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Instability

Instability in systems is generally characterized by some of the outputs or internal state (controls)|states growing without bounds. Not all systems that are not stability|stable are unstable; systems can also be marginal stability|marginally stable or exhibit limit cycle behavior. In control theory, a system is unstable if any of the Root (mathematics)|roots of its characteristic equation has real part greater than zero. This is equivalent to any of the eigenvalues of the State space (controls)|state matrix having real part greater than zero. In structural engineering, a structure can become unstable when excessive load is applied. Beyond a certain threshold, structural deflections magnify stress (physics)|stresses, which in turn increases deflections. This can take the form of buckling or crippling. The general field of study is called structural stability.

Fluid instabilities

Fluid instabilities occur in liquids, gases and Plasma physics|plasmas, and are often characterized by the shape that form; they are studied in fluid dynamics and magnetohydrodynamics. Fluid instabilities include:
- Ballooning mode instability (some analogy to the Rayleigh–Taylor instability); found in the magnetosphere
- Atmospheric instability
    - Hydrodynamic instability or dynamic instability (atmospheric dynamics)
    - * Inertial instability; baroclinic instability; symmetric instability, conditional symmetric instability|conditional symmetric or conditional symmetric instability|convective symmetric instability; barotropic instability; Helmholtz instability|Helmholtz or Helmholtz instability|shearing instability; rotational instability
    - Hydrostatic instability or static instability/static instability|vertical instability (static instability|parcel instability), thermodynamic instability (atmospheric thermodynamics)
    - * Conditional instability|Conditional or static instability, buoyant instability, latent instability, nonlocal static instability, conditional-symmetric instability; convective instability|convective, convective instability|potential, or convective instability|thermal instability, convective instability of the first kind|convective instability of the first and convective instability of the second kind|second kind; absolute instability|absolute or absolute instability|mechanical instability
- Bénard cells|Bénard instability
- Drift mirror instability
- Kelvin–Helmholtz instability (similar, but different from the diocotron instability in plasmas)
- Rayleigh–Taylor instability
- Plateau-Rayleigh instability (similar to the Rayleigh–Taylor instability)
- Richtmyer-Meshkov instability (similar to the Rayleigh–Taylor instability)

Plasma instabilities

Plasma (physics)|Plasma instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic instabilities. Plasma instabilities are also categorised into different modes:

'''Mode''' (azimuthal wave number)	'''Note'''	'''Description'''	'''Radial modes'''	'''Description'''
m=0		''Sausage'' instability: displays harmonic variations of beam radius with distance along the beam axis	n=0	Axial hollowing
			n=1	Standard sausaging
			n=2	Axial bunching
m=1		''Sinuous'', ''kink'' or ''hose'' instability: represents transverse displacements of the beam cross-section without change in the form or in a beam characteristics other than the position of its center of mass
m=2	Filamentation modes: growth leads towards the breakup of the beam into separate filaments.	Gives an elliptic cross-section
m=3		Gives a pyriform (pear-shaped) cross-section

Source: Andre Gsponer, "Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas" (2004)

List of plasma instabilities

- Bennett pinch instability (also called the z-pinch instability )
- Beam acoustic instability
- Bump-in-tail instability
- Oscar Buneman|Buneman instability,Buneman, O., "Instability, Turbulence, and Conductivity in Current-Carrying Plasma" (1958) ''Physical Review Letters'', vol. 1, Issue 1, pp. 8-9 (same as Farley-Buneman instability?)
- Pavel Alekseyevich Cherenkov|Cherenkov instability,Kho, T. H.; Lin, A. T., "Cyclotron-Cherenkov and Cherenkov instabilities" (1990) ''IEEE Transactions on Plasma Science'' (ISSN 0093-3813), vol. 18, June 1990, p. 513-517
- Chute instability
- Coalescence instability,Finn, J. M.; Kaw, P. K., "Coalescence instability of magnetic islands" (1977) ''Physics of Fluids'', vol. 20, Jan. 1977, p. 72-78. (More citations)
- Collapse instability
- Counter-streaming instability
- Cyclotron instabilities, including:
- *Alfven cyclotron instability
- *Electron cyclotron instability
- *Electrostatic ion cyclotron Instability
- *Ion cyclotron instability
- *Magnetoacoustic cyclotron instability
- *Proton cyclotron instability
- *Nonresonant Beam-Type cyclotron instability
- *Relativistic ion cyclotron instability
- *Whistler cyclotron instability
- Diocotron instability,Uhm, H. S.; Siambis, J. G., "Diocotron instability of a relativistic hollow electron beam" (1979) ''Physics of Fluids'', vol. 22, Dec. 1979, p. 2377-2381. (similar to the Kelvin-Helmholtz instability|Kelvin-Helmholtz fluid instability).
- Disruptive instability (in tokamaks)
- Double emission instability
- Drift wave instability
- Edge-Localized Mode|Edge-localized modes http://news.bbc.co.uk/1/hi/sci/tech/3260985.stm
- Electrothermal instability
- Farley-Buneman instability
- Fan instability
- Filamentation instability
- Firehose instability (also called Hose instability)

- Flute instability
- Free electron maser instability
- Gyrotron instability
- Helical instability (helix instability)
- Helical kink instability
- Hose instability (also called Firehose instability)
- Interchange instability
- Ion beam instability
- Kink instability
- Lower hybrid (drift) instability (in the Critical ionization velocity mechanism)
- Magnetic drift instability
- Magnetic buoyancy instability (Parker instability)
- Modulation instability
- Non-Abelian instability (see also Chromo-Weibel instability)
- Chromo-Weibel Instability
- Non-linear coalescence instability
- Oscillating two stream instability, see two stream instability
- Pair instability
- Parker instability (magnetic buoyancy instability)
- Peratt instability (stacked toroids)
- Pinch instability
- Sausage instability
- Slow Drift Instability
- Tearing mode instability
- Two stream instability
- Weak beam instability
- Weibel instability
- z-pinch instability, also called Bennett pinch instability

Notes

External links

- eFluids Fluid Flow Image Gallery Category:Systems theory Category:Fundamental physics concepts Category:Plasma physics Category:Stability theory

Related Images

- A ball on the top of a hill is an unstable situation.

Sources: StartLearningNow, Wikipedia | Usage license: GNU FDL

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