Classical diffusion is a key concept in fusion power and other fields where a plasma is confined by a magnetic field within a vessel. It considers collisions between ions in the plasma that causes the particles to move to different paths and eventually leave the confinement volume and strike the sides of the vessel.
The rate of diffusion scales with 1/B2, where B is the magnetic field strength, implies that confinement times can be greatly improved with small increases in field strength. In practice, the rates suggested by classical diffusion have not been found in real-world machines, where a host of previously unknown plasma instabilities caused the particles to leave confinement at rates closer to B, not B2, as had been seen in Bohm diffusion.
The failure of classical diffusion to predict real-world plasma behavior led to a period in the 1960s known as "the doldrums" where it appeared a practical fusion reactor would be impossible. Over time, the instabilities were found and addressed, especially in the tokamak. This has led to a deeper understanding of the diffusion process, known as neoclassical transport.
Diffusion is a random walk process that can be quantified by the two key parameters: Δx, the step size, and Δt, the time interval when the walker takes a step. Thus, the diffusion coefficient is defined as D≡(Δx)2/(Δt). Plasma is a gas-like mixture of high-temperature particles, the electrons and ions that would normally be joined to form neutral atoms at lower temperatures. Temperature is a measure of the average velocity of particles, so high temperatures imply high speeds, and thus a plasma will quickly expand at rates that make it difficult to work with unless some form of "confinement" is applied.
At the temperatures involved in nuclear fusion, no material container can hold a plasma. The most common solution to this problem is to use a magnetic field to provide confinement, sometimes known as a "magnetic bottle". When a charged particle is placed in a magnetic field, it will orbit the field lines while continuing to move along that line with whatever initial velocity it had. This produces a helical path through space. The radius of the path is a function of the strength of the magnetic field. Since the axial velocities will have a range of values, often based on the Maxwell-Boltzmann statistics, this means the particles in the plasma will pass by others as they overtake them or are overtaken.
If one considers two such ions traveling along parallel axial paths, they can collide whenever their orbits intersect. In most geometries, this means there is a significant difference in the instantaneous velocities when they collide - one might be going "up" while the other would be going "down" in their helical paths. This causes the collisions to scatter the particles, making them random walks. Eventually, this process will cause any given ion to eventually leave the boundary of the field, and thereby escape "confinement".
In a uniform magnetic field, a particle undergoes random walk across the field lines by the step size of gyroradius ρ≡vth/Ω, where vth denotes the thermal velocity, and Ω≡qB/m, the gyrofrequency. The steps are randomized by the collisions to lose the coherence. Thus, the time step, or the decoherence time, is the inverse of the collisional frequency νc. The rate of diffusion is given by νcρ2, with the rather favorable B−2 scaling law.
When the topic of controlled fusion was first being studied, it was believed that the plasmas would follow the classical diffusion rate, and this suggested that useful confinement times would be relatively easy to achieve. However, in 1949 a team studying plasma arcs as a method of isotope separation found that the diffusion time was much greater than what was predicted by the classical method. David Bohm suggested it scaled with B. If this is true, Bohm diffusion would mean that useful confinement times would require impossibly large fields. Initially, Bohm diffusion was dismissed as a side-effect of the particular experimental apparatus being used and the heavy ions within it, causing turbulence within the plasma that led to faster diffusion. It seemed the larger fusion machines using much lighter atoms would not be subject to this problem.
When the first small-scale fusion machines were being built in the mid-1950s, they appeared to follow the B−2 rule, so there was great confidence that simply scaling the machines to larger sizes with more powerful magnets would meet the requirements for practical fusion. In fact, when such machines were built, like the British ZETA and U.S. Model-B stellarator were built, they demonstrated confinement times much more in line with Bohm diffusion. To examine this, the Model-B2 stellarator was run at a wide variety of field strengths and the resulting diffusion times were measured. This demonstrated a linear relationship, as predicted by Bohm. As more machines were introduced this problem continued to hold, and by the 1960s the entire field had been taken over by "the doldrums".
Further experiments demonstrated that the problem was not diffusion per se, but a host of previously unknown plasma instabilities caused by the magnetic and electric fields and the motion of the particles. As critical operating conditions were passed, these processes would start and quickly drive the plasma out of confinement. Over time, a number of new designs attacked these instabilities, and by the late 1960s there were several machines that were clearly beating the Bohm rule. Among these was the Soviet tokamak, which quickly became the focus of most research to this day.
As tokamaks took over the research field, it became clear that the original estimates based on the classical formula still did not apply exactly. This was due to the toroidal arrangement of the device; particles on the inside of the ring-shaped reactor see higher magnetic fields than on the outside, simply due to geometry, and this introduced a number of new effects. Consideration of these effects led to the modern concept of neoclassical transport.
A stellarator is a plasma device that relies primarily on external magnets to confine a plasma. Scientists researching magnetic confinement fusion aim to use stellarator devices as a vessel for nuclear fusion reactions. The name refers to the possibility of harnessing the power source of the stars, such as the Sun. It is one of the earliest fusion power devices, along with the z-pinch and magnetic mirror.
A tokamak is a device which uses a powerful magnetic field to confine plasma in the shape of a torus. The tokamak is one of several types of magnetic confinement devices being developed to produce controlled thermonuclear fusion power. As of 2016, it was the leading candidate for a practical fusion reactor. The word "tokamak" is derived from a Russian acronym meaning "toroidal chamber with magnetic coils".
A magnetic mirror, known as a magnetic trap in Russia and briefly as a pyrotron in the US, is a type of magnetic confinement fusion device used in fusion power to trap high temperature plasma using magnetic fields. The mirror was one of the earliest major approaches to fusion power, along with the stellarator and z-pinch machines.
This timeline of nuclear fusion is an incomplete chronological summary of significant events in the study and use of nuclear fusion.
The Tokamak Fusion Test Reactor (TFTR) was an experimental tokamak built at Princeton Plasma Physics Laboratory (PPPL) circa 1980 and entering service in 1982. TFTR was designed with the explicit goal of reaching scientific breakeven, the point where the heat being released from the fusion reactions in the plasma is equal or greater than the heating being supplied to the plasma by external devices to warm it up.
Magnetic confinement fusion (MCF) is an approach to generate thermonuclear fusion power that uses magnetic fields to confine fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of controlled fusion research, along with inertial confinement fusion.
The diffusion of plasma across a magnetic field was conjectured to follow the Bohm diffusion scaling as indicated from the early plasma experiments of very lossy machines. This predicted that the rate of diffusion was linear with temperature and inversely linear with the strength of the confining magnetic field.
ZETA, short for Zero Energy Thermonuclear Assembly, was a major experiment in the early history of fusion power research. Based on the pinch plasma confinement technique, and built at the Atomic Energy Research Establishment in the United Kingdom, ZETA was larger and more powerful than any fusion machine in the world at that time. Its goal was to produce large numbers of fusion reactions, although it was not large enough to produce net energy.
The National Compact Stellarator Experiment, NCSX in short, was a magnetic fusion energy experiment based on the stellarator design being constructed at the Princeton Plasma Physics Laboratory (PPPL).
The beta of a plasma, symbolized by β, is the ratio of the plasma pressure (p = nkBT) to the magnetic pressure (pmag = B²/2μ0). The term is commonly used in studies of the Sun and Earth's magnetic field, and in the field of fusion power designs.
The polywell is a design for a fusion reactor based on two ideas: heating ions by concentrating (-) charge to accelerate the ions and trapping a diamagnetic plasma inside a cusp field.
The Helically Symmetric Experiment, is an experimental plasma confinement device at the University of Wisconsin–Madison, with design principles that are intended to be incorporated into a fusion reactor. The HSX is a modular coil stellarator which is a toroid-shaped pressure vessel with external electromagnets which generate a magnetic field for the purpose of containing a plasma. It began operation in 1999.
Magnetically confined fusion plasmas such as those generated in tokamaks and stellarators are characterized by a typical shape. Plasma shaping is the study of the plasma shape in such devices, and is particularly important for next step fusion devices such as ITER. This shape is conditioning partly the performance of the plasma. Tokamaks, in particular, are axisymmetric devices, and therefore one can completely define the shape of the plasma by its cross-section.
A spherical tokamak is a type of fusion power device based on the tokamak principle. It is notable for its very narrow profile, or aspect ratio. A traditional tokamak has a toroidal confinement area that gives it an overall shape similar to a donut, complete with a large hole in the middle. The spherical tokamak reduces the size of the hole as much as possible, resulting in a plasma shape that is almost spherical, often compared to a cored apple. The spherical tokamak is sometimes referred to as a spherical torus and often shortened to ST.
The Tandem Mirror Experiment was a magnetic mirror machine operated from 1979 to 1987 at the Lawrence Livermore National Laboratory. It was the first large-scale machine to test the "tandem mirror" concept in which two mirrors trapped a large volume of plasma between them in an effort to increase the efficiency of the reactor.
The Hybrid Illinois Device for Research and Applications (HIDRA) is a medium-sized toroidal magnetic fusion device housed in the Nuclear Radiation Laboratory and operated by the Center for Plasma-Material Interactions (CPMI) within the Department of Nuclear, Plasma and Radiological Engineering at the University of Illinois at Urbana–Champaign, United States. HIDRA had its first plasma at the end of April 2016 and started experimental campaigns by December of that year. HIDRA is the former WEGA classical stellarator that was operated at the Max Planck Institute for Plasma Physics in Greifswald Germany from 2001 to 2013.
The Princeton Large Torus, was an early tokamak built at the Princeton Plasma Physics Laboratory (PPPL). It was one of the first large scale tokamak machines, and among the most powerful in terms of current and magnetic fields. Originally built to demonstrate that larger devices would have better confinement times, it was later modified to perform heating of the plasma fuel, a requirement of any practical fusion power device.
The interchange instability, also known as the Kruskal–Schwarzchild instability or flute instability, is a type of plasma instability seen in magnetic fusion energy that is driven by the gradients in the magnetic pressure in areas where the confining magnetic field is curved.
Wendelstein 7-AS was an experimental stellarator which was in operation from 1988 to 2002 by the Max Planck Institute for Plasma Physics (IPP) in Garching. It was the first of a new class of advanced stellarators with modular coils, designed with the goal of developing a nuclear fusion reactor to generate electricity.
Theta-pinch, or θ-pinch, is a type of fusion power reactor design. The name refers to the configuration of currents used to confine the plasma fuel in the reactor, arranged to run around a cylinder in the direction normally denoted as theta in polar coordinate diagrams. The name was chosen to differentiate it from machines based on the pinch effect that arranged their currents running down the centre of the cylinder; these became known as z-pinch machines, referring to the Z-axis in cartesian coordinates.