The structure of strong collision-free hydromagnetic waves

Adlam, J.H.; Allen, J. E.

doi:10.1080/14786435808236833

Cited by 90 publications

(119 citation statements)

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“…In Sec. III, we carry out a numerical analysis of the nonlinear equations which reveals that the solitary electromagnetic pulses are composed of density and magnetic field humps and have some similarities with the compressional Alfvénic solitons in a cold electronion plasma [32]. The properties and existence criteria of the solitary electromagnetic pulses are discussed, and examples of profiles of the solitary pulses are displayed graphically.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic solitary pulses in a magnetized electron-positron plasma

2011

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A theory for large amplitude compressional electromagnetic solitary pulses in a magnetized electron-positron (e-p) plasma is presented. The pulses, which propagate perpendicular to the external magnetic field, are associated with the compression of the plasma density and the wave magnetic field. Here the solitary wave magnetic field pressure provides the restoring force, while the inertia comes from the equal mass electrons and positrons. The solitary pulses are formed due to a balance between the compressional wave dispersion arising from the curl of the inertial forces in Faradays law and the nonlinearities associated with the divergence of the electron and positron fluxes, the nonlinear Lorentz forces, the advection of the e-p fluids, and the nonlinear plasma current densities. The compressional solitary pulses can exist in a well-defined speed range above the Alfven speed. They can be associated with localized electromagnetic field excitations in magnetized laboratory and space plasmas composed of electrons and positrons.

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Section: Introductionmentioning

confidence: 99%

Electromagnetic solitary pulses in a magnetized electron-positron plasma

2011

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“…Moreover, it is puzzling to read (McKenzie et al, 2007) that in the classic nonlinear wave propagating perpendicular to the ambient magnetic field (Adlam and Allen, 1958) the circumstances are not quasi-charge neutral, and that in fact such an assumption would violate conservation of longitudinal momentum, whereas Adlam and Allen (1958) use quasi-neutrality in the form |n i −n e | n i (my change of their notation for the electron and ion densities) to arrive at their conclusions. McKenzie et al (2007) have presented an estimate of the relative charge imbalance when studying nonlinear phenomena like the whistler oscillitons (Sauer et al, 2002;Dubinin et al, 2003;Verheest et al, 2004) based on linear wave theory.…”

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confidence: 99%

Reply to J. F. McKenzie et al.'s comment on "Obliquely propagating large amplitude solitary waves in charge neutral plasmas"

Verheest

2007

Nonlin. Processes Geophys.

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I note the comments by McKenzie et al. (2007), but it may be wise to remember that the plasma approximation, in which quasi-neutrality holds with n i n e but ∇·E =0 (Chen, 1974), is precisely that: an approximation. Arguments given by McKenzie et al. (2007), and indeed by several other authors, indicating how reasonable the plasma approximation is, are almost all based on linear wave theory and on keeping the relativistic effects small. In addition, it should be borne in mind that the plasma approximation is true only for lowfrequency motions where the electron inertia is not a factor (Chen, 1974;Nicholson, 1983), and, as has been noted before (Verheest, 2007), the concept of frequency might be borrowed from the linear counterparts of the nonlinear waves studied, but it is not a well defined property of stationary modes studied in their own reference frames.Although the plasma approximation has been used extensively in linear and small amplitude work, it is a legitimate question to ask what its effects might be for large nonlinear structures. In this context, the step was taken (Verheest, 2007) of considering the extreme case in which n i =n e and ∇·E=0.An indication of what might happen is given by the reductive perturbation treatment of moderately nonlinear electromagnetic waves propagating parallel to the ambient field. As is well known from many papers since the original derivation by Rogister (1971), these waves are governed by the derivative nonlinear Schrödinger (DNLS) equation. If one starts the description from the full set of Maxwell's equations, including Poisson's equation and the displacement current, one finds that to lowest order the parallel electric field vanishes, by combining the equations of motion to that order and without having assumed charge neutrality or relied upon Poisson's equation (see e.g. Verheest, 2000). Charge neutrality Correspondence to: F. Verheest (frank.verheest@ugent.be) then follows to lowest order from Poisson's equation, without having been assumed a priori.Continuing the iterative procedure, one eliminates the higher-order electromagnetic fields by combining in a judicious way the results obtained from the continuity and momentum equations and plugging these into Ampère's law, to arrive at the DNLS equation governing the perpendicular wave magnetic field. Usually the discussion then focuses on the solutions of the DNLS equation and the higher-order fields are not further investigated. The DNLS equation admits only envelope solitons, where the amplitude of the wave magnetic field shows the profile of a traditional solitary wave, but the phase increases linearly on the slow timescale.However, once the wave magnetic field obeys the DNLS equation, one can evaluate the higher-order electric fields and finds that a parallel electric field has been generated to that order by the nonlinearities (Verheest, 2004). This subsequently tells us that, although at the linear level there is automatically charge neutrality, this cannot be maintained to higher order. Since the cited treat...

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“…͑Stationary finiteamplitude waves are known. [19][20][21][22][23] positrons suffering acceleration. In the first type, particles move nearly parallel to B 0 as in the early phase; its mechanism is thus the same as that discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Persistent acceleration of positrons in a nonstationary shock wave

2005

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Interaction features of different propellants under plasma impingement J. Appl. Phys. 112, 063303 (2012) Ion velocity and plasma potential measurements of a cylindrical cusped field thruster J. Appl. Phys. 111, 093303 (2012) Three-dimensional particle-in-cell simulation of discharge characteristics in cylindrical anode layer hall plasma accelerator Phys. Plasmas 19, 043507 (2012) Additional information on Phys. Plasmas Long-time evolution of positrons accelerated in an oblique shock wave in an electron-positron-ion plasma is studied with relativistic, electromagnetic, particle simulations. In the early stage, some positrons move nearly parallel to the external magnetic field in the shock transition region and gain energy from the parallel electric field. The acceleration can become stagnant owing to the deformation of the wave profile. After the recovery of the shock profile, however, the acceleration can start again. By the end of simulation runs, pe t = 5000, positron Lorentz factors reached values ϳ2000. In this second stage, three different types of acceleration are found. In the first type, the acceleration process is the same as that in the early stage. In the second type, positrons make gyromotions in the wave frame and gain energy mainly from the perpendicular electric field. In the third type, particle orbits are similar to curtate cycloids. Theoretical estimate for this energy increase is given.

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The structure of strong collision-free hydromagnetic waves

Cited by 90 publications

References 3 publications

Electromagnetic solitary pulses in a magnetized electron-positron plasma

Electromagnetic solitary pulses in a magnetized electron-positron plasma

Reply to J. F. McKenzie et al.'s comment on "Obliquely propagating large amplitude solitary waves in charge neutral plasmas"

Persistent acceleration of positrons in a nonstationary shock wave

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The structure of strong collision-free hydromagnetic waves

Cited by 90 publications

References 3 publications

Electromagnetic solitary pulses in a magnetized electron-positron plasma

Electromagnetic solitary pulses in a magnetized electron-positron plasma

Reply to J. F. McKenzie et al.'s comment on &quot;Obliquely propagating large amplitude solitary waves in charge neutral plasmas&quot;

Persistent acceleration of positrons in a nonstationary shock wave

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Reply to J. F. McKenzie et al.'s comment on "Obliquely propagating large amplitude solitary waves in charge neutral plasmas"