MagnetohydrodynamicsMagnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in numerous fields including geophysics, astrophysics, and engineering. The word magnetohydrodynamics is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement.
Pinch (plasma physics)A pinch (or: Bennett pinch (after Willard Harrison Bennett), electromagnetic pinch, magnetic pinch, pinch effect, or plasma pinch.) is the compression of an electrically conducting filament by magnetic forces, or a device that does such. The conductor is usually a plasma, but could also be a solid or liquid metal. Pinches were the first type of device used for experiments in controlled nuclear fusion power. Pinches occur naturally in electrical discharges such as lightning bolts, planetary auroras, current sheets, and solar flares.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Magnetic reconnectionMagnetic reconnection is a physical process occurring in electrically conducting plasmas, in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection involves plasma flows at a substantial fraction of the Alfvén wave speed, which is the fundamental speed for mechanical information flow in a magnetized plasma. The concept of magnetic reconnection was developed in parallel by researchers working in solar physics and in the interaction between the solar wind and magnetized planets.
Current sheetA current sheet is an electric current that is confined to a surface, rather than being spread through a volume of space. Current sheets feature in magnetohydrodynamics (MHD), the study of the behavior of electrically conductive fluids: if there is an electric current through part of the volume of such a fluid, magnetic forces tend to expel it from the fluid, compressing the current into thin layers that pass through the volume.
Flux tubeA flux tube is a generally tube-like (cylindrical) region of space containing a magnetic field, B, such that the cylindrical sides of the tube are everywhere parallel to the magnetic field lines. It is a graphical visual aid for visualizing a magnetic field. Since no magnetic flux passes through the sides of the tube, the flux through any cross section of the tube is equal, and the flux entering the tube at one end is equal to the flux leaving the tube at the other.
Birkeland currentA Birkeland current (also known as field-aligned current) is a set of electrical currents that flow along geomagnetic field lines connecting the Earth's magnetosphere to the Earth's high latitude ionosphere. In the Earth's magnetosphere, the currents are driven by the solar wind and interplanetary magnetic field and by bulk motions of plasma through the magnetosphere (convection indirectly driven by the interplanetary environment). The strength of the Birkeland currents changes with activity in the magnetosphere (e.
Plasma arc weldingPlasma arc welding (PAW) is an arc welding process similar to gas tungsten arc welding (GTAW). The electric arc is formed between an electrode (which is usually but not always made of sintered tungsten) and the workpiece. The key difference from GTAW is that in PAW, the electrode is positioned within the body of the torch, so the plasma arc is separated from the shielding gas envelope. The plasma is then forced through a fine-bore copper nozzle which constricts the arc and the plasma exits the orifice at high velocities (approaching the speed of sound) and a temperature approaching 28,000 °C (50,000 °F) or higher.
Glass transitionThe glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased. An amorphous solid that exhibits a glass transition is called a glass. The reverse transition, achieved by supercooling a viscous liquid into the glass state, is called vitrification.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
