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Lecture# Plasma Instabilities: Non-Linear Effects in Plasmas

Description

This lecture delves into the non-linear effects in plasmas, focusing on the Vlasov-Maxwell system of equations and the interaction between plasma species and electromagnetic fields. It explores the justification for weakly coupled plasmas, the role of Maxwell's equations, and the impact of collisional effects. The discussion extends to parametric instabilities, illustrating the resonant interaction between waves and the reinforcement of plasma waves. The lecture also covers the derivation of linear Landau damping invoking energy conservation and the evolution of traveling Langmuir waves. The study concludes with the analysis of three-wave interactions and the initiation of parametric instabilities in plasma, particularly in the context of inertial fusion.

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Instructors (2)

PHYS-736: Plasma instabilities

To complete the theoretical knowledge acquired before the graduate studies.

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Related concepts (452)

Equation

In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.

Electronic oscillator

An electronic oscillator is an electronic circuit that produces a periodic, oscillating or alternating current (AC) signal, usually a sine wave, square wave or a triangle wave, powered by a direct current (DC) source. Oscillators are found in many electronic devices, such as radio receivers, television sets, radio and television broadcast transmitters, computers, computer peripherals, cellphones, radar, and many other devices.

Kink instability

A kink instability (also kink oscillation or kink mode), is a current-driven plasma instability characterized by transverse displacements of a plasma column's cross-section from its center of mass without any change in the characteristics of the plasma. It typically develops in a thin plasma column carrying a strong axial current which exceeds the Kruskal–Shafranov limit and is sometimes known as the Kruskal–Shafranov (kink) instability. The kink instability was first widely explored in fusion power machines with Z-pinch configurations in the 1950s.

Linear algebra

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In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

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