dorsal/arxiv
View SchemaLandau damping: is it real?
| Authors | V. N. Soshnikov |
|---|---|
| Categories | |
| ArXiv ID | physics/9712013 |
| URL | https://arxiv.org/abs/physics/9712013 |
Abstract
To calculate linear oscillations and waves in dynamics of gas and plasma one uses as a rule the old classical method of dispersion equation for complex frequencies $\omega$ and wave numbers $k$: $\epsilon(\omega,k)=0$. This method appears to be inapplicable, f.e., in the case of waves in Maxwellian collisionless plasma when dispersion equation has no solutions. By means of some refined sophistication L.~Landau in 1946 has suggested in this case actually to replace the dispersion equation with another one, having a specific solution (``Landau damping'') and being now widely used in plasma physics. Recently we have suggested a quite new universal method of two-dimensional Laplace transformation (in coordinate $x$ and time $t$ for plane wave case), that allows to obtain asymptotical solutions of original Vlasov plasma equations as inseparable sets of coupled oscillatory modes (but not a single wave like $\exp(-i\omega t+i k x)$). The mode parameters are defined in this case by double-poles ($\omega_n$,$k_n$) of Laplace image $E(\omega_n,k_n)$ of electrical field $E(x,t)$. This method allows one to obtain the whole set of oscillatory modes for every concrete problem. It leads to some new ideology in the theory of plasma oscillations, which are considered as a combination of coupled oscillatory modes (characterized by pairs ($\omega_n$,$k_n$) and amplitudes) and depend not only on the intrinsic plasma parameters, but also on mutually dependent self-consistent initial and boundary conditions and on method of plasma oscillations excitation.
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"abstract": "To calculate linear oscillations and waves in dynamics of gas and plasma one\nuses as a rule the old classical method of dispersion equation for complex\nfrequencies $\\omega$ and wave numbers $k$: $\\epsilon(\\omega,k)=0$. This method\nappears to be inapplicable, f.e., in the case of waves in Maxwellian\ncollisionless plasma when dispersion equation has no solutions. By means of\nsome refined sophistication L.~Landau in 1946 has suggested in this case\nactually to replace the dispersion equation with another one, having a specific\nsolution (``Landau damping\u0027\u0027) and being now widely used in plasma physics.\nRecently we have suggested a quite new universal method of two-dimensional\nLaplace transformation (in coordinate $x$ and time $t$ for plane wave case),\nthat allows to obtain asymptotical solutions of original Vlasov plasma\nequations as inseparable sets of coupled oscillatory modes (but not a single\nwave like $\\exp(-i\\omega t+i k x)$). The mode parameters are defined in this\ncase by double-poles ($\\omega_n$,$k_n$) of Laplace image $E(\\omega_n,k_n)$ of\nelectrical field $E(x,t)$. This method allows one to obtain the whole set of\noscillatory modes for every concrete problem. It leads to some new ideology in\nthe theory of plasma oscillations, which are considered as a combination of\ncoupled oscillatory modes (characterized by pairs ($\\omega_n$,$k_n$) and\namplitudes) and depend not only on the intrinsic plasma parameters, but also on\nmutually dependent self-consistent initial and boundary conditions and on\nmethod of plasma oscillations excitation.",
"arxiv_id": "physics/9712013",
"authors": [
"V. N. Soshnikov"
],
"categories": [
"physics.plasm-ph"
],
"title": "Landau damping: is it real?",
"url": "https://arxiv.org/abs/physics/9712013"
},
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