Short description: Magnetic field component encircling the plasma cross-section in toroidal systems

The poloidal field is the component of the magnetic field that runs around the short (poloidal) direction of a toroidal plasma, such as in a tokamak. Together with the toroidal field, it forms helical magnetic field lines that confine charged particles within the plasma.

In magnetic confinement systems, the combination of toroidal and poloidal fields is essential for achieving stable confinement. Without a poloidal component, particles would drift across field lines and escape the plasma.

File:Tokamak poloidal toroidal fields.svg

Magnetic field geometry in a tokamak: the toroidal field wraps around the torus, while the poloidal field encircles the plasma cross-section, producing helical field lines.

Physical meaning

In a toroidal geometry, two directions are defined:

Toroidal direction — around the major axis of the torus
Poloidal direction — around the minor cross-section

The poloidal field follows the second direction and is typically weaker than the toroidal field. However, it plays a crucial role in shaping the magnetic topology.

The resulting helical field lines guide charged particles, preventing them from drifting freely across the plasma.

Generation of the poloidal field

In a tokamak, the poloidal field is primarily generated by an electric current flowing through the plasma itself. This current is induced by transformer action and produces a magnetic field that encircles the plasma column.

Additional external coils can also contribute to the poloidal field, allowing control of plasma position and shape.

Role in confinement

The poloidal field is essential for magnetic confinement:

It twists magnetic field lines into helices
It reduces particle drift losses
It contributes to closed magnetic surfaces

Without the poloidal component, the magnetic field would be purely toroidal, and charged particles would gradually escape due to curvature and gradient drifts.

Relation to safety factor

The ratio between toroidal and poloidal field components determines the safety factor:

$q = \frac{toroidal turns}{poloidal turns}$

This parameter describes how magnetic field lines wind around the torus and is a key quantity in plasma stability analysis.

Connection to plasma stability

The strength and structure of the poloidal field influence many plasma instabilities:

Kink instability depends on field line twist
Tearing mode occurs at rational surfaces
Ballooning instability is affected by field curvature

Careful control of the poloidal field is therefore required to maintain stable confinement.

Applications

Poloidal fields are central to:

Tokamak operation
Magnetic confinement systems
Plasma shaping and equilibrium control
Fusion reactor design

They are also relevant in astrophysical plasmas where toroidal and poloidal field components coexist.

Physical interpretation

The poloidal field represents the coupling between plasma current and magnetic confinement. It transforms a simple toroidal field into a structured, self-consistent system capable of confining high-temperature plasma.

Together with the toroidal field, it defines the geometry of magnetically confined plasmas.