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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Ion acoustic wave ： ウィキペディア英語版 Ion acoustic wave In plasma physics, an ion acoustic wave is one type of longitudinal oscillation of the ions and electrons in a plasma, much like acoustic waves traveling in neutral gas. However, because the waves propagate through positively charged ions, ion acoustic waves can interact with their electromagnetic fields, as well as simple collisions. In plasmas, ion acoustic waves are frequently referred to as acoustic waves or even just sound waves. They commonly govern the evolution of mass density, for instance due to pressure gradients, on time scales longer than the frequency corresponding to the relevant length scale. Ion acoustic waves can occur in an unmagnetized plasma or in a magnetized plasma parallel to the magnetic field. For a single ion species plasma and in the long wavelength limit, the waves are dispersionless ($\backslash omega=v\_sk$) with a speed given by (see derivation below) :$v\_s\; =\; \backslash sqrtT\_e+\backslash gamma\_K\_T\_i\}\}$ where $K\_$ is Boltzmann's constant, $M$ is the mass of the ion, $Z$ is its charge, $T\_e$ is the temperature of the electrons and $T\_i$ is the temperature of the ions. Normally γe is taken to be unity, on the grounds that the thermal conductivity of electrons is large enough to keep them isothermal on the time scale of ion acoustic waves, and γi is taken to be 3, corresponding to one-dimensional motion. In collisionless plasmas, the electrons are often much hotter than the ions, in which case the second term in the numerator can be ignored. == Derivation == We derive the ion acoustic wave dispersion relation for a linearized fluid description of a plasma with N ion species. A subscript 0 denotes constant equilibrium quantities, and 1 denotes first-order perturbations. We assume the pressure perturbations for each species (electrons and ions) are a Polytropic_process, namely $p\_\; =\; \backslash gamma\_s\; T\_\; n\_$ for species s. To justify this assumption and determine the value of $\backslash gamma\_s$, one must use a kinetic treatment that solves for the species distribution functions in velocity space. Using the ion continuity equation, the ion momentum equation becomes :$(-m\_i\backslash partial\_+\backslash gamma\_iT\_i\backslash nabla^2)n\_\; =\; Z\_ien\_\backslash nabla\backslash cdot\backslash vec\; E$ We relate the electric field $\backslash vec\; E\_1$ to the electron density by the electron momentum equation: :$n\_m\_e\backslash partial\_t\backslash vec\; v\_\; =\; -n\_e\backslash vec\; E\_1\; -\; \backslash gamma\_eT\_e\backslash nabla\; n\_$ We now neglect the left-hand side, which is due to electron inertia. This is valid for waves with frequencies much less than the electron plasma frequency. The resulting electric field is :$\backslash vec\; E\_1\; =\; -\; \backslash nabla\; n\_$ Since we have already solved for the electric field, we cannot also find it from Poisson's equation. The ion momentum equation now relates $n\_$ for each species to $n\_$: :$(-m\_i\backslash partial\_+\backslash gamma\_iT\_i\backslash nabla^2)n\_\; =\; -\backslash gamma\_e\; T\_e\; \backslash nabla^2\; n\_$ We arrive at a dispersion relation via Poisson's equation: :$\backslash nabla\backslash cdot\backslash vec\; E\; =\; \backslash left(\backslash sum\_^N\; n\_Z\_i\; -\; n\_\; \backslash right)\; +\; \backslash left(\backslash sum\_^N\; n\_Z\_i\; -\; n\_\; \backslash right)$ The first bracketed term on the right is zero by assumption (charge-neutral equilibrium). We substitute for the electric field and rearrange to find :$(1-\backslash gamma\_e\; \backslash lambda\_^2\backslash nabla^2)n\_\; =\; \backslash sum\_^N\; Z\_in\_$. $\backslash lambda\_^2\; \backslash equiv\; \backslash epsilon\_0T\_e/(n\_e^2)$ defines the electron Debye length. The second term on the left arises from the $\backslash nabla\backslash cdot\backslash vec\; E$ term, and reflects the degree to which the perturbation is not charge-neutral. If $k\backslash lambda\_$ is small we may drop this term. This approximation is sometimes called the plasma approximation. We now work in Fourier space, and find :$n\_\; =\; \backslash gamma\_eT\_eZ\_i\; \}\; ()^\; n\_$ $v\_s=\backslash omega/k$ is the wave phase velocity. Substituting this into Poisson's equation gives us an expression where each term is proportional to $n\_$. To find the dispersion relation for natural modes, we look for solutions for $n\_$ nonzero and find: $n\_=f\_in\_$ where $n\_=\backslash Sigma\_i\; n\_$, and $\backslash bar\; Z\; =\; \backslash Sigma\_i\; Z\_if\_i$. A unitless version of this equation is :$\backslash sum\_^N\; =\; 1+\backslash gamma\_e\; k^2\backslash lambda\_^2$ with $A\_i=m\_i/m\_u$, $m\_u$ is the atomic mass unit, $u^2=m\_uv\_s^2/T\_e$, and :$F\_i\; =\; ,\; \backslash quad\; \backslash tau\_i\; =$ If $k\backslash lambda\_$ is small (the plasma approximation), we can neglect the second term on the right-hand side, and the wave is dispersionless $\backslash omega\; =\; v\_sk$ with $v\_s$ independent of k. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ion acoustic wave」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.