Is there plasma in space?

Have you ever thought about what is contained in interstellar or intergalactic space? In space, technical vacuum, and therefore nothing is contained (not in an absolute sense, that nothing is contained, but in a relative sense). And you will be right, because on average in the interstellar space about 1000 atoms per cubic centimeter and at very large distances the density of matter is negligible. But here is not so simple and straightforward. The spatial distribution of the interstellar medium is nontrivial. In addition to galactic structures such as a jumper (bar) and spiral arms of galaxies, there are also separate cold and warm clouds surrounded by hotter gas. There are a huge number of structures in the interstellar medium (MZS): giant molecular clouds, reflective nebulae, protoplanetary nebulae, planetary nebulae, globules, etc. This leads to a wide spectrum of observational manifestations and processes occurring in the medium. The following list lists the structures present in the MZS:

• Coronal gas
• Bright HII areas
• Low density zone hii
• Intercloud environment
• HI warm areas
• Maser condensation
• HI Clouds
• Giant molecular clouds
• Molecular clouds
• Globules

We will not go into details now that there is each structure, since the topic of this publication is plasma. Plasma structures include: coronal gas, bright HII regions, HI warm regions, HI clouds, i.e. almost the entire list can be called a plasma. But, you object, space 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 a plasma and by what parameters do physicists consider a given state of matter as a plasma?

According to modern ideas about plasma, this is the fourth state of a substance that is in a gaseous state, highly ionized (the first state is a solid, the second is a liquid state, and finally the third is gaseous). 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 concentration of a particular sort of particles. A plasma is considered to be weakly ionized, if the so-called degree of ionization is equal to

$$

$$r = N_e / N_n$$

Where $$$N_e$ - electron concentration $$$N_n$ - the concentration of all neutral particles in the plasma lies in the range $$$(r <10 ^ {- 2} - 10 ^ {- 3})$ . A fully ionized plasma has a degree of ionization. $$$r \ to \ infty$



But as mentioned above, not every ionized gas is a plasma. It is necessary for the plasma to have the property of quasineutrality , i.e. on average, over sufficiently long time intervals and at sufficiently large distances, the plasma was generally neutral. But what are these periods of time and distance at which gas can be considered a plasma?



So, the quasi-neutrality requirement is as follows:

$$

$$\ sum _ {\ alpha} e _ {\ alpha} N _ {\ alpha} = 0$$

Let's first find out how physicists estimate the time scale of charge separation. Let us imagine that a certain electron in a plasma deviates from its initial equilibrium position in space. The Coulomb force begins to act on the electron, seeking to return the electron to an equilibrium state, i.e. $$$F \ approx e ^ 2 / {r ^ 2} _ {cf}$ where $$$r_ {cf}$ - the average distance between electrons. This distance is roughly estimated as follows. Assume the concentration of electrons (i.e. the number of electrons per unit volume) is $$$N_e$ . Electrons are on average at each other's distance. $$$r_ {cf}$ it means that they occupy an average volume $$$V = \ frac {4} {3} \ pi r_ {cf} ^ 3$ . From here, if in this volume 1 electron, $$$r_ {avg} = (\ frac {3} {4 \ pi N_e}) ^ {1/3}$ . As a result, the electron will begin to oscillate around an equilibrium position with a frequency

$$

$$\ omega \ approx \ sqrt {\ frac {F} {mr_ {cf}}} \ approx \ sqrt {\ frac {4 \ pi e ^ 2 N_e} {3m}}$$

More accurate formula

$$

$$\ omega_ {Le} = \ sqrt {\ frac {4 \ pi e ^ 2 N_e} {m}}$$

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



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

$$

$$\ tau = 2 \ pi / \ omega_ {Le}$$

In space, on a huge scale, for periods of time $$$t >> \ tau$ particles make many oscillations around the equilibrium position and the plasma as a whole will be quasi-neutral, i.e. on time scales, the interstellar medium can be taken as plasma.



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

$$

$$r_ {De} \ approx \ frac {\ upsilon_ {Te}} {\ omega_ {Le}} = \ sqrt {\ frac {kT_e} {4 \ pi e ^ 2 N_e}}$$

Where $$$\ upsilon_ {Te} = \ sqrt {\ frac {kT_e} {m}}$ . Where did this wonderful formula come from, you ask. We will reason like this. Electrons in a plasma at an equilibrium thermostat temperature constantly moving with kinetic energy. $$$E_k = \ frac {m \ upsilon ^ 2} {2}$ . On the other hand, the law of uniform distribution of energy is known from statistical thermodynamics, and on average there is $$$E = \ frac {1} {2} kT_e$ . If we compare these two energies, we get the velocity formula presented above.



So, we have obtained the length, which in physics is called the electronic Debye radius or length .



Now I will show a more rigorous derivation of the Debye equation. Let us again imagine N electrons, which under the action of an electric field are displaced by a certain amount. This forms a layer of space charge with a density equal to $$$\ sum e_j n_j$ where $$$e_j$ - electron charge, $$$n_j$ - electron concentration. Electrostatics is well known for the Poisson formula.

$$

$$\ bigtriangledown ^ 2 \ phi ({r}) = - \ frac {1} {\ epsilon \ epsilon_0} \ sum e_j n_j$$

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

$$

$$n_j ({r}) = n_0 \ exp (- \ frac {e_j \ phi ({r})} {kT_e})$$

Substitute the Boltzmann equation into the Poisson equation, we get

$$

$$\ bigtriangledown ^ 2 \ phi ({r}) = - \ frac {1} {\ epsilon \ epsilon_0} \ sum e_j n_0 \ exp (- \ frac {e_j \ phi ({r})} {kT_e})$$

This is the Poisson-Boltzmann equation. We expand the exponent in this equation into a Taylor series and discard values ​​of second order and higher.

$$

$$\ exp (- \ frac {e_j \ phi ({r})} {kT_e}) = 1 - \ frac {e_j \ phi ({r})} {kT_e}$$

Substitute this decomposition into the Poisson-Boltzmann equation and get

$$

$$\ bigtriangledown ^ 2 \ phi ({r}) = (\ sum \ frac {n_ {0j} e_ {j} ^ 2} {\ epsilon \ epsilon_0 kT_e}) \ phi ({r}) - \ frac {1 } {\ epsilon \ epsilon_0} \ sum n_ {0j} e_ {j}$$

This is the Debye equation. A more accurate name is the Debye-Hückel equation. As we found out above, in a plasma, as in a quasineutral medium, the second term in this equation is zero. In the first term, we essentially have the Debye length .



In the interstellar medium, the Debye length is about 10 meters, in the intergalactic medium about $$$10 ^ 5$ meters We see that these are rather large quantities compared with, for example, dielectrics. This means that the electric field propagates without attenuation over these distances, distributing the charges into volume charged layers whose particles oscillate around equilibrium positions with a frequency equal to the Langmuir one.



From this article, we learned two fundamental quantities that determine whether the cosmic medium is a 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 a local scale, we have either gas, dust, or plasma.