- Coronal gas
- Bright areas of the HII
- Low-density HII regions
- Interstage Wednesday
- Warm regions of HI
- Maser condensation
- Clouds of the HI
- Giant Molecular Clouds
- Molecular clouds
- Globules

We will not go into details now that there is every structure, since the topic of this publication is plasma. The plasma structures include coronal gas, bright regions HII, warm regions HI, clouds HI, i.e. Almost the entire list can be called a plasma. But, you object, the cosmos is a physical vacuum, and how can there be a plasma with such a concentration of particles?

To answer this question, it is necessary to give a definition: what is plasma and by what parameters of physics do we consider the given state of matter as a plasma?

According to modern ideas about plasma, this is the fourth state of matter that is in the gaseous state, strongly ionized (the first state is a solid, the second is a liquid state and finally the third is a gaseous state). But not every gas, even ionized, is a plasma.

Plasma consists of charged and neutral particles. Positively charged particles are positive ions and holes (solid-state plasma), and negatively charged particles are electrons and negative ions. First of all, it is necessary to know the concentrations of one or another type of particles. Plasma is considered to be weakly ionized if the so-called degree of ionization, equal to

$\$\$\; display\; \$\$\; r\; =\; N\_e\; /\; N\_n\; \$\$\; display\; \$\$$

Where

$\$\; inline\; \$\; N\_e\; \$\; inline\; \$$is the electron concentration,

$\$\; inline\; \$\; N\_n\; \$\; inline\; \$$– the concentration of all neutral particles in the plasma lies in the range

$\$\; inline\; \$\; (r\; <10\; ^\; \{-\; 2\}\; \u2013\; 10\; ^\; \{-3\})\; \$\; inline\; \$$. A completely ionized plasma has a degree of ionization

$\$\; inline\; \$\; r\; to\; infty\; \$\; inline\; \$$ But as it was said above, not every ionized gas is a plasma. It is necessary that the plasma possess the property ** of quasineutrality **i.e. On average, for sufficiently large intervals of time and at sufficiently large distances, the plasma was generally neutral. But what are the time and distance intervals at which the gas can be considered a plasma?

So, the quasi-neutrality requirement is as follows:

$\$\$\; display\; \$\$\; sum\; \_\; \{\; alpha\}\; e\; \_\; \{\; Alpha\}\; N\; \_\; \{\; alpha\}\; =\; 0\; \$\$\; display\; \$\$$

Let us first find out how physicists assess the time scale of charge separation. Let us imagine that some electron in the plasma deviated from its original equilibrium position in space. ** the Coulomb force **which tends to return the electron to the equilibrium state, begins to act on the electron.

where

$\$\; inline\; \$\; r\_\; \{cp\}\; \$\; inline\; \$$is the average distance between Electrons. This distance is roughly estimated as follows. Let us assume that the electron concentration (ie, the number of electrons per unit volume) is

$\$\; inline\; \$\; N\_e\; \$\; inline\; \$$. Electrons are on average at a distance of one another

$\$\; inline\; \$\; r\_\; \{cp\}\; \$\; inline\; \$$which means that they occupy the average volume

$\$\; inline\; \$\; V\; =\; frac\; \{4\}\; \{3\}\; pi\; r\_\; \{\; Cp\}\; ^\; 3\; \$\; inline\; \$$. Hence, if there is 1 electron in this volume,

$\$\; inline\; \$\; r\_\; \{cp\}\; =\; (\; frac\; \{3\}\; \{4\; pi\; N\_e\})\; ^\; \{1/3\}\; \$\; inline\; \$$. As a result, the electron will begin to oscillate about the equilibrium position with a frequency

$\$\$\; display\; \$\$\; omega\; approx\; sqrt\; \{\; frac\; \{F\}\; \{mr\_\; \{cp\}\}\; approx\; sqrt\; \{\; frac\; \{4\; Pi\; e\; ^\; 2\; N\_e\}\; \{3m\}\}\; \$\$\; display\; \$\$$

More precise formula

$\$\$\; display\; \$\$\; omega\_\; \{Le\}\; =\; sqrt\; \{\; frac\; \{4\; pi\; e\; ^\; 2\; N\_e\}\; \{m\}\}\; \$\$\; display\; \$\$$

This frequency is called * the electron Langmuir frequency *. It was brought out by American chemist Irwin Langmuir, winner of the Nobel Prize in Chemistry "for discoveries and research in the field of surface phenomena chemistry."

Thus, it is natural to take as the time scale of charge separation the inverse of the Langmuir frequency

$\$\$\; display\; \$\$\; tau\; =\; 2\; pi\; /\; omega\_\; \{Le\}\; \$\$\; display\; \$\$$

In space, on a huge scale, for time intervals

$\$\; inline\; \$\; t\; >>\; tau\; \$\; inline\; \$$the particles make many oscillations around the equilibrium position and the plasma as a whole will be quasineutral, i.e. On time scales, the interstellar medium can be taken as plasma.

But it is also necessary to estimate spatial scales to accurately show that space is a plasma. From physical considerations it is clear that this spatial scale is determined by the length to which the perturbation of the density of charged particles can shift due to their thermal motion in a time equal to the period of plasma oscillations. Thus, the spatial scale is equal to

$\$\$\; display\; \$\$\; r\_\; \{De\}\; approx\; frac\; \{\; upsilon\_\; \{Te\}\}\; \{\; omega\_\; \{Le\}\}\; =\; sqrt\; \{\; frac\; \{kT\_e\; \}\; \{4\; pi\; e\; ^\; 2\; N\_e\}\}\; \$\$\; display\; \$\$$

Where

$\$\; inline\; \$\; upsilon\_\; \{Te\}\; =\; sqrt\; \{\; frac\; \{kT\_e\}\; \{m\}\}\; \$\; inline\; \$$. Where did this wonderful formula come from, you ask. We will reason this way. Electrons in a plasma at the equilibrium temperature of a thermostat constantly move with kinetic energy

$\$\; inline\; \$\; E\_k\; =\; frac\; \{m\; upsilon\; ^\; 2\}\; \{2\}\; \$\; inline\; \$$. On the other hand, the law of uniform energy distribution is known from statistical thermodynamics, and on average each particle has

$\$\; inline\; \$\; E\; =\; frac\; \{1\}\; \{2\}\; kT\_e\; \$\; inline\; \$$. If we compare these two energies, we get the speed formula presented above.

So, we got the length, which in physics is called the * electronic Debye radius or length *.

Now I will show more Rigorous derivation of the Debye equation. Again, imagine the N electrons that are displaced by some amount under the action of the electric field. In this case, a layer of a space charge with a density equal to

$\$\; inline\; \$\; sum\; e\_j\; n\_j\; \$\; inline\; \$$where

$\$\; inline\; \$\; e\_j\; \$\; inline\; \$$– charge of an electron,

$\$\; inline\; \$\; N\_j\; \$\; inline\; \$$is the electron concentration. The Poisson formula is well known from electrostatics

$\$\$\; display\; \$\$\; bigtriangledown\; ^\; 2\; phi\; (\{r\})\; =\; \u2013\; frac\; \{1\}\; \{\; epsilon\; epsilon\_0\}\; sum\; e\_j\; n\_j\; \$\$\; Display\; \$\$$

Here

$\$\; inline\; \$\; epsilon\; \$\; inline\; \$$is the dielectric constant of the medium. On the other hand, the electrons move due to thermal motion and the electrons are distributed according to the Boltzmann distribution

$\$\$\; display\; \$\$\; n\_j\; (\{r\})\; =\; n\_0\; exp\; (-\; frac\; \{e\_j\; phi\; (\{R\})\}\; \{kT\_e\})\; \$\$\; display\; \$\$$

We substitute the Boltzmann equation for the Poisson equation, we obtain

$\$\$\; display\; \$\$\; bigtriangledown\; ^\; 2\; phi\; (\{r\})\; =\; \u2013\; frac\; \{1\}\; \{\; epsilon\; epsilon\_0\}\; sum\; e\_j\; n\_0\; exp\; (\; \u2013\; frac\; \{e\_j\; phi\; (\{r\})\}\; \{kT\_e\})\; \$\$\; display\; \$\$$

This is the Poisson-Boltzmann equation. Expand the exponent in this equation in the Taylor series and discard the second-order quantities and higher.

$\$\$\; display\; \$\$\; exp\; (-\; frac\; \{e\_j\; phi\; (\{r\})\}\; \{kT\_e\})\; =\; 1\; \u2013\; Frac\; \{e\_j\; phi\; (\{r\})\}\; \{kT\_e\}\; \$\$\; display\; \$\$$

We substitute this expansion in the Poisson-Boltzmann equation and obtain

$\$\$\; display\; \$\$\; bigtriangledown\; ^\; 2\; phi\; (\{r\})\; =\; (\; sum\; frac\; \{n\_\; \{0j\}\; e\_\; \{j\}\; ^\; 2\}\; \{\; Epsilon\; epsilon\_0\; kT\_e\})\; phi\; (\{r\})\; \u2013\; frac\; \{1\}\; \{\; epsilon\; epsilon\_0\}\; sum\; n\_\; \{0j\}\; e\_\; \{j\}\; \$\$\; display\; \$\$$

]
This is the Debye equation. A more precise name is the Debye-HÃ¼ckel equation. As we have explained above, in a plasma, as in a quasineutral medium, the second term in this equation is zero. In the first term, we actually have the Debye length *. *

In the interstellar medium, the Debye length is about 10 meters, in the intergalactic medium about

$\$\; inline\; \$\; 10\; ^\; 5\; \$\; inline\; \$$meters. We see that these are quite large quantities, in comparison, for example, with dielectrics. This means that the electric field propagates without damping by these distances, distributing the charges into bulk charged layers whose particles oscillate near the equilibrium positions at a frequency equal to the Langmuir frequency.

From this article we learned two fundamental quantities that determine whether Space environment with plasma, despite the fact that the density of this medium is extremely small and the cosmos as a whole is a physical vacuum on a macroscopic scale. On local scales we have as a gas, dust, or ** plasma **

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