Response to “Comment on ‘Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma'” [Phys. Plasmas 14, 084701 (2007)]

Trines, R. M. G. M.; Norreys, P.

doi:10.1063/1.2752523

Cited by 5 publications

(8 citation statements)

References 21 publications

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“…͑Note to reader: we have read the Response by TN, 5 and all the published equations are accurately plotted in Fig. 1.͒ ͑5͒ TN incorrectly claim that no trapping can occur for field amplitudes below the wave-breaking limit.…”

Section: ͑3͒mentioning

confidence: 99%

“…͑Note to reader: we have read the Response of TN 5 and we stand by all the points made above in our Comment͒. This work was supported by the U.S. DOE under Contract No.…”

Section: ͑3͒mentioning

confidence: 99%

“…5 The error made by TN is inconsistently expanding quantities only to order O͑⑀ 2 ͒ and then incorrectly making conclusions about terms of order O͑⑀ 4 ͒.͔ ͑2͒ TN state that the heat flow can be expressed in firstorder and second-order centered moments. This statement is false for a collisionless plasma.…”

mentioning

confidence: 99%

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Comment on “Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma” [Phys. Plasmas 13, 123102 (2006)]

2007

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Section: ͑3͒mentioning

confidence: 99%

“…͑Note to reader: we have read the Response of TN 5 and we stand by all the points made above in our Comment͒. This work was supported by the U.S. DOE under Contract No.…”

Section: ͑3͒mentioning

confidence: 99%

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Comment on “Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma” [Phys. Plasmas 13, 123102 (2006)]

2007

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“…Models of non-linear plasma waves near breaking are approaching the limits of their domain of applicability, and different models exhibit different wave-breaking limits. Although recent experiments [16][17][18] operate in the 3-dimensional 'bubble' (or 'blow-out') regime [19] and exploit transverse wave-breaking [20], recent work [13][14][15] has rekindled interest in the theory of longitudinal wave-breaking.…”

Section: Introductionmentioning

confidence: 99%

“…Wave-breaking limits were first calculated for cold plasmas [7,8] undergoing non-linear longitudinal electrostatic oscillations, and thermal effects were later included in non-relativistic [9] and relativistic [10][11][12] contexts. The results for the cold plasma are uncontroversial, but recent discussion [13][14][15] has uncovered difficulties with establishing an agreed analytical description of longitudinal wave-breaking in warm plasmas; in particular, it has been noted that different plasma models based on different assumptions yield different results. Models of non-linear plasma waves near breaking are approaching the limits of their domain of applicability, and different models exhibit different wave-breaking limits.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal wave-breaking limits in a unified geometric model of relativistic warm plasmas

Burton¹,

Noble²

2010

J. Phys. A: Math. Theor.

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The covariant Vlasov-Maxwell system is used to study breaking of relativistic warm plasma waves. The well-known theory of relativistic warm plasmas due to Katsouleas and Mori (KM) is subsumed within a unified geometric formulation of the 'waterbag' paradigm over spacetime. We calculate the maximum amplitude Emax of non-linear longitudinal electric waves for a particular class of waterbags whose geometry is a simple 3-dimensional generalization (in velocity) of the 1-dimensional KM waterbag (in velocity). It is well known that the value of limv→c Emax (with the effective temperature of the plasma electrons held fixed) diverges for the KM model; however, we show that a certain class of simple 3-dimensional waterbags yields a finite value for limv→c Emax, where v is the phase velocity of the wave and c is the speed of light.

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Large amplitude relativistic plasma waves

Coffey

2010

Physics of Plasmas

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Relativistic, longitudinal plasma oscillations are studied for the case of a simple water bag distribution of electrons having cylindrical symmetry in momentum space with the axis of the cylinder parallel to the velocity of wave propagation. The plasma is required to obey the relativistic Vlasov–Poisson equations, and solutions are sought in the wave frame. An exact solution for the plasma density as a function of the electrostatic field is derived. The maximum electric field is presented in terms of an integral over the known density. It is shown that when the perpendicular momentum is neglected, the maximum electric field approaches infinity as the wave phase velocity approaches the speed of light. It is also shown that for any nonzero perpendicular momentum, the maximum electric field will remain finite as the wave phase velocity approaches the speed of light. The relationship to previously published solutions is discussed as is some recent controversy regarding the proper modeling of large amplitude relativistic plasma waves.

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Response to “Comment on ‘Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma'” [Phys. Plasmas 14, 084701 (2007)]

Cited by 5 publications

References 21 publications

Comment on “Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma” [Phys. Plasmas 13, 123102 (2006)]

Comment on “Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma” [Phys. Plasmas 13, 123102 (2006)]

Longitudinal wave-breaking limits in a unified geometric model of relativistic warm plasmas

Large amplitude relativistic plasma waves

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