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Fix Matter see-also invoke

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Fix Matter see-also invoke

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{{Quantum matter backlink|Plasma and fusion physics}}

A tokamak is a device designed to confine high-temperature plasma using magnetic fields in order to achieve controlled nuclear fusion.

It is the most widely studied configuration for fusion energy and is used in experiments such as:

* DIII-D
* JET
* ITER<ref name="wesson">J. Wesson, ''Tokamaks'', Oxford University Press.</ref>

[[File:Tokamak fusion-reactor and plasma-analysis-1.jpg|thumb|300px|Conceptual illustration of tokamak physics, showing magnetic confinement of high-temperature plasma, external heating methods, and transport processes governing confinement and edge behavior.]]
== Basic principle ==
'''Fusion requires:'''

* Extremely high temperatures (~10⁸ K)
* Sufficient particle density
* Long confinement time

These conditions are summarized by the Lawson criterion.

In a tokamak, plasma is confined in a toroidal (donut-shaped) geometry using magnetic fields.

== Magnetic confinement ==
Charged particles spiral around magnetic field lines due to the Lorentz force:

<math>
\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})
</math>

Tokamaks use two main magnetic fields:

* Toroidal field (around the donut)
* [[Physics:Quantum Poloidal field|Poloidal field]] (around the cross-section)

Together, these create helical field lines that improve confinement.<ref name="wesson" />

== Plasma heating and current drive ==
A strong electric current flows through the plasma:

* Generates the poloidal magnetic field
* Heats the plasma (ohmic heating)

This current is essential for confinement but also introduces instabilities.
== Plasma heating ==
In an operating fusion reactor, part of the energy generated will serve to maintain the plasma temperature as fresh [[Physics:Deuterium|Deuterium]] and [[Physics:Tritium|tritium]] are introduced. However, in the startup of a reactor, either initially or after a temporary shutdown, the plasma will have to be heated to its [[Physics:Operating temperature|operating temperature]] of greater than 10 keV (over 100 million degrees Celsius). In current tokamak (and other) magnetic fusion experiments, insufficient fusion energy is produced to maintain the plasma temperature, and constant external heating must be supplied. Chinese researchers set up the [[Physics:Experimental Advanced Superconducting Tokamak|Experimental Advanced Superconducting Tokamak]] (EAST) in 2006, which can supposedly sustain a plasma temperature of 100 million degree Celsius for initiating fusion between hydrogen atoms, according to a November 2018 test.

=== Ohmic heating ~ inductive mode ===

Since the plasma is an electrical conductor, it is possible to heat the plasma by inducing a current through it; the induced current that provides most of the [[Physics:Quantum Poloidal field|poloidal field]] is also a major source of initial heating.

The heating caused by the induced current is called ohmic (or resistive) heating; it is the same kind of heating that occurs in an electric light bulb or in an electric heater. The heat generated depends on the resistance of the plasma and the amount of electric current running through it. But as the temperature of heated plasma rises, the resistance decreases and ohmic heating becomes less effective. It appears that the maximum plasma temperature attainable by ohmic heating in a tokamak is 20–30 million degrees Celsius. To obtain still higher temperatures, additional heating methods must be used.

The current is induced by continually increasing the current through an electromagnetic winding linked with the plasma torus: the plasma can be viewed as the secondary winding of a transformer. This is inherently a pulsed process because there is a limit to the current through the primary (there are also other limitations on long pulses). Tokamaks must therefore either operate for short periods or rely on other means of heating and current drive.

=== Magnetic compression ===
A gas can be heated by sudden compression. In the same way, the temperature of a plasma is increased if it is compressed rapidly by increasing the confining magnetic field. In a tokamak, this compression is achieved simply by moving the plasma into a region of higher magnetic field (i.e., radially inward). Since plasma compression brings the ions closer together, the process has the additional benefit of facilitating attainment of the required density for a fusion reactor.

Magnetic compression was an area of research in the early "tokamak stampede", and was the purpose of one major design, the ATC. The concept has not been widely used since then, although a somewhat similar concept is part of the General Fusion design.

=== Neutral-beam injection ===
[[File:Neutral Beam Injection.png|center|500px|First, plasma is formed by microwaving gas. Next, the plasma is accelerated across a voltage drop. This heats the ions to fusion conditions. After this the ions are re-neutralizing. Lastly, the neutrals are injected into the machine.]]

Neutral-beam injection involves the introduction of high energy (rapidly moving) atoms or molecules into an ohmically heated, magnetically confined plasma within the tokamak.

The high energy atoms originate as ions in an arc chamber before being extracted through a high voltage grid set. The term "ion source" is used to generally mean the assembly consisting of a set of electron emitting filaments, an arc chamber volume, and a set of extraction grids. A second device, similar in concept, is used to separately accelerate electrons to the same energy. The much lighter mass of the electrons makes this device much smaller than its ion counterpart. The two beams then intersect, where the ions and electrons recombine into neutral atoms, allowing them to travel through the magnetic fields.

Once the neutral beam enters the tokamak, interactions with the main plasma ions occur. This has two effects. One is that the injected atoms re-ionize and become charged, thereby becoming trapped inside the reactor and adding to the fuel mass. The other is that the process of being ionized occurs through impacts with the rest of the fuel, and these impacts deposit energy in that fuel, heating it.

This form of heating has no inherent energy (temperature) limitation, in contrast to the ohmic method, but its rate is limited to the current in the injectors. Ion source extraction voltages are typically on the order of 50–100 kV, and high voltage, negative ion sources (-1 MV) are being developed for ITER. The ITER Neutral Beam Test Facility in Padova will be the first ITER facility to start operation.<ref>{{Cite web|url=https://www.igi.cnr.it/www/sites/default/files/home201511/SchedaNBTF_MIUR_EN.pdf|title=Neutral Beam Test Facility|access-date=9 October 2016|archive-date=10 October 2016|archive-url=https://web.archive.org/web/20161010212050/https://www.igi.cnr.it/www/sites/default/files/home201511/SchedaNBTF_MIUR_EN.pdf}}</ref>

While neutral beam injection is used primarily for plasma heating, it can also be used as a diagnostic tool and in feedback control by making a pulsed beam consisting of a string of brief 2–10 ms beam blips. Deuterium is a primary fuel for neutral beam heating systems and hydrogen and helium are sometimes used for selected experiments.

=== Radio-frequency heating ===
[[File:Gyrotron plateforme.jpg|thumb|Set of hyperfrequency tubes (84 GHz and 118 GHz) for plasma heating by electron cyclotron waves on the Tokamak à configuration variable (TCV). Courtesy of SPC-EPFL.]]

''See also'': [[Physics:Quantum Radio frequency heating|radio-frequency heating]] and [[Physics:Quantum Dielectric heating|dielectric heating]]

High-frequency electromagnetic waves are generated by oscillators (often by [[Physics:Quantum Gyrotron|gyrotrons]] or [[Physics:Quantum Klystron|klystrons]]) outside the torus. If the waves have the correct frequency and polarization, their energy can be transferred to charged particles in the [[Physics:Quantum matter/plasma|plasma]]. These particles then collide with others, increasing the temperature of the bulk plasma.

Common methods include [[Physics:Quantum Electron cyclotron resonance|electron cyclotron resonance heating]] (ECRH) and [[Physics:Quantum Ion cyclotron resonance|ion cyclotron resonance heating]] (ICRH). In practice, this energy is typically delivered in the form of microwaves.

== Stability and confinement ==
Plasma stability is governed by magnetohydrodynamics (MHD).

Important concepts:

* Safety factor <math>q</math>
* Magnetic shear
* Instabilities (kink, tearing modes)

Maintaining stability is crucial for sustained operation.<ref name="freidberg">J. P. Freidberg, ''Ideal MHD''.</ref>

== Heating methods ==
Additional heating is required to reach fusion temperatures:

* Neutral beam injection
* Radio-frequency heating
* Ohmic heating

These methods increase particle energy and sustain the plasma.

== Transport and losses ==
Particles and energy are not perfectly confined.

Loss mechanisms include:

* Diffusion
* Turbulence
* Drift effects

Transport processes determine how long plasma can be confined.

== Divertor and edge region ==
The edge of the plasma includes:

* Scrape-off layer (SOL)
* Divertor region

In this region:

* Magnetic field lines intersect material surfaces
* Particles are exhausted and recycled

This region is critical for:

* Heat removal
* Plasma-wall interaction
* Impurity control

== Connection to edge physics ==
The behavior of the edge plasma strongly influences overall performance.

Key phenomena:

* Drift-driven transport
* Plasma rotation
* Recycling of neutrals

These effects determine how particles are distributed at the divertor.

Detailed studies are presented in:

* [[Physics:Tokamak edge physics and recycling asymmetries|Tokamak edge physics and recycling asymmetries]]<ref name="emdee">Emdee, E. D. et al., ''Combined Influence of Rotation and Scrape-Off Layer Drifts on Recycling Asymmetries in Tokamak Plasmas''.</ref>

== Physical interpretation ==
Tokamaks represent a controlled environment where:

* Electromagnetic forces dominate
* Collective plasma behavior emerges
* Macroscopic confinement arises from microscopic particle motion

They are a key application of plasma physics and kinetic theory.

== Summary ==
Tokamak physics:

* Uses magnetic fields to confine plasma
* Combines kinetic, fluid, and electromagnetic effects
* Enables experimental study of fusion energy

It forms the direct link between plasma theory and practical fusion devices.

==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also/Matter}}

=References=
{{Reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Tokamak physics|1}}

Physics:Quantum Tokamak - Revision history

imported>WikiHarold: Fix Matter see-also invoke

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