Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
StellaratorA 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.
Electromagnetic radiationIn physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. Types of EMR include radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays, all of which are part of the electromagnetic spectrum. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields.
Fusion powerFusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices designed to harness this energy are known as fusion reactors. Research into fusion reactors began in the 1940s, but as of 2023, no device has reached net power. Fusion processes require fuel and a confined environment with sufficient temperature, pressure, and confinement time to create a plasma in which fusion can occur.
Astrophysical plasmaAstrophysical plasma is plasma outside of the Solar System. It is studied as part of astrophysics and is commonly observed in space. The accepted view of scientists is that much of the baryonic matter in the universe exists in this state. When matter becomes sufficiently hot and energetic, it becomes ionized and forms a plasma. This process breaks matter into its constituent particles which includes negatively charged electrons and positively charged ions. These electrically charged particles are susceptible to influences by local electromagnetic fields.
Electromagnetic spectrumThe electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from below one hertz to above 1025 hertz, corresponding to wavelengths from thousands of kilometers down to a fraction of the size of an atomic nucleus.
Electrothermal instabilityNOTOC The electrothermal instability (also known as ionization instability, non-equilibrium instability or Velikhov instability in the literature) is a magnetohydrodynamic (MHD) instability appearing in magnetized non-thermal plasmas used in MHD converters. It was first theoretically discovered in 1962 and experimentally measured into a MHD generator in 1963 by Evgeny Velikhov. "This paper shows that it is possible to assert sufficiently specifically that the ionization instability is the number one problem for the utilization of a plasma with hot electrons.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
Conservation lawIn physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc.
