Collision-free Hydromagnetic Disturbances of Large Amplitude in a Plasma

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

doi:10.1088/0370-1328/75/5/302

Cited by 25 publications

(20 citation statements)

References 3 publications

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“…Later, extensive work was done to examine the properties of this mode; see, e.g., Refs. [4][5][6][7][8]. Some of these works incorporated the effect of electron-ion collisions, so a compressional dispersive Alfvén (CDA) wave exists.…”

Section: Introductionmentioning

confidence: 99%

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

2012

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It is shown that the dynamics of amplitude-modulated compressional dispersive Alfvénic (CDA) waves in a collisional megnetoplasma is governed by a complex Ginzburg-Landau (CGL) equation. The nonlinear dispersion relation for the modulational instability of the CDA waves is derived and investigated numerically. It is found that the growth rate of the modulational instability decreases (increases) with the increase of the normalized electron-ion collision frequency α (the plasma β). The modulational instability criterion for the CGL equation is defined precisely and investigated numerically. The region of the modulational instability becomes narrower with the increase of α and β, indicating that the system dissipates the wave energy by collisions, and a stable CDA wave envelope packet in the form of a hole will be a dominant localized pulse. For a collisionless plasma, i.e., α=0, the CGL equation reduces to the standard nonlinear Schrödinger (NLS) equation. The latter is used to investigate the modulational (in)stability region for the CDA waves in a collisionless magnetoplasma. It is shown that, within unstable regions, a random set of nonlinearly interacting CDA perturbations leads to the formation of CDA rogue waves. In order to demonstrate that the characteristics of the CDA rogue waves are influenced by the plasma β, the relevant numerical analysis of the appropriate nonlinear solution of the NLS equation is presented. The application of our investigation to space and laboratory magnetoplasmas is discussed.

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Section: Introductionmentioning

confidence: 99%

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

2012

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“…The quantity α is the Alfvén Mach number and the analytical solution is valid for 1 < α < 2. In a second paper [9] we considered the experiment shown in figure 7, where a plasma containing a magnetic field is compressed by a stronger field. Numerical work in this case showed the generation of a series of "solitary waves", as depicted in figure 8.…”

Section: Research At Harwellmentioning

confidence: 99%

“…Schematic diagram of an experiment for the compression of a plasma by a magnetic field which is parallel to the internal magnetic field [9].…”

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Some Researches in Plasma Physics

Allen¹

2004

Contrib. Plasma Phys.

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“…In analogous nonstationary flows, electron acceleration is more straightforward. Numerical solutions of nonstationary hydromagnetic problems (Cauchy's problem, 1 the given regime on the boundary 16 ) have shown nonlinear steepening of the sinusoidal wave to result in soliton formation. The results of these computations 1 ' 16 are confirmed by experiments in laboratory plasmas.…”

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Origin of Radiation Belts

Gintzburg¹

1966

Phys. Rev. Lett.

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We shall discuss acceleration of solar plasma electrons to energies of 30-100 keV by nonlinear waves (called "solitons" 1 )-the mechanism already used 2 " 4 to explain the acceleration of soft electrons of E ~ 1 keV.Solitons were discovered in the transition region between the magnetosphere and the interplanetary medium in Pioneer-I magnetic measurements. 5 The theory shows that with decreasing angle 6 between the undisturbed magnetic field H 0 and soliton velocity u 0 , the amplitude #+ of the magnetic field pulse and the maximum energy of its electrons E^ e ~mv L -\ 2 /2 increase 6 ? 3 : cos0/MY /2 >~~ COS0/M\ 1/2 TTl^ >9tt>^b ) > H *= H^-> rn/Hence to the electrons is imparted not the energy of the undisturbed magnetic field H 0 , but that of the field H 0 (M/m) 1/2 (at 0 = 0) enhanced within the soliton, H-\ 2 being three orders of magnitude higher than H 2 .Let us call the solitons running along the undisturbed magnetic field (6 = 0) parallel solitons. This solution of hydromagnetic equations was obtained by Saffman 7 and Tverskoi. 8 Experimental evidence gained in the last years allows us to consider now the hypothesis that 30-to 100-keV electrons are accelerated in parallel solitons and corresponding nonstationary pro-~ m-3 cesses.The relations (1) give (for 0 = 0) the required electron energy range. From Fig. 46 of Ness et al., 9 just before electron flux spikes H Q = 10-20 y. If ^ = 5 cm"" 3 then E^ e = 45 keV at H 0 = 10 y and E^e = 180 keV at H 0 = 20 y.But there remain two more soliton properties to be checked: the high field H^ and ion energy E-f i = E^ £>30 keV. In geostationary (3H ~7) solitons observed on Pioneer I, H^< 100 y, so we interpreted them 3 as oblique ones with 6 = 70-80°. The parallel solitons, having WL= 20-30, cannot be geostationary; they move relative to earth with the velocity 10 8 cm/sec and pass the device within a time of C/U)Q e u o~ 10" sec. The amplifier of the Pioneer-I magnetometer could not record such rapid flux variations. They could be observed by means of a simple induction coil and a broad pass-band amplifier. The 100-keV protons were detected on Explorer-12. 10 But the instrument limitations did not permit observation of real soliton pulses (because, e.g., of too high an energy range, small acceptance angle, time resolution limitations, etc.). The ion pulse flux is always much lower than the electronic one, due to lower ion velocity.The parallel alignment of plasma flow and the magnetic field H 0 can also occur in several cases: (1) On the day side-during systematic field reversals when passing from some solar magnetic field sector 11 to the next one.(2) During spontaneous interplanetary field 327

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Collision-free Hydromagnetic Disturbances of Large Amplitude in a Plasma

Cited by 25 publications

References 3 publications

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

Amplitude modulation of hydromagnetic waves and associated rogue waves in magnetoplasmas

Some Researches in Plasma Physics

Origin of Radiation Belts

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