Dispersion Relation
The dispersion relation is
where
,
The ballooning instability (a.k.a. ballooning mode instability) is a type of internal pressure-driven plasma instability usually seen in tokamak fusion power reactors [1] or in space plasmas. [2] It is important in fusion research as it determines a set of criteria for the maximum achievable plasma beta. [3] The name refers to the shape and action of the instability, which acts like the elongations formed in a long balloon when it is squeezed. In literature, the structure of these elongations are commonly referred to as 'fingers'. [4] [5] [6]
The narrow fingers of plasma produced by the instability are capable of accelerating and pushing aside the surrounding magnetic field in order to cause a sudden, explosive release of energy. Thus, the instability is also known as the explosive instability. [7] [8] [9]
The dispersion relation is
where
,
The interchange instability can be derived from the equations of the ballooning instability as a special case in which the ballooning mode does not perturb the equilibrium magnetic field. [2] This special limit is known as the Mercier criterion. [3]
In plasma physics, plasma stability concerns the stability properties of a plasma in equilibrium and its behavior under small perturbations. The stability of the system determines if the perturbations will grow, oscillate, or be damped out. It is an important consideration in topics such as nuclear fusion and astrophysical plasma.
Plasma oscillations, also known as Langmuir waves, are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency depends only weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the plasmon.
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.
An edge-localized mode (ELM) is a plasma instability occurring in the edge region of a tokamak plasma due to periodic relaxations of the edge transport barrier in high-confinement mode. Each ELM burst is associated with expulsion of particles and energy from the confined plasma into the scrape-off layer. This phenomenon was first observed in the ASDEX tokamak in 1981. Diamagnetic effects in the model equations expand the size of the parameter space in which solutions of repeated sawteeth can be recovered compared to a resistive MHD model. An ELM can expel up to 20 percent of the reactor's energy.
Ion cyclotron resonance is a phenomenon related to the movement of ions in a magnetic field. It is used for accelerating ions in a cyclotron, and for measuring the masses of an ionized analyte in mass spectrometry, particularly with Fourier transform ion cyclotron resonance mass spectrometers. It can also be used to follow the kinetics of chemical reactions in a dilute gas mixture, provided these involve charged species.
John Bryan Taylor is a British physicist known for his contributions to plasma physics and their application in the field of fusion energy. Notable among these is the development of the "Taylor state", describing a minimum-energy configuration that conserves magnetic helicity. Another development was his work on the ballooning transformation, which describes the motion of plasma in toroidal (donut) configurations, which are used in the fusion field. Taylor has also made contributions to the theory of the Earth's Dynamo, including the Taylor constraint.
A ball-pen probe is a modified Langmuir probe used to measure the plasma potential in magnetized plasmas. The ball-pen probe balances the electron and ion saturation currents, so that its floating potential is equal to the plasma potential. Because electrons have a much smaller gyroradius than ions, a moving ceramic shield can be used to screen off an adjustable part of the electron current from the probe collector.
Sir Steven Charles Cowley is a British theoretical physicist and international authority on nuclear fusion and astrophysical plasmas. He has served as director of the United States Department of Energy (DOE) Princeton Plasma Physics Laboratory (PPPL) since 1 July 2018. Previously he served as president of Corpus Christi College, Oxford, since October 2016. and head of the EURATOM / CCFE Fusion Association and chief executive officer of the United Kingdom Atomic Energy Authority (UKAEA).
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.
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.
The Prairie View (PV) Rotamak is a plasma physics experiment at Prairie View A&M University. The experiment studies magnetic plasma confinement to support controlled nuclear fusion experiments. Specifically, the PV Rotamak can be used as either a spherical tokamak or a field-reversed configuration. Some time between 2015 and 2017, most personnel moved on to advanced career opportunities. In 2017, a Final Report to Department of Energy (DOE) was prepared and submitted by Dr. Saganti of PVAMU on the entire research work supported by DOE for 12 years.
Jose A. Boedo is a Spanish plasma physicist and a researcher at University of California, San Diego. He was elected as a fellow of the American Physical Society in 2016 for "his ground-breaking contributions to the studies of plasma drifts and intermittent plasma transport in the peripheral region of tokamaks".
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.
Dmitri Dmitriyevich Ryutov is a Russian theoretical plasma physicist.
Keith Howard Burrell is an American plasma physicist.
Kunioki Mima is a Japanese plasma physicist. He is known for his contributions to the theory of turbulent transport in plasmas, and in particular the derivation of the Hasegawa–Mima equation in 1977, which won him the 2011 Hannes Alfvén Prize.
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.
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.
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.
In magnetic confinement fusion, a flux surface is a surface on which magnetic field lines lie. Since the magnetic field is divergence-free, the Poincare-Hopf theorem implies that such a surface must be either a torus, or a knot. In the tokamak and the stellarator flux surfaces have toroidal shapes, whereas the more exotic knotatron has a knotted flux surface. Flux surfaces are typically characterized by the poloidal magnetic flux or the toroidal magnetic flux. The poloidal flux is the magnetic flux passing through a ribbon going from the magnetic axis to the flux surface, and the toroidal flux is the magnetic flux passing through a circle which encloses the magnetic axis. The total flux passing through flux surface itself is zero, as magnetic field lines are everywhere tangent to the surface.
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