On the relativistic plasma-dynamical and hydrodynamical normal modes (original) (raw)
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Kinetic theory of the plasma-dynamical modes and the transport coefficients of a relativistic plasma
Physica A: Statistical Mechanics and its Applications, 1975
The kinetic equation of an inhomogeneous relativistic plasma, consisting of an electron gas and a radiation field, is studied with particular regard to its eigenvalues in the hydrodynamical limit. The treatment is classical for the particles and quantum-mechanical for the field oscillators. After a suitable regularization, the eigenvalues are obtained by a perturbation theory through second order in the strength of the gradients. It is shown that these eigenvalues are in exact correspondence with the macroscopic relativistic plasma-dynamical modes. The important role played by the Vlassov operator in building up the peculiar structure of these modes is underlined. From a comparison of the macroscopic and microscopic eigenvalues we obtain general expressions for the thermal conductivity, the shear viscosity and the bulk viscosity of a relativistic plasma. The contribution of the radiation field to these quantities is a noteworthy feature of these expressions.
Electromagnetic wave instability in a relativistic electron-positron-ion plasma
Astrophysics and Space Science, 2014
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Some recent developments in nonlinear relativistic plasma dynamics
2002
Some recent developments in the analytical and numerical study of the interaction of ultra-intense ultra-short laser pulses with relativistic plasmas are reviewed. Special attention is given to the subject of ion acceleration in view of its applications which range from proton imaging to the acceleration of collimated ion bunches and to the effect of fast magnetic field line reconnection on the evolution of the self-generated magnetic field.
Physical Review, 1968
The behavior of the relativistic scalar plasma in the Viasov approximation is analyzed. Equilibrium properties are discussed (equation of state, Debye-Huckel law"phase transitions). A dispersion relation for the propagation of a small disturbance is derived. Hydrodynamical equations are obtained. A number of ambiguities inherent in the theory are emphasized and discussed.
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The combined effect of special relativity and electron degeneracy on Langmuir waves is analyzed by utilizing a rigorous fully relativistic hydrodynamic model. Assuming a traveling wave solution form, a set of conservation laws is identified, together with a pseudo-potential function depending on the relativistic parameter p F /(m c) (where p F is the Fermi momentum, m is the mass of the charge carriers and c the speed of light), as well as on the amplitude of the electrostatic energy perturbation.
Dispersion relation of low-frequency electrostatic waves in plasmas with relativistic electrons
Laser and Particle Beams, 2016
The dispersion relation of electrostatic waves with phase velocities smaller than the electron thermal velocity is investigated in relativistic temperature plasmas. The model equations are the electron relativistic collisionless hydrodynamic equations and the ion non-relativistic Vlasov equation, coupled to the Poisson equation. The complex frequency of electrostatic modes are calculated numerically as a function of the relevant parameterskλDeandZTe/Tiwherekis the wavenumber, λDe, the electron Debye length,TeandTithe electron and ion temperature, andZ, the ion charge number. Useful analytic expressions of the real and imaginary parts of frequency are also proposed. The non-relativistic results established in the literature from the kinetic theory are recovered and the role of the relativistic effects on the dispersion and the damping rate of electrostatic modes is discussed. In particular, it is shown that in highly relativistic regime the electrostatic waves are strongly damped.
Relaxation of Relativistic Plasmas Under the Effect of Wave‐Particle Interactions
The Astrophysical Journal, 2007
We simulate the acceleration of electrons to relativistic energies due to the interaction of electrons with waves generated by longitudinal (i.e., electrostatic) streaming instabilities in plasmas. Two equal systems undergoing a streaming instability evolve, one according to the classical Newton's law and one according to the special relativity dynamics equation. The system that obeys Newton's law relaxes to a Maxwellian equilibrium distribution. In the case of the relativistic dynamics, the equilibrium distribution exhibits peaks in the phase space at high momenta and a larger number of particles at high energies. This steady electron population at higher energies could explain power-law energy distribution in many plasma physics and astrophysical systems.
2021
The choice of the expansion parameter employed in the analysis of the equations of weakly relativistic plasma affects the physical significance of the results. Traditionally, the small parameter employed in the non-relativistic and weak relativistic limits has been the order of magnitude of (v/v 0), where v is the ion velocity, and v 0 is proportional to the average electron velocity. However, in the weak relativistic case, the order of magnitude of (v/c), where c is the speed of light is the more natural choice. The resulting KdV equation with perturbations through second order is analyzed through a Normal Form expansion. The analysis exposes physical effects in corrections beyond lowest order, which hitherto have not be identified: (1) Effect of localized soliton interaction region; (2) Long-range interactions among solitons; (3) Dispersive waves generated by soliton interactions. In addition, the analysis provides information regarding: (1) Clear distinction between non-relativistic and weak relativistic effects; (2) Clear separation between relativistic and electron-temperature effects; (3) Variation of the effective small parameter used in the series expansion of the solution as the average electron kinetic energy is increased. These qualitative features do not depend on the details of the electron-gas thermodynamic distribution.