There are many variants and types of plasma instabilities on the Sun which play both major and minor roles in events ranging from X-class solar flares to coronal mass ejections and even filament ejection-displacement. In this post I look at a few of these.

Conveniently, many of these instabilities are defined in terms of

**specific velocities**. One of the more important of these is known as

*the electron drift velocity*

**v**

_{ d}**:**

**v**

_{ d}

**= I/ n e**

where I is the current, n the number density (per cubic meter, for example) and e the electron charge. Often

**v**

_{ d }is defined instead based on

*current density*(

**J)**where:

**J**= I/A (current in amps flowing through a magnetic flux tube or channel of some cross-section area A)

So:

**v**

_{ d }=

**J /**n e

In many other cases, where

**J**, I are not so easily obtained,

**v**

_{ d }will be the electron drift velocity in a combined magnetic and gravitational field, i.e.:

**v**

_{ d }= m

_{e}

**g**c / e

_{s}**B**

where

**B**is the magnetic induction, e the electronic charge (1.6 x 10

^{-19}C) ,

**g**= 273 ms -2 the gravitational acceleration on the Sun, c is the velocity of light (2.98 x 10

_{s}^{8}m/s) and m

_{e}the electron mass (9.1 x 10

^{-31}kg) .

In the case of

*the ion-acoustic instability*, the threshold for its onset is when:

**v**

_{ d }> 43

**v**

_{ s}

that is, the drift velocity is at least 43 times the ion sound speed, where:

**v**

_{ s }=

**Ö**(kT/ m

_{i})

where k is the Boltzmann constant (1.38 x 10

^{-23}J/K), T the (Kelvin) temperature and m

_{i }the ion mass (e.g. m

_{i }~ 1.7 x 10

^{-27}kg).

Sen and White in a 1972 paper dealing with the role of the Hall effect in flares, showed that the

*two-stream instability*is incepted when the drift velocity:

**v**

_{ d }>

**v**

_{ ith}

where

**v**

_{ ith }is

*the ion-thermal velocity*:

**v**

_{ ith }=

**Ö**(2kT/ m

_{i})

(rms value =

**Ö**3(kT/ m

_{i})

_{ ov}) and perturbed one ( f

_{ eb}) applicable to the electron beam (See diagram ).

In the region where the slope is positive (df

_{ v }

**/**d v > 0) there is

*a greater number of faster i.e.*than slower particles so a greater amount of energy is transferred from particles to associated (e.g. Alfven) waves. Since f

_{ eb}contains more fast than slow particles a wave is excited, and there is inverse Landau damping such that plasma oscillations with

**v**

_{ph}(phase velocity) in the positive gradient region are unstable.

Resonant electrons (at

**v**

_{ ph }> w

_{ e }

**/**k) where w

_{ e }is the electron plasma frequency, i.e.

w

_{ e}= [n

_{e}e

^{2}/ m

_{e}ε

_{o}]

^{½ }are the first to be affected by the local wave-particle interactions and have distributions altered by the wave electric field, E1, such that the total energy balance:

E1 (TOT) = ½ E1

_{w}+ ½ E1

_{k}

referencing the wave and kinetic (particle) contributions respectively.

Thus, for E1(TOT) = const. then as the electron velocity decreases, the particle kinetic energy decreases and the wave energy density increases.

In

*Landau damping*the exact opposite occurs, so the gradient df(v)/d v decreases, and with it the wave amplitude, while the particle kinetic energy increases- i.e. wave energy lost is fed to the particles (electrons) which gain energy.

Note also that the "

*plasma beam instability*" is just the

**analog for the two stream instability. In other words, if one has a "two stream instability" one**

*finite temperature**de facto*also has the beam instability.

Lastly, for the Buneman instability, the relevant condition is:

**v**

_{ d }>

**v**

_{ eth}

where

**v**

_{ eth }is the

*electron thermal velocity:*

**v**

_{ eth }=

**Ö**(2k T

_{e}/ m

_{e})

where T

_{e }is the electron temperature and k the Boltzmann constant.

The rms (root mean square) value for

**v**

_{ eth }is

**Ö**3 (k T

_{e}/ m

_{e})

See also:

A Closer Analytical Look At Two Stream Instabilit...

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