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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.
Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science.
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion. The properties of that substance are carried with it. Generally the majority of the advected substance is a fluid. The properties that are carried with the advected substance are conserved properties such as energy. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. Another commonly advected quantity is energy or enthalpy. Here the fluid may be any material that contains thermal energy, such as water or air. In general, any substance or conserved, extensive quantity can be advected by a fluid that can hold or contain the quantity or substance.
A magnetohydrodynamic drive or MHD accelerator is a method for propelling vehicles using only electric and magnetic fields with no moving parts, accelerating an electrically conductive propellant with magnetohydrodynamics. The fluid is directed to the rear and as a reaction, the vehicle accelerates forward.
The particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points.
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.
A magnetohydrodynamic generator is a magnetohydrodynamic converter that utilizes a Brayton cycle to transform thermal energy and kinetic energy directly into electricity. MHD generators are different from traditional electric generators in that they operate without moving parts to limit the upper temperature. They therefore have the highest known theoretical thermodynamic efficiency of any electrical generation method. MHD has been extensively developed as a topping cycle to increase the efficiency of electric generation, especially when burning coal or natural gas. The hot exhaust gas from an MHD generator can heat the boilers of a steam power plant, increasing overall efficiency.
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.
The Grad–Shafranov equation is the equilibrium equation in ideal magnetohydrodynamics (MHD) for a two dimensional plasma, for example the axisymmetric toroidal plasma in a tokamak. This equation takes the same form as the Hicks equation from fluid dynamics. This equation is a two-dimensional, nonlinear, elliptic partial differential equation obtained from the reduction of the ideal MHD equations to two dimensions, often for the case of toroidal axisymmetry. Taking
as the cylindrical coordinates, the flux function
is governed by the equation,
The magnetic Reynolds number (Rm) is the magnetic analogue of the Reynolds number, a fundamental dimensionless group that
occurs in magnetohydrodynamics. It gives an estimate of the relative effects of advection or induction of a magnetic field by the motion of a conducting medium, often a fluid, to magnetic diffusion. It is typically defined by:
Plasma Modeling refers to solving equations of motion that describe the state of a plasma. It is generally coupled with Maxwell's Equations for electromagnetic fields or Poisson's Equation for electrostatic fields. There are several main types of plasma models: single particle, kinetic, fluid, hybrid kinetic/fluid, gyrokinetic and as system of many particles.
Computational magnetohydrodynamics (CMHD) is a rapidly developing branch of magnetohydrodynamics that uses numerical methods and algorithms to solve and analyze problems that involve electrically conducting fluids. Most of the methods used in CMHD are borrowed from the well established techniques employed in Computational fluid dynamics. The complexity mainly arises due to the presence of a magnetic field and its coupling with the fluid. One of the important issues is to numerically maintain the
condition, from Maxwell's equations, to avoid the presence of unrealistic effects, namely magnetic monopoles, in the solutions.
Magnetohydrodynamic turbulence concerns the chaotic regimes of magnetofluid flow at high Reynolds number. Magnetohydrodynamics (MHD) deals with what is a quasi-neutral fluid with very high conductivity. The fluid approximation implies that the focus is on macro length-and-time scales which are much larger than the collision length and collision time respectively.
How the plasma transport is reduced by the strength of the external magnetic field is of great concern in studying magnetic confinement of fusion plasma. The plasma diffusion may be classified by the classical diffusion of B−2 scaling, the Bohm diffusion conjectured to follow the B−1 scaling, and the Hsu diffusion of B−3/2 scaling. Here, B is the external magnetic field.
The Reversed-Field eXperiment (RFX) is the largest reversed field pinch device presently in operation, situated in Padua, Italy. It was constructed from 1985 to 1991, and is operated since 1992.
In magnetohydrodynamics, the Alfvén's theorem, also known as Alfvén's frozen in theorem, "states that in a fluid with infinite electric conductivity, magnetic field lines are frozen into the fluid and have to move along with it". Hannes Alfvén put the idea forward for the first time in 1942. In his own words:
"In view of the infinite conductivity, every motion of the liquid in relation to the lines of force is forbidden because it would give infinite eddy currents. Thus the matter of the liquid is “fastened” to the lines of force...".
As an even stronger result, the magnetic flux through a co-moving surface is conserved in a perfectly conducting fluid.
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.
In applied computational mathematics, numerical dispersion is a difficulty with computer simulations of continua wherein the simulated medium exhibits a higher dispersivity than the true medium. This phenomenon can be particularly egregious when the system should not be dispersive at all, for example a fluid acquiring some spurious dispersion in a numerical model.
