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Oscillations in a Relativistic Plasma

dc.contributor.authorImre, Kayaen_US
dc.date.accessioned2010-05-06T20:33:39Z
dc.date.available2010-05-06T20:33:39Z
dc.date.issued1962-04en_US
dc.identifier.citationImre, K. (1962). "Oscillations in a Relativistic Plasma." Physics of Fluids 5(4): 459-466. <http://hdl.handle.net/2027.42/69410>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/69410
dc.description.abstractThe linear oscillations in a hot plasma which is representable by the relativistic Vlasov equation with the self‐consistent fields are investigated. The generalization of Bernstein's method for the relativistic case is used to obtain the formal solution of the linearized problem. Particular attention is given to the case when the system initially is in the relativistic equilibrium state. The dispersion equation is derived and studied for the case when the propagation is along the direction of the unperturbed magnetic field, considering the spatial dispersions explicitly. The asymptotic expansions are developed corresponding to the dispersion relations of the cases studied. It is found that transverse waves propagating along the unperturbed field are Landau damped if ν2 ≥ 1 − Ω2∕ω2, ν and Ω being the index of refraction and the gyrofrequency, respectively. In the absence of the external field the cutoff frequency, which is found to be the same for both longitudinal and the transverse modes, is shown to be a monotonically decreasing function of the temperature.en_US
dc.format.extent3102 bytes
dc.format.extent468252 bytes
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dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleOscillations in a Relativistic Plasmaen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Nuclear Engineering and Radiation Laboratory, University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/69410/2/PFLDAS-5-4-459-1.pdf
dc.identifier.doi10.1063/1.1706639en_US
dc.identifier.sourcePhysics of Fluidsen_US
dc.identifier.citedreferenceF. Jüttner, Ann. Physik 34, 856 (1911a).en_US
dc.identifier.citedreferenceFor details see K. Imre [The University of Michigan Radiation Laboratory Rept. 2756‐1‐F, (ARL‐TR‐60‐274, Part II) (1961)].en_US
dc.identifier.citedreferenceThe Kronecker delta δν1ν2⋯νnμ1μ2⋯μnδν1ν2⋯νnμ1μ2⋯μn may be defined as δν1ν2⋯νnμ1μ2⋯μn≡det(δνjμi) = ∣δν1μ1⋯δνnμ1⋮⋮δν1μn⋯δνnμn∣. Also, δjα = 0δjα = 0 for α = 4α = 4 and = δjk= δjk for α = k(= 1,2,3).α = k(= 1,2,3).en_US
dc.identifier.citedreferenceW. E. Drummond and M. N. Rosenbluth, Phys. Fluids 3, 45 (1960).en_US
dc.identifier.citedreferenceB. A. Trubnikov, in Plasma Physics and the Problem of Controlled Thermonuclear Reactions, edited by M. A. Leontovich, translation editor, J. Turkevich (Pergamon Press, New York, 1960), Vol. 3.en_US
dc.identifier.citedreferenceP. C. Clemmow and A. J. Willson, Proc. Roy. Soc. (London) A237, 117 (1956).en_US
dc.identifier.citedreferenceJ. Landau, J. Phys. (U.S.S.R.) 10, 25 (1946).en_US
dc.identifier.citedreferenceV. P. Silin, J. Exptl. Theoret. Phys. 38, 1577 (1960) [Soviet Phys.‐JETP 11, 1136 (1960)].en_US
dc.identifier.citedreferenceShortly it will be seen that in the absence of the external field one has ν<1ν<1 [cf. Eq. (44)]. Hence, in this case, there is no Landau damping [cf. Eq. (33)]. However, in some particular problems due to additional effects the total refractive index may exceed unity (e.g., this is the case for plasmas in the proximity of strong dielectrics). Klimontovich and Silin [cf. Plasma Physics, edited by J. E. Drummond (McGraw‐Hill Book Company, Inc., New York 1961), p. 45] derived a damping factor for such problems using a different method. Equation (39) leads to their result.en_US
dc.identifier.citedreferenceBecause of the divergent character of the involved series, extra care should be exercised in dealing with the asymptotic expansions given in this paper.en_US
dc.identifier.citedreferenceO. Buneman, Phys. Rev. 112, 1504 (1958).en_US
dc.identifier.citedreferenceOur formula differs from the one given by Silin by a factor of 2∕3.en_US
dc.identifier.citedreferenceE. G. Harris, Phys. Rev. 108, 1358 (1957).en_US
dc.identifier.citedreferenceHere, it should be pointed out that the correlations, which are ignored completely in this work, can provide an additional damping mechanism which is different from the one discussed above.en_US
dc.owningcollnamePhysics, Department of


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