A sawtooth is a relaxation that is commonly observed in the core of tokamak plasmas, first reported in 1974.The relaxations occur quasi-periodically and cause a sudden drop in the temperature and density in the center of the plasma. A soft-xray pinhole camera pointed toward the plasma core during sawtooth activity will produce a sawtooth-like signal. Sawteeth effectively limit the amplitude of the central current density. The Kadomtsev model of sawteeth is a classic example of magnetic reconnection. Other repeated relaxation oscillations occurring in tokamaks include the edge localized mode (ELM) which effectively limits the pressure gradient at the plasma edge and the fishbone instability which effectively limits the density and pressure of fast particles.
An often cited description of the sawtooth relaxation is that by Kadomtsev. is below unity, a linear eigenmode will be unstable, where is the poloidal mode number. This instability may be the internal kink mode, resistive internal kink mode or tearing mode. The eigenfunction of each of these instabilities is a rigid displacement of the region inside . The mode amplitude will grow exponentially until it saturates, significantly distorting the equilibrium fields, and enters the nonlinear phase of evolution. In the nonlinear evolution, the plasma core inside the surface is driven into a resistive reconnection layer. As the flux in the core is reconnected, an island grows on the side of the core opposite the reconnection layer. The island replaces the core when the core has completely reconnected so that the final state has closed nested flux surfaces, and the center of the island is the new magnetic axis. In the final state, the safety factor is greater than unity everywhere. The process flattens temperature and density profiles in the core.The Kadomtsev model uses a resistive magnetohydrodynamic (MHD) description of the plasma. If the amplitude of the current density in the plasma core is high enough so that the central safety factor
After a relaxation, the flattened temperature and safety factor profiles become peaked again as the core reheats on the energy confinement time scale, and the central safety factor drops below unity again as the current density resistively diffuses back into the core. In this way, the sawtooth relaxation occurs repeatedly with average period .
The Kadomtsev picture of sawtoothing in a resistive MHD model was very successful at describing many properties of the sawtooth in early tokamak experiments. However as measurements became more accurate and tokamak plasmas got hotter, discrepancies appeared. One discrepancy is that relaxations caused a much more rapid drop in the central plasma temperature of hot tokamaks than predicted by the resisive reconnection in the Kadomtsev model. Some insight into fast sawtooth crashes was provided by numerical simulations using more sophisticated model equations and by the Wesson model. Another discrepancy found was that the central safety factor was observed to be significantly less than unity immediately after some sawtooth crashes. Two notable explanations for this are incomplete reconnectionand rapid rearrangement of flux immediately after a relaxation.
The Wesson model offers an explanation fast sawtooth crashes in hot tokamaks. profiles in tokamaks were developed later. It was found that the profiles during sawtoothing discharges are not necessarily flat with as needed by Wesson's description of the sawtooth. Nevertheless, Wesson-like relaxations have been observed experimentally on occasion.Wesson's model describes a sawtooth relaxation based on the non-linear evolution of the quasi-interchange (QI) mode. The nonlinear evolution of the QI does not involve much reconnection, so it does not have Sweet-Parker scaling and the crash can proceed much faster in high temperature, low resistivity plasmas given a resistive MHD model. However more accurate experimental methods for measuring
The first results of a numerical simulation that provided verification of the Kadomtsev model were published in 1976.This simulation demonstrated a single Kadomtsev-like sawtooth relaxation. In 1987 the first results of a simulation demonstrating repeated, quasi-periodic sawtooth relaxations was published. Results from resistive MHD simulations of repeated sawtoothing generally give reasonably accurate crash times and sawtooth period times for smaller tokamaks with relatively small Lundquist numbers.
In large tokamaks with larger Lundquist numbers, sawtooth relaxations are observed to occur much faster than predicted by the resistive Kadomtsev model. Simulations using two-fluid model equations or non-ideal terms in Ohm's law besides the resistive term, such as the Hall and electron inertia terms, can account for the fast crash times observed in hot tokamaks.These models can allow much faster reconnection at low resistivity.
Large, hot tokamaks with significant populations of fast particles sometimes see so called "giant sawteeth". drops well below unity during the long period of stabilization, until instability is triggered, and the resulting crash is very large.Giant sawteeth are much larger relaxations and may cause disruptions. They are a concern for ITER. In hot tokamaks, under some circumstances, minority hot particle species can stabilize the sawtooth instability.
The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it. The stability of the system determines if the perturbations will grow, oscillate, or be damped out.
Magnetohydrodynamics is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, salt water, and electrolytes. The word "magnetohydrodynamics" is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén, for which he received the Nobel Prize in Physics in 1970.
Magnetic reconnection is a physical process occurring in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection occurs on timescales intermediate between slow resistive diffusion of the magnetic field and fast Alfvénic timescales.
An edge-localized mode (ELM) is a disruptive instability occurring in the edge region of a tokamak plasma due to the quasi-periodic relaxation of a transport barrier previously formed during a transition from low to high-confinement mode. This phenomenon was first observed in the ASDEX tokamak in 1981.
A non-neutral plasma is a plasma whose net charge creates an electric field large enough to play an important or even dominant role in the plasma dynamics. The simplest non-neutral plasmas are plasmas consisting of a single charge species. Examples of single species non-neutral plasmas that have been created in laboratory experiments are plasmas consisting entirely of electrons, pure ion plasmas, positron plasmas, and antiproton plasmas.
Searches for Lorentz violation involving photons provide one possible test of relativity. Examples range from modern versions of the classic Michelson–Morley experiment that utilize highly stable electromagnetic resonant cavities to searches for tiny deviations from c in the speed of light emitted by distant astrophysical sources. Due to the extreme distances involved, astrophysical studies have achieved sensitivities on the order of parts in 1038.
The Spitzer resistivity is an expression describing the electrical resistance in a plasma, which was first formulated by Lyman Spitzer in 1950. The Spitzer resistivity of a plasma decreases in proportion to the electron temperature as .
Sibylle Günter is a German theoretical physicist researching tokamak plasmas. Since February 2011, she has headed the Max Planck Institute for Plasma Physics. In October 2015, she was elected a member of the Academia Europaea in recognition of her contribution to research.
Hartmut Zohm is a German plasma physicist who is known for his work on the ASDEX Upgrade machine. He received the 2014 John Dawson Award and the 2016 Hannes Alfvén Prize for successfully demonstrating that neoclassical tearing modes in tokamaks can be stabilized by electron cyclotron resonance heating, which is an important design consideration for pushing the performance limit of the ITER.
Tihiro Ohkawa was a Japanese physicist whose field of work was in plasma physics and fusion power. He was a pioneer in developing ways to generate electricity by nuclear fusion when he worked at General Atomics. Ohkawa died September 27, 2014 in La Jolla, California at the age of 86.
Bernstein–Greene–Kruskal modes are nonlinear electrostatic waves that propagate in an unmagnetized, collisionless plasma. They are nonlinear solutions to the Vlasov–Poisson equation in plasma physics, and are named after physicists Ira B. Bernstein, John M. Greene, and Martin D. Kruskal, who solved and published the exact solution for the one-dimensional case in 1957.
Guy Laval is a French physicist, professor at the École polytechnique and member of the French Academy of Sciences.
Akira Hasegawa is a theoretical physicist and engineer who has worked in the US and Japan. He is known for his work in the derivation of the Hasegawa–Mima equation, which describes fundamental plasma turbulence and the consequent generation of zonal flow that controls plasma diffusion. Hasegawa also made the discovery of optical solitons in glass fibers, a concept that is essential for high speed optical communications.
Keith Howard Burrell is an American plasma physicist.
William Henry Matthaeus is an American astrophysicist and plasma physicist. He is known for his research on turbulence in magnetohydrodynamics (MHD) and astrophysical plasmas, for which he was awarded the 2019 James Clerk Maxwell Prize for Plasma Physics.
Boris Borisovich Kadomtsev was a Russian plasma physicist who worked on controlled fusion problems. He developed a theory of transport phenomena in turbulent plasmas and a theory of the so-called anomalous behavior of plasmas in magnetic fields. In 1966, he discovered plasma instability with trapped particles.
Patrick Henry Diamond is an American theoretical plasma physicist. He is currently a professor at the University of California, San Diego, and a director of the Fusion Theory Institute at the National Fusion Research Institute in Daejeon, South Korea, where the KSTAR Tokamak is operated.
Patrick Mora is a French theoretical plasma physicist who specializes in laser-plasma interactions. He was awarded the 2014 Hannes Alfvén Prize and 2019 Edward Teller Award for his contributions to the field of laser-plasma physics.
Toshiki Tajima is a Japanese theoretical plasma physicist known for pioneering the laser wakefield acceleration technique with John M. Dawson in 1979. The technique is used to accelerate particles in a plasma and was experimentally realized in 1994, for which Tajima received several awards such as the Nishina Memorial Prize (2006), the Enrico Fermi Prize (2015), the Robert R. Wilson Prize (2019), the Hannes Alfvén Prize (2019) and the Charles Hard Townes Award (2020).
Friedrich E. Wagner is a German physicist and emeritus professor who specializes in plasma physics. He was known to have discovered the high-confinement mode of magnetic confinement in fusion plasmas while working at the ASDEX tokamak in 1982. For this discovery and his subsequent contributions to fusion research, was awarded the John Dawson Award in 1987, the Hannes Alfvén Prize in 2007 and the Stern–Gerlach Medal in 2009.