43-6 Controlled Thermonuclear Fusion

43-6 Controlled Thermonuclear Fusion#

Prompts

  • On Earth we lack gravitational confinement (section 43-5). What are the two main approaches to confining a fusion plasma? How does each work in one sentence?

  • Magnetic confinement (tokamaks): charged particles follow magnetic field lines. Why does a toroidal (doughnut) geometry help? What prevents the plasma from drifting to the walls?

  • Inertial confinement: lasers or particle beams compress a fuel pellet. Why is the confinement time \(\tau\) very short? How does compression achieve the needed density and temperature?

  • The Lawson criterion requires \(n\tau T\) above a threshold for ignition (fusion power \(\geq\) losses). What do \(n\), \(\tau\), and \(T\) represent? Why does “triple product” \(n\tau T\) matter?

  • What advantages does fusion offer over fission (fuel, waste)? What are the main challenges to achieving net power?

Lecture Notes#

Overview#

  • Controlled fusion on Earth requires confining and heating a plasma without gravity (section 43-5). Two main approaches: magnetic confinement (tokamaks) and inertial confinement (laser/beam compression).

  • Ignition — fusion power exceeds losses — requires the Lawson criterion: \(n\tau T\) above a threshold, where \(n\) is density, \(\tau\) is confinement time, and \(T\) is temperature.

  • Fusion offers abundant fuel (deuterium from seawater) and less long-lived radioactive waste than fission (section 43-1).

The Confinement Challenge#

Stars use gravitational confinement (section 43-5). On Earth, we must create \(T \sim 10^8\) K and sufficient density by other means. A hot plasma cannot touch solid walls (it would cool and contaminate). Two strategies:

Approach

Idea

Confinement

Magnetic

Charged particles follow \(\vec{B}\); field keeps plasma away from walls

Long \(\tau\), moderate \(n\)

Inertial

Compress a pellet so fast that fusion occurs before it explodes

Short \(\tau\), very high \(n\)

Magnetic Confinement: Tokamaks#

A tokamak uses a toroidal (doughnut-shaped) magnetic field. Charged particles spiral along field lines and are trapped in the torus. Additional poloidal field (from a plasma current) twists the field lines into a helix, reducing drifts that would push the plasma to the walls.

Key parameters: Large volume, strong magnetic field (\(B \sim\) several tesla), heating by neutral beams or radio waves. Experiments (e.g., ITER, JET) aim to reach the Lawson criterion for D–T (section 43-4).

Why toroidal?

A simple solenoid would have particles drifting to the ends. Bending into a torus closes the geometry. The twist (rotational transform) prevents another instability (the “bad curvature” of a simple torus).

Inertial Confinement#

Inertial confinement compresses a small fuel pellet (D–T) with intense lasers or particle beams. The outer layer ablates and blows off; reaction forces compress the core to very high density and temperature. Fusion occurs in a brief burst (~nanoseconds) before the pellet explodes — confinement is by the inertia of the imploding fuel.

National Ignition Facility (NIF): Lasers compress a capsule; recent experiments have achieved ignition (fusion energy out \(\geq\) laser energy in) in the lab.

The Lawson Criterion#

For a fusion plasma to sustain itself, the fusion power must at least balance the power lost (radiation, conduction, etc.). This leads to the Lawson criterion (or triple product):

(466)#\[ n\tau T \gtrsim \text{threshold} \]

  • \(n\): particle density (m\(^{-3}\))

  • \(\tau\): energy confinement time (s)

  • \(T\): temperature (K or keV)

For D–T, the threshold is \(n\tau T \sim 10^{21}\) m\(^{-3}\cdot\)s\(\cdot\)keV (order of magnitude). Magnetic confinement seeks high \(\tau\) at moderate \(n\); inertial confinement uses very high \(n\) and short \(\tau\).

Fusion vs Fission: Benefits and Challenges#

Benefits:

  • Fuel: Deuterium is abundant in seawater (~0.015% of H); tritium can be bred from lithium.

  • Waste: No long-lived actinides; neutron activation of structural materials is the main waste concern, generally less severe than fission.

Challenges:

  • Reaching and sustaining the Lawson criterion.

  • Materials that withstand neutron flux and heat.

  • Tritium breeding and handling.

Summary#

  • Magnetic confinement (tokamaks): toroidal \(B\) traps plasma; long \(\tau\), moderate \(n\).

  • Inertial confinement: lasers/beams compress pellet; short \(\tau\), very high \(n\).

  • Lawson criterion: \(n\tau T \gtrsim\) threshold for ignition.

  • Fusion: abundant D, less long-lived waste; challenges remain for net power.