Ion-Beam-Driven Electrostatic Instability in a Magnetized, Relativistically Degenerate Plasma with Quantum Diffraction and Exchange–Correlation Effects
Author
Iqbal Ahsan, Muhammad Rizwan, Shahnaz Maryam
Abstract
The linear stability of an ion beam streaming along a magnetic field through a dense plasma with relativistically degenerate electrons is investigated using a three-fluid quantum hydrodynamic model. Electrons obey the Chandrasekhar equation of state and include quantum diffraction (Bohm potential) and exchange–correlation effects, while the background ions and the beam are warm and magnetized and the waves propagate obliquely to the field. A closed dispersion relation is derived and reduced to a degree-eight polynomial whose complex roots yield the growth rate. Analytical limits are obtained for the quantum ion-acoustic mode, the two magnetized oblique modes, and a weak, cold beam. In the last case the growth rate scales as the cube root of the beam density, and the relevant wavenumber is the field-aligned component for a magnetized beam but the full wavenumber for an unmagnetized one. For a helium plasma at ne0=1029 cm−3, a beam density ratio of 0.1 and a beam speed of 1.6 times the quantum ion-acoustic speed, the maximum growth rate is 0.0615 ωpi, or 1.7×1016 s−1. Parallel propagation is unstable only for beam speeds between about 0.7 and 1.8 times the ion-acoustic speed, whereas oblique propagation extends the instability, with the largest growth at about 53∘. Relativistic degeneracy is the dominant correction: the non-relativistic Fermi pressure overestimates the peak growth rate by 34% at 1029 cm−3. Quantum diffraction and exchange–correlation change it by about 1% in the regime of validity of the fluid model. The results are relevant to white dwarf interiors and compressed inertial-fusion targets.
Keywords
Ion-beam Instability; Relativistic Degenerate Plasma; Chandrasekhar Equation of State; Quantum Hydrodynamics; Exchange–Correlation; Magnetized Plasma
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References
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