inventory, verbatim: "The regular NbTi liquid Helium-bathed magnets operate at 4.2 K and contain approximately 1500-2000 liters of liquid Helium"; Table 1's NbTi minimum quench energy "MQE (mJ): 1-10"; the zero-boil-off description ("The cryocooler recondenses the Helium gas that evaporates from the cryogen bath... eliminating the need for any refill except after a quench event"); and the sealed low-inventory magnets at 7 L, 0.7 L and 12 L. - Nugteren, J. van, *et al.* / Baig, T., *et al.* (2020). "Mechanical analysis of an MgB2 1.5 T MRI main magnet." *Superconductor Science and Technology*; PMC copy [PMC7405900](https://pmc.ncbi.nlm.nih.gov/articles/PMC7405900/) — the hot-spot design rule, verbatim: "the peak temperature inside the magnet should not exceed 200 K"; and a worked second design point, "inductance is 90 H, and the total stored energy is 2.94 MJ" at an operating current of 256 A (which checks: (1/2)(90)(256)² = 2.95 MJ). **Author attribution not independently confirmed; the quoted text and the numbers were read directly from the PMC copy.** - mriquestions.com, "What is a quench?" [mriquestions.com](https://mriquestions.com/what-is-a-quench.html) — the clinical description of the runaway, the burst disc "designed to open at a scanner-specific pressure, for example 10 or 26 psi", the oxygen-displacement hazard, and the clinical-literature expansion ratio "approximately 700–760:1" — quoted here precisely because that spread is the ambiguity this article resolves. **Helium's thermophysical numbers** - Air Products Safetygram 22, *Liquid Helium*, physical-properties table; stable copy republished by MIT Environment, Health & Safety. [ehs.mit.edu](https://ehs.mit.edu/wp-content/uploads/2020/01/safety_gram_22_HELIUM.pdf) — "Latent Heat of Vaporization 8.72 Btu/lb (20.28 kJ/kg)"; "Density, Liquid @ B.P., 1 atm 7.802 lb/ft3 (124.98 kg/m3)"; "Density, Gas @ 70°F (21.1°C), 1 atm 0.0103 lb/ft3 (0.165 kg/m3)"; and "Expansion Ratio, Liquid to Gas, B.P. to 32°F (0°C) 1 to 754". **The internal inconsistency flagged in the body is this article's own finding:** 754 does not reproduce from a 0 °C gas density (which gives 700) but does reproduce, to three figures, from the table's own 70 °F row. - Wikipedia, "Expansion ratio" — helium "1 to 745", with the table's stated conditions being boiling point to ambient. Tertiary; used to show that the ~745–757 family is the room-temperature reference, not a competing measurement. - Kitt Peak National Observatory / NOIRLab, "A Quick Guide to Cryogens". [noao.edu/kpno](https://www.noao.edu/kpno/manuals/irim/cryo.html) — the independent per-litre cross-check, verbatim: liquid helium's latent heat "is only about 2.6 kJ/l" against liquid nitrogen at "about 160 kJ/l", and "A heat input of only 1 watt will boil away 1.4 l of LHe in an hour". - The 2.53 kJ/L, the 1 : 700 and 1 : 754 ratios, the 4.3 MJ bath capacity, the 3 160 L required to absorb 8 MJ, and the 1 190 / 1 280 m³ vent volumes are **this article's own arithmetic** on the sourced densities, latent heat and inventory, using the ideal-gas law at 101.325 kPa and a molar mass of 4.002602 g/mol. Likewise the copper heat-capacity figure of about 900 J m⁻³ K⁻¹ at 4.2 K, computed from the Sommerfeld constant 0.695 mJ mol⁻¹ K⁻² and Debye temperature 343 K given in the JLab magnet group's *Low-Temperature Materials Properties* chapter 2, against the Dulong–Petit limit 3R for the room-temperature comparison. **Demand** - U.S. Geological Survey, *Mineral Commodity Summaries 2026*, Helium. [pubs.usgs.gov](https://pubs.usgs.gov/periodicals/mcs2026/mcs2026-helium.pdf) — **the current figure**, verbatim: "Helium was used for, in decreasing quantity of use, analytical, engineering, lab, science, and specialty gases (22%); controlled atmospheres, fiber optics, and semiconductors (17%); lifting gas (17%); magnetic resonance imaging (15%); aerospace (9%); welding (8%); diving (5%); leak detection (5%); and other applications (2%)". Also 2025 US sales of 81 million cubic metres valued near $970 million. - U.S. Geological Survey, *Mineral Commodity Summaries 2025*, Helium. [pubs.usgs.gov](https://pubs.usgs.gov/periodicals/mcs2025/mcs2025-helium.pdf) — the previous year's split with MRI at 17 %, behind analytical/specialty gases at 22 % and lifting gas at 18 %. - U.S. Geological Survey, *Mineral Commodity Summaries 2023*, Helium. [pubs.usgs.gov](https://pubs.usgs.gov/periodicals/mcs2023/mcs2023-helium.pdf) — the earlier ranking, verbatim: "in descending order by estimated quantity, magnetic resonance imaging, lifting gas, analytical and laboratory applications, electronics and semiconductor manufacturing, welding, engineering and scientific applications". The three editions together are why the body gives a trend rather than a single number. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Superconducting_magnet) : [Wikitube](https://en.wikitube.io/wiki/Superconducting_magnet) ## Previous hub tags Tree parent: [[Helium]]. Legacy hubs: none. Hubs: `Life_Physics`. Portals: [[PORTAL_Helium]]. *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order). Promoted under §5 on 2026-08-05: three.js section added above the existing p5 microsim, thin Overview replaced with a sourced body; no generated block altered.*