How to Understand Tokamak Physics: Plasma Confinement and Magnetic Fields

Step-by-Step Guide

1. 1

   Understand Fusion Reactions

   Fusion combines light nuclei, releasing energy (E=mc²). The most accessible reaction is D-T: Deuterium + Tritium → Helium-4 (3.5 MeV) + Neutron (14.1 MeV). D is abundant in seawater; T is bred from lithium. The 14 MeV neutron carries 80% of energy and must be captured in a blanket.

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   D-T Fusion:
   ²H + ³H → ⁴He (3.5 MeV) + n (14.1 MeV)
   Total: 17.6 MeV per reaction
   Temp needed: ~150 million K
   Energy/g D-T: 3.4×10¹¹ J (8M× coal)

2. 2

   Master Plasma Physics

   At 150M K, hydrogen is fully ionized — a plasma of protons and electrons governed by magnetohydrodynamics (MHD). Key: quasi-neutrality, collective behavior, Debye shielding. Fusion plasma density ~10²⁰/m³ — about 10⁶ times less dense than air. Energy comes from temperature, not density.

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   Tip: Fusion plasma is one-millionth of atmospheric density. The energy comes from extreme temperature (150M K), not density. This is why magnetic confinement works — plasma pressure is manageable.
3. 3

   Understand Magnetic Confinement

   Charged particles spiral around magnetic field lines (Larmor orbit). Toroidal field coils create a field around the torus; plasma current creates a poloidal field. The combination produces helical field lines that confine particles. Without the poloidal field, particles drift outward due to field gradient and curvature.

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   Warning: Magnetic confinement is never perfect. Particles drift across field lines due to collisions, turbulence, and MHD instabilities. Energy confinement time is typically 0.1-3 seconds. Improving confinement is the central challenge.
4. 4

   Learn the Lawson Criterion

   The Lawson criterion: n·T·τ > 3×10²¹ keV·s/m³ for D-T fusion at T~15 keV. You need high density, high temperature, and long confinement time. ITER targets n·T·τ ≈ 3×10²¹ for Q=10.

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   Lawson Criterion (D-T):
   n·T·τ > 3×10²¹ keV·s/m³
   n: ~10²⁰ m⁻³, T: ~15 keV, τ: ~3 s
   ITER: Q=10, JET record: Q=0.67
   Ignition (Q=∞): n·T·τ > 5×10²¹

5. 5

   Understand Tokamak Components

   Key systems: 1) Toroidal field coils (18 in ITER) — main confining field, 2) Central solenoid — induces plasma current, 3) Poloidal field coils — shape and position plasma, 4) Vacuum vessel, 5) Blanket — captures neutrons, breeds tritium, 6) Divertor — exhausts heat and helium ash, 7) Heating systems (NBI, ICRH, ECRH).

   

6. 6

   Master Plasma Heating

   Ohmic heating is insufficient. Three auxiliary methods: NBI (neutral beam injection), ICRH (ion cyclotron RF), ECRH (electron cyclotron RF). ITER: 50 MW heating for 500 MW output. Alpha particle self-heating becomes dominant at Q>5.

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   Tip: Alpha heating is key to ignition. D-T reactions produce 3.5 MeV alphas that deposit energy in the plasma. At Q>5, alpha heating exceeds external heating. At ignition, alpha heating alone sustains the plasma.
7. 7

   Understand MHD Instabilities

   Key instabilities: kink modes (current-driven), ballooning modes (pressure-driven), tearing modes (magnetic reconnection), ELMs (edge bursts that can damage the divertor). Stability controlled by plasma shaping, current profile, and active feedback coils.

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   Warning: ELMs are a major concern for ITER. Type I ELMs deposit several MJ in milliseconds on the divertor — potentially causing material damage. Mitigation: pellet injection, RMP coils, or ELM-free regimes.
8. 8

   Learn Transport and Confinement

   Energy confinement τ is set by transport: classical (collisional), neoclassical (toroidal effects), anomalous (turbulence — dominates, 10-100x higher). H-mode reduces edge turbulence, improving τ by 2-3x. ITER98y2 scaling: τ ∝ I^0.93 × B^0.15 × n^0.41 × P^-0.69 × R^1.97.

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   ITER98y2 H-mode Scaling:
   τ_E = 0.056 × I_p^0.93 × B_t^0.15 × n^0.41
         × P^-0.69 × R^1.97 × κ^0.78
   Key: bigger R and higher I_p improve confinement most.

9. 9

   Understand the Divertor

   The divertor is the plasma exhaust — handles heat, particles, and impurities. Magnetic fields channel plasma edge to strike points on target plates. Heat flux can exceed 10 MW/m² steady-state. Materials: tungsten (high melting point, low tritium retention). ITER: 54 cassettes, water-cooled.

   

10. 10

    Study Key Experiments

    ITER (France, 500 MW, Q=10, first plasma 2034), JET (UK, Q=0.67 record), KSTAR (Korea, 30s H-mode), EAST (China, 100s H-mode). Private: CFS SPARC (HTS magnets, Q>1 by 2027), Tokamak Energy (spherical tokamak + HTS).

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    Tip: HTS magnets (REBCO, 20+ T) enable compact tokamaks. CFS SPARC achieves ITER-equivalent performance at 1/40 the volume. Fusion power scales as B⁴ — doubling field gives 16x more power.
11. 11

    Project the Path to Fusion Power

    ITER first plasma 2034, D-T 2039, Q=10. CFS SPARC Q>1 by 2027, ARC power plant 2030s. First fusion power plant likely 2045-2055. Key milestones: sustained Q>1, tritium self-sufficiency, steady-state operation, net electricity. Key risk: ITER delays could push timeline 5-10 years.

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    Warning: Fusion timelines are notoriously optimistic. ITER was originally 2016 first plasma — now 2034. Private timelines (CFS 2027) are more credible but still ambitious.