Abstract
It is not only the atmosphere and the ocean that constitute the Earth’s environment. Once you leave the Earth and travel into space, you will find that the space is not a vacuum as is often misunderstood, but is filled with a medium called plasma, an extremely high-temperature fluid (gas) that conducts electricity. Via this plasma, the Earth’s environment is linked to outer space, in particular, to dynamic activities of the sun.
The original version of this chapter was revised: See the “Chapter Note” section at the end of this chapter for details. The erratum to this chapter is available at 10.1007/978-4-431-56499-7_10
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Notes
- 1.
The “auroral particles” are believed to be energetic electrons and protons stored in the magnetosphere , a region created by the confinement of the Earth’s magnetic field by the solar wind. Some changes of the solar wind conditions, such as the direction of the magnetic field there, triggers these particles to start precipitating into the ionosphere.
- 2.
The radiation pressure of sunlight is not sufficient to explain the rapid movement of the fine structure of the plasma tail such as twists and kinks.
- 3.
SOHO mission by ESA (European Space Agency) and NASA (National Aeronautics and Space Administration), http://sohowww.nascom.nasa.gov/.
- 4.
YOHKOH mission by JAXA (Japan Aerospace eXploration Agency), http://www.darts.isas.ac.jp/solar/yohkoh/data.html.
- 5.
HINODE mission by JAXA, http://hinode.nao.ac.jp.
- 6.
1 \(\mathrm {atm} = 1.013 \times 10^{5}~\mathrm {Pa}\). Pa is a SI unit equivalent to \(\mathrm {N} \mathrm {m}^{-2}\).
- 7.
Magnetic reconnection is a process where the magnetic energy is converted to gas thermal and kinetic energies via merging of two magnetic field lines. Alfven wave is one of the fundamental waves in the plasma, which can carry energy from the solar surface to a higher altitude by propagating into the corona, and release the energy to the gas by wave damping.
- 8.
In case of the isothermal gas, \(\varGamma =1\), the energy equation cannot be defined. One can see this in (9.23) where the factor \(\varGamma -1\) is included in the denominator of the enthalpy per unit mass (second term in the definition of \(F_e\)).
- 9.
If there are not many people, they all may be able to exit smoothly, because nobody needs to avoid hitting other people, which significantly reduces the reaction time scale. When the human flow is very smooth, the flow speed can increase near the exit.
- 10.
To be precise, here we are talking about the interaction between collective motion of particles and the electromagnetic field at macroscopic scales (spatial scale greater than the Debye scale length, to be defined in a moment).
- 11.
Temperature can be defined in the unit of energy by multiplying the usual temperature in \(\mathrm {K}\) by the Boltzman constant, \(k_B = 1.38\times 10^{-23}~\mathrm {J ~K^{-1}}\). Temperature of \(1~\mathrm {eV}\) is equivalent to 11,600 \(\mathrm {K}\).
- 12.
We have encountered an example of a gas obeying the Boltzmann statistics in (9.6), which can be re-written as \(\rho (z)=\rho _0 \exp (-mgh/T)\).
- 13.
For example, the skin depth (or the electron inertial length), \(c/\omega _e\), where c is the speed of light, gives the scale that a light wave can penetrate into a plasma.
- 14.
One can show that \(n^2\) is either real or pure imaginary.
- 15.
According to a Fourier analysis, a solitary wave is expressed as a superposition of many monochromatic waves with different wavelengths, i.e., waves with different frequencies if the waves satisfy the whistler mode dispersion relation.
- 16.
The frequency-time spectrogram of plasma waves can be obtained from: http://space.rish.kyoto-u.ac.jp/gtlpwi/gtldata.html. General information on GEOTAIL wave experiments can be found at: http://space.rish.kyoto-u.ac.jp/gtlpwi/.
- 17.
This type of procedure, however, always confront the difficulty of closure: in order to specify the time evolution of the pressure tensor , one has to compute the higher order moment of the distribution function, which, in this case, is the heat flux tensor.
- 18.
According to the special theory of relativity, the electric field in a frame moving with velocity \(\varvec{u}\) is given approximately by \(\varvec{E}+\varvec{u}\times \varvec{B}\), i.e., the motional electric field is superposed to the electric field in the original frame, when \(|\varvec{u}|\) is not too close to the speed of light.
- 19.
One should be careful that, in the communities of nuclear fusion and laboratory experiments, the beta ratio is often defined as \(\beta =P/(\varvec{B}^2/2 \mu _0 +P)\), i.e., the total pressure is used for the denominator.
- 20.
The temperature here does not contain the Boltzmann constant.
- 21.
In our analysis of the cold plasma, the wave mode corresponding to the sound wave did exist also, but the sound speed was zero and the wave was not propagating.
- 22.
To be precise, there is another mode called the entropy wave, in which all the perturbations are zero except for \(\delta \rho \) and \(\delta T\), which are given in such a way that the plasma pressure is constant, i.e., \(T_0 \delta \rho + \rho _0 \delta T = 0\). For the entropy wave, \(\omega =0\) for any \(\varvec{k}\) and is non-propagating. Nevertheless, it can carry information by being convected by a plasma flow. Including the entropy wave, there exit seven independent MHD waves for fixed \(\varvec{k}\), corresponding to the number of independent variables in the MHD system.
- 23.
One can tell the origin of the plasma by examining the “heavy ion elements” included in the plasma. Plasma from the ionosphere includes such ions as \(\mathrm {O}^+\) and \(\mathrm {He}^{+}\), while solar wind plasma contains \(\mathrm {He}^{++}\).
- 24.
Time scale for the plasma to reach thermal equilibrium.
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Department of Earth System Science and Technology, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University. (2017). Space Plasma Environment. In: Fluid Dynamics for Global Environmental Studies. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56499-7_9
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