- Instability
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Hydrodynamic s simulation of theRayleigh–Taylor instability [*Shengtai Li, Hui Li "Parallel AMR Code for Compressible MHD or HD Equations" (Los Alamos National Laboratory) [*] ]*http://math.lanl.gov/Research/Highlights/amrmhd.shtml*]**Instability**in systems is generally characterized by some of theoutputs or internal states growing withoutbounds . Not all systems that are not stable are unstable; systems can also be marginally stable or exhibitlimit cycle behavior.In

control theory , a system is unstable if any of the roots of itscharacteristic equation hasreal part greater than zero. This is equivalent to any of theeigenvalues of the 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, structuraldeflection s magnify stresses, which in turn increases deflections. This can take the form ofbuckling or crippling. The general field of study is calledstructural stability .**Fluid instabilities**Fluid instabilities occur inliquids ,gases and plasmas, and are often characterized by the shape that form; they are studied influid dynamics andmagnetohydrodynamics . Fluid instabilities include:* Ballooning mode instability (some analogy to the Rayleigh–Taylor instability); found in the

magnetosphere

*Atmospheric instability

**Hydrodynamic instability ordynamic instability (atmospheric dynamics )

***Inertial instability ;baroclinic instability ;symmetric instability , conditional symmetric or convective symmetric instability;barotropic instability ; Helmholtz or shearing instability;rotational instability

**Hydrostatic instability orstatic instability /vertical instability (parcel instability),thermodynamic instability (atmospheric thermodynamics )

*** Conditional orstatic instability ,buoyant instability ,latent instability ,nonlocal static instability ,conditional-symmetric instability ; convective, potential, or thermal instability, convective instability of the first and second kind; absolute or mechanical instability

* Bénard instability

* Drift mirror instability

*Kelvin–Helmholtz instability (similar, but different from thediocotron 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 instabilities can be divided into two general groups (1) hydrodynamic instabilities (2) kinetic instabilities. Plasma instabilities are also categorised into different modes:

Source: Andre Gsponer, " [**Mode**

(azimuthal wave number)**Note****Description****Radial modes****Description**m=0 "Sausage" instability:

displays harmonic variations of beam radius with distance alongthe beam axisn=0 Axial hollowing n=1 Standard sausaging n=2 Axial bunching m=1 "Sinuous", "kink" or "hose" instability:

represents transversedisplacements of the beam cross-section without change in the form or in a beam characteristics other than the position of its center of massm=2 Filamentation modes:

growth leads towards the breakupof the beam into separate filaments.Gives an elliptic cross-section m=3 Gives a pyriform (pear-shaped) cross-section *http://arxiv.org/abs/physics/0409157 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 thez-pinch instability )

* Beam acoustic instability

* Bump-in-tail instability

* Buneman instability, [*Buneman, O., " [*] (same as Farley-Buneman instability?)*http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1958PhRvL...1....8B&db_key=PHY&data_type=HTML&format= Instability, Turbulence, and Conductivity in Current-Carrying Plasma*] " (1958) "Physical Review Letters", vol. 1, Issue 1, pp. 8-9

* Cherenkov instability, [*Kho, T. H.; Lin, A. T., " [*]*http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990ITPS...18..513K&db_key=PHY&data_type=HTML&format=&high=4521318e0232018 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., " [*]*http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1977PhFl...20...72F&db_key=PHY&data_type=HTML&format=&high=4521318e0202808 Coalescence instability of magnetic islands*] " (1977) "Physics of Fluids", vol. 20, Jan. 1977, p. 72-78. ( [*http://adsabs.harvard.edu/cgi-bin/nph-abs_connect?db_key=AST&db_key=PHY&qform=AST&sim_query=YES&ned_query=YES&aut_logic=OR&obj_logic=OR&author=&object=&start_mon=&start_year=&end_mon=&end_year=&ttl_logic=OR&title=%22Diocotron+instability%22&txt_logic=OR&text=&nr_to_return=100&start_nr=1&jou_pick=ALL&ref_stems=&data_and=ALL&group_and=ALL&start_entry_day=&start_entry_mon=&start_entry_year=&end_entry_day=&end_entry_mon=&end_entry_year=&min_score=&sort=SCORE&data_type=SHORT&aut_syn=YES&ttl_syn=YES&txt_syn=YES&aut_wt=1.0&obj_wt=1.0&ttl_wt=0.3&txt_wt=3.0&aut_wgt=YES&obj_wgt=YES&ttl_wgt=YES&txt_wgt=YES&ttl_sco=YES&txt_sco=YES&version=1 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., " [*] (similar to the Kelvin-Helmholtz fluid instability).*http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1979PhFl...22.2377U&db_key=PHY&data_type=HTML&format=&high=4521318e0204112 Diocotron instability of a relativistic hollow electron beam*] " (1979) "Physics of Fluids", vol. 22, Dec. 1979, p. 2377-2381.

* Disruptive instability (intokamak s)

* Double emission instability

* Drift wave instability

*Edge-localised 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 theCritical ionization velocity mechanism)

* Magnetic drift instability

* Magnetic buoyancy instability (Parker instability)

* Modulation instability

* Non-Abelian instability (see alsoChromo-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 (stackedtoroid s)

* 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*** [

*http://www.efluids.com/efluids/pages/gallery.htm eFluids Fluid Flow Image Gallery*]

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