Plasma instability

A Plasma instability is a region where turbulence occurs due to changes in the characteristics of a plasma (eg. temperature, density, electric fields, magneti fields). As the name suggests, instabilities are unstable, though they may appear to evolve through different forms (morphology). Similar types of instability are common in fluids (liquids and gases).


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

(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 crosssection 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
  • Buneman instability,[1] (same as Farley-Buneman instability?)
  • Cherenkov instability,[2]
  • Chute instability
  • Coalescence instability,[3]
  • 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
  • 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)
  • Microfilamentation instability (Weibel instability) [5]
  • Modulation instability
  • Non-Abelian instability
  • Non-linear coalescence instability
  • Oscillating two stream instability, see two stream instability
  • Pair instability
  • Parker instability (magnetic buoyancy instability)
  • Pinch instability
  • Sausage instability
  • Slow Drift Instability
  • Tearing mode instability
  • Two stream instability
  • Weak beam instability
  • Weibel instability (microfilamentation instability) [5]
  • z-pinch instability, also called Bennett pinch instability


  1. Buneman, O., “Instability, Turbulence, and Conductivity in Current-Carrying Plasma” (1958) Physical Review Letters, vol. 1, Issue 1, pp. 8-9
  2. 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
  3. Finn, J. M.; Kaw, P. K., “Coalescence instability of magnetic islands” (1977) Physics of Fluids, vol. 20, Jan. 1977, p. 72-78. (More citations)
  4. 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.
  5. 5.0 5.1 Andre Gsponer, “Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas” (2004)
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