Physics:Quantum Tokamak
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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[1]
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:
Tokamaks use two main magnetic fields:
- Toroidal field (around the donut)
- Poloidal field (around the cross-section)
Together, these create helical field lines that improve confinement.[1]
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 Deuterium and 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 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 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 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
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.[2]
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
See also: radio-frequency heating and dielectric heating
High-frequency electromagnetic waves are generated by oscillators (often by gyrotrons or klystrons) outside the torus. If the waves have the correct frequency and polarization, their energy can be transferred to charged particles in the plasma. These particles then collide with others, increasing the temperature of the bulk plasma.
Common methods include electron cyclotron resonance heating (ECRH) and 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
- Magnetic shear
- Instabilities (kink, tearing modes)
Maintaining stability is crucial for sustained operation.[3]
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:
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
Table of contents (136 articles)
Index
Full contents
- Physics:Quantum Interpretations of quantum mechanics
- Physics:Quantum Wave–particle duality
- Physics:Quantum Complementarity principle
- Physics:Quantum Uncertainty principle
- Physics:Quantum Measurement problem
- Physics:Quantum Bell's theorem
- Physics:Quantum Hidden variable theory
- Physics:Quantum A Spooky Action at a Distance
- Physics:Quantum A Walk Through the Universe
- Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together
- Physics:Quantum Density matrix
- Physics:Quantum Exactly solvable quantum systems
- Physics:Quantum Formulas Collection
- Physics:Quantum A Matter Of Size
- Physics:Quantum Symmetry in quantum mechanics
- Physics:Quantum Angular momentum operator
- Physics:Quantum Runge–Lenz vector
- Physics:Quantum Approximation Methods
- Physics:Quantum Matter Elements and Particles
- Physics:Quantum Dirac equation
- Physics:Quantum Klein–Gordon equation
- Physics:Quantum Atomic structure and spectroscopy
- Physics:Quantum Hydrogen atom
- Physics:Quantum Multi-electron atoms
- Physics:Quantum Fine structure
- Physics:Quantum Hyperfine structure
- Physics:Quantum Isotopic shift
- Physics:Quantum Zeeman effect
- Physics:Quantum Stark effect
- Physics:Quantum Spectral lines and series
- Physics:Quantum Selection rules
- Physics:Quantum Fermi's golden rule
- Physics:Quantum Wavefunction
- Physics:Quantum Superposition principle
- Physics:Quantum Eigenstates and eigenvalues
- Physics:Quantum Boundary conditions and quantization
- Physics:Quantum Standing waves and modes
- Physics:Quantum Normal modes and field quantization
- Physics:Number of independent spatial modes in a spherical volume
- Physics:Quantum Density of states
- Physics:Quantum Time evolution
- Physics:Quantum Schrödinger equation
- Physics:Quantum Time-dependent Schrödinger equation
- Physics:Quantum Stationary states
- Physics:Quantum Perturbation theory
- Physics:Quantum Time-dependent perturbation theory
- Physics:Quantum Adiabatic theorem
- Physics:Quantum Scattering theory
- Physics:Quantum S-matrix
- Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
- Physics:Quantum optics beam splitter experiments
- Physics:Quantum Ultra fast lasers
- Physics:Quantum Experimental quantum physics Template:Quantum optics operators
- Physics:Quantum field theory (QFT) basics
- Physics:Quantum field theory (QFT) core
- Physics:Quantum Fields and Particles
- Physics:Quantum Second quantization
- Physics:Quantum Harmonic Oscillator field modes
- Physics:Quantum Creation and annihilation operators
- Physics:Quantum vacuum fluctuations
- Physics:Quantum Propagators in quantum field theory
- Physics:Quantum Feynman diagrams
- Physics:Quantum Path integral formulation
- Physics:Quantum Renormalization in field theory
- Physics:Quantum Renormalization group
- Physics:Quantum Field Theory Gauge symmetry
- Physics:Quantum Non-Abelian gauge theory
- Physics:Quantum Electrodynamics (QED)
- Physics:Quantum chromodynamics (QCD)
- Physics:Quantum Electroweak theory
- Physics:Quantum Standard Model
- Physics:Quantum Statistical mechanics
- Physics:Quantum Partition function
- Physics:Quantum Distribution functions
- Physics:Quantum Liouville equation
- Physics:Quantum Kinetic theory
- Physics:Quantum Boltzmann equation
- Physics:Quantum BBGKY hierarchy
- Physics:Quantum Relaxation and thermalization
- Physics:Quantum Thermodynamics
- Physics:Quantum Fusion reactions and Lawson criterion
- Physics:Quantum Plasma (fusion context)
- Physics:Quantum Magnetic confinement fusion
- Physics:Quantum Inertial confinement fusion
- Physics:Quantum Plasma instabilities and turbulence
- Physics:Quantum Tokamak core plasma
- Physics:Quantum Tokamak edge physics and recycling asymmetries
- Physics:Quantum Stellarator
- Physics:Quantum mechanics/Timeline
- Physics:Quantum mechanics/Timeline/Pre-quantum era
- Physics:Quantum mechanics/Timeline/Old quantum theory
- Physics:Quantum mechanics/Timeline/Modern quantum mechanics
- Physics:Quantum mechanics/Timeline/Quantum field theory era
- Physics:Quantum mechanics/Timeline/Quantum information era
- Physics:Quantum mechanics/Timeline/Quantum technology era
- Physics:Quantum mechanics/Timeline/Quiz
References
- ↑ 1.0 1.1 J. Wesson, Tokamaks, Oxford University Press.
- ↑ "Neutral Beam Test Facility". https://www.igi.cnr.it/www/sites/default/files/home201511/SchedaNBTF_MIUR_EN.pdf.
- ↑ J. P. Freidberg, Ideal MHD.
- ↑ Emdee, E. D. et al., Combined Influence of Rotation and Scrape-Off Layer Drifts on Recycling Asymmetries in Tokamak Plasmas.
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