Plasma instability: Difference between revisions

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~~Below is a list of instabilities relevant to fusion~~ plasmas ~~(to be completed).~~

Instabilities in plasmas are often referred to as 'modes'. Strictly speaking, these terms correspond to different concepts:

~~Instabilities~~ are often referred to as 'modes', ~~while noting that~~ these terms correspond to different concepts:

* Instability: the existence of an instability is determined by calculating the growth rate of an infinitesimal perturbation. If this growth rate is positive, the perturbation is unstable.

the existence of an instability is determined by calculating the growth rate of an infinitesimal perturbation, ~~while~~ a mode is a (global) solution of a (linear) (wave) equation.

* Mode: a (normal) mode is a (global) solution of a (linear) equation. Typically, this solution is a (standing or propagating) wave. The linearity of the equation allows any solution to be composed into a sum of mutually orthogonal normal modes. If the equation is non-linear, the term 'mode' has to be used with care.

Plasma instabilities can be classified into a number of types according to their drive (or free energy source):

* Rayleigh-Taylor instabilities due to density gradients or boundaries, associated with non-electromagnetic forces (e.g., gravity)

* Gradient driven instabilities, associated with thermodynamic forces due to gradients in an otherwise Maxwellian plasma

* Kinetic instabilities, associated with deviations from Maxwellianity, i.e., the anisotropy of the velocity distribution function

* Streaming instabilities, associated with energetic particles or electric currents interacting with the plasma, producing waves

Below is a list of some instabilities relevant to fusion plasmas (to be completed).

* Alfvén eigenmode

* Ballooning instability

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-Below is a list of instabilities relevant to fusion plasmas (to be completed).
+Instabilities in plasmas are often referred to as 'modes'. Strictly speaking, these terms correspond to different concepts:
-Instabilities are often referred to as 'modes', while noting that these terms correspond to different concepts:
+* Instability: the existence of an instability is determined by calculating the growth rate of an infinitesimal perturbation. If this growth rate is positive, the perturbation is unstable.
-the existence of an instability is determined by calculating the growth rate of an infinitesimal perturbation, while a mode is a (global) solution of a (linear) (wave) equation.
+* Mode: a (normal) mode is a (global) solution of a (linear) equation. Typically, this solution is a (standing or propagating) wave. The linearity of the equation allows any solution to be composed into a sum of mutually orthogonal normal modes. If the equation is non-linear, the term 'mode' has to be used with care.
+Plasma instabilities can be classified into a number of types according to their drive (or free energy source):
+* Rayleigh-Taylor instabilities due to density gradients or boundaries, associated with non-electromagnetic forces (e.g., gravity)
+* Gradient driven instabilities, associated with thermodynamic forces due to gradients in an otherwise Maxwellian plasma
+* Kinetic instabilities, associated with deviations from Maxwellianity, i.e., the anisotropy of the velocity distribution function
+* Streaming instabilities, associated with energetic particles or electric currents interacting with the plasma, producing waves
+Below is a list of some instabilities relevant to fusion plasmas (to be completed).
 * Alfvén eigenmode
 * Ballooning instability