Confinement Methods

To sustain fusion reactions, high-temperature plasma exceeding 100 million degrees must be held without touching the vessel walls. This section explains the principles and characteristics of major confinement methods.

Why Confinement Is Necessary

For fusion reactions to occur at a sufficient rate, the plasma must satisfy the following conditions:

1. High temperature (ion temperature $T_i \sim 10$ keV or higher)
2. High density (particle density $n \sim 10^{20}$ m$^{-3}$)
3. Sufficient confinement time ($\tau_E \sim 1$ second or longer)

These conditions are summarized in the Lawson criterion, a measure of fusion ignition:

$$n \cdot T \cdot \tau_E > 3 \times 10^{21} \text{ keV} \cdot \text{s} / \text{m}^3$$

Classification of Confinement Methods

There are broadly three approaches to plasma confinement.

Magnetic Confinement

This method uses magnetic fields to confine charged particles. Since charged particles gyrate around magnetic field lines (Larmor motion), plasma can be contained by configuring an appropriate magnetic field geometry.

The Larmor radius $r_L$ is expressed as:

$$r_L = \frac{m v_\perp}{q B}$$

where $m$ is the particle mass, $v_\perp$ is the velocity component perpendicular to the magnetic field, $q$ is the charge, and $B$ is the magnetic field strength.

Major magnetic confinement devices:

• Tokamak - Toroidal confinement using plasma current
• Stellarator/Helical - Confinement using external coils only

Inertial Confinement

This method rapidly compresses and heats fuel pellets with powerful lasers or particle beams, using the fuel’s own inertia to secure the reaction time.

Details: Inertial Confinement Fusion

Gravitational Confinement

This method is realized in stars like the Sun. The enormous gravitational force confines the high-temperature plasma in the core. It is not achievable on Earth and is outside the scope of research.

Comparison of Magnetic and Inertial Confinement

Feature	Magnetic Confinement	Inertial Confinement
Density	$\sim 10^{20}$ m$^{-3}$	$\sim 10^{31}$ m$^{-3}$
Confinement time	$\sim 1$ s	$\sim 10^{-11}$ s
Operation mode	Steady/quasi-steady	Pulsed
Main devices	Tokamak, Stellarator	Laser facilities
Reactor challenges	Material lifetime, steady operation	Repetition rate, efficiency

Plasma Beta Value

An important metric for evaluating confinement performance is the beta value $\beta$, the ratio of plasma pressure to magnetic pressure:

$$\beta = \frac{n k_B T}{B^2 / 2\mu_0} = \frac{2\mu_0 n k_B T}{B^2}$$

A higher beta value means more plasma pressure can be confined with the same magnetic field strength, improving economics. However, MHD instabilities are more likely to occur in the high-beta regime.

Related Topics

• Tokamak Confinement - The most advanced magnetic confinement method
• Stellarator/Helical Confinement - Magnetic confinement suited for steady operation
• Inertial Confinement Fusion - Fusion by laser compression
• Glossary: Confinement - Basic definition