The structure of strong collision-free hydromagnetic waves

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

doi:10.1080/14786435808244566

Cited by 238 publications

(17 citation statements)

References 3 publications

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“…6(a)). Furthermore, the pulse propagation velocity inferred from the magnetic field maximum for 0 ≤ tω ci ≤ 5 is 1.048 V A , which is consistent with the phase velocity v φ = V A (1 + B m )/2 of MS solitons 6,19,20 for the normalized pulse amplitude B m = 0.1 used here.…”

Section: Numerical Validationsupporting

confidence: 81%

“…Although rarefaction soliton solutions do not exist for transverse magnetosonic waves in cold plasma 17 , it is further assumed that a rarefaction pulse such as defined in Eq. (20) propagates with negligible change in form, i. e. as a soliton. The Mach number of the n th reflected pulse is related to the Mach number of the (n − 1) th reflected pulse by…”

Section: Displacement After N Reflections In a Plasma Slabmentioning

confidence: 99%

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Cumulative displacement induced by a magnetosonic soliton bouncing in a bounded plasma slab

2018

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The passage of a magnetosonic (MS) soliton in a cold plasma leads to the displacement of charged particles in the direction of a compressive pulse and in the opposite direction of a rarefaction pulse. In the overdense plasma limit, the displacement induced by a weakly nonlinear MS soliton is derived analytically. This result is then used to derive an asymptotic expansion for the displacement resulting from the bouncing motion of a MS soliton reflected back and forth in a vacuum-bounded cold plasma slab. Particles' displacement after the pulse energy has been lost to the vacuum region is shown to scale as the ratio of light speed to Alfvén velocity. Results for the displacement after a few MS soliton reflections are corroborated by particle-in-cell simulations.

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Section: Numerical Validationsupporting

confidence: 81%

Section: Displacement After N Reflections In a Plasma Slabmentioning

confidence: 99%

Cumulative displacement induced by a magnetosonic soliton bouncing in a bounded plasma slab

2018

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“…We have studied the structure of stationary, nonlinear, periodic waves and solitons propagating perpendicular and obliquely to the magnetic field in a cold bi‐ion plasma, using multifluid equations. It is well known that in transverse solitons propagating in a plasma consisting only of protons and electrons, finite ion inertia plays no role and dispersion effects appear only at smaller length scales where finite electron inertia progressively decouples the magnetic field from the fluid [see, e.g., Adlam and Allen , 1958; Sagdeev , 1966; Tidman and Krall , 1971; McKenzie et al , 2001b]. However, even a small admixture of alpha particles into a proton‐electron plasma introduces a new dispersion length which can drastically change the transverse solution.…”

Section: Discussionmentioning

confidence: 99%

“…Taking into account the results of this paper, the absence of very thin subcritical shocks is not surprising because of multi‐ion nature of the solar wind. Therefore one example [ Newbury and Russell , 1996] of a very thin shock (the ramp thickness is about of two electon inertial lengths) as the first example of observations of a classical shock postulated by Adlam and Allen [1958] and Sagdeev [1966] would appear to be the exception thus requiring explanation.…”

Section: Discussionmentioning

confidence: 99%

Solitons, oscillitons, and stationary waves in a cold p − α plasma

et al. 2003

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[1] We investigate the structure of nonlinear stationary waves propagating transverse and obliquely to the magnetic field in a cold plasma consisting of two ion populations, protons and alpha particles. By using the constants of motion which follow from the multifluid equations, the system may be described by a single first-order differential equation for the transverse case and four coupled first-order differential equations in the case of oblique propagation. In the transverse case solitons exist if the wave speed lies between the Alfven speed, based on the total mass density, and the Alfven speed modified by the density and charge ratios. At speeds in excess of this latter velocity, periodic solutions exist in which protons and alphas gyrate around each other. An analog of RankineHugoniot type relations for the amplitude of the solitons and periodic waves is found for structures propagating transverse to the magnetic field. In the case of an oblique stationary wave it is shown that the tip of the proton (alpha ion) flow velocity vector moves on the surface of a sphere whose radius is determined only by the obliquity and the wave speed. Soliton solutions representing both compressions and rarefactions in the ion fluids exist in specific windows in the ''Alfven Mach number-obliquity'' space. In other windows, solutions characterized by both oscillating and soliton properties (''oscillitons'') exist. Critical Mach numbers and critical propagation angles limit the size of the windows in which smooth solitons can be constructed.

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“…Expansion techniques permits to investigate the evolution and stability of the various solutions. Earlier attempts at a fully nonlinear stationary wave treatment include those of Adlam and Allen [1958], Sagdeev [1966] for the case of perpendicular propagation, and Karpman [1964] for the case of oblique propagation. Recently, McKenzie and Doyle [2001] developed a fully nonlinear theory for stationary waves propagating obliquely to the magnetic field in a cold plasma and found soliton solutions representing both compressions and rarefactions in the magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Solitons, oscillitons, and stationary waves in a warm p − α plasma

Dubinin¹

2003

J. Geophys. Res.

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[1] This paper generalizes the treatment by Dubinin et al. [2003] on solitons, oscillitons, and stationary waves in a two ion species (protons and alpha particles) cold magnetized plasma to include the effects of plasma thermal pressures. A fully nonlinear approach is used. For waves propagating transverse to the magnetic field the system of equations again reduces to a first-order differential equation which may be analyzed by the method of phase portraits and the necessary conditions for solitons and periodic waves found. Solutions exist in specific windows of the sonic and Alfvenic Mach numbers. The inclusion of pressure effects leads to the appearance of singularities or critical Mach numbers which lie on certain loci of the speeds of the species. For waves propagating obliquely to the magnetic field, another class of solutions appears, which we call oscillitons, since they exhibit solitary as well as oscillatory wave properties. ''Existence windows'' in parameter space (speed and propagation angle and ion and electron betas) in which solitons and oscillitons may be constructed are found from the dispersion equation for stationary waves. Possible applications of the results to different space plasma phenomena are discussed.

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The structure of strong collision-free hydromagnetic waves

Cited by 238 publications

References 3 publications

Cumulative displacement induced by a magnetosonic soliton bouncing in a bounded plasma slab

Cumulative displacement induced by a magnetosonic soliton bouncing in a bounded plasma slab

Solitons, oscillitons, and stationary waves in a cold p − α plasma

Solitons, oscillitons, and stationary waves in a warm p − α plasma

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