We obtain, and discuss, the roots of the dispersion relation describing normal mode propagation in a weakly ionized, collision dominated turbulent plasma with an isotropically distributed turbulent magnetic field. We demonstrate that, depending on the level of the turbulent field relative to the collision frequency, there may, or may not, be propagating, but decaying, modes present in the system. The structure and properties of the modes depend on both the precise level of the turbulent magnetic field and its spatial and temporal correlation.
For simple correlation functions we estimate the decay rate of the radiative modes. Using galactic parameters as an illustration we show that only the long-wavelength (low-frequency) modes last for a significant length of time (≳ a collision time).
We have done this calculation to demonstrate that the response of turbulent plasma systems is more complicated than simple order of magnitude calculations indicate; and to illustrate a method which may, perhaps, be gainfully employed in more complex turbulent astrophysical plasma situations than considered here.
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Lerche, I. Radiative modes of a weakly ionized, collision-dominated, turbulent plasma. Astrophys Space Sci 18, 94–103 (1972). https://doi.org/10.1007/BF00645283
- Dispersion Relation
- Normal Mode
- Radiative Mode
- Temporal Correlation
- Collision Frequency