Ion streaming instabilities with application to collisionless shock wave structure

Golden, Kenneth I.; Linson, Lewis M.; Mani, S. A.

doi:10.1063/1.1694299

Cited by 32 publications

(9 citation statements)

References 12 publications

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“…The scaling of the wavelength at maximum growth as a function of Mach number (beam speed) should also be observable upstream and downstream of the shock. If spatial amplification is important, then the group-standing condition will be important [Golden et al, 1973]. In later sections the predictions obtained here will be shown to be in good agreement with the results of one-dimensional hybrid simulations.…”

Section: Instabilitiessupporting

confidence: 69%

“…Thus Parker proved that a long precursor is an expected result of an electromagnetic shock that evaporates a small fraction of ions off the region of strong disorder. Golden et al [1973] pursued the hypothesis of parallel shock dissipation generated by electromagnetic ion beamdriven modes. They assumed that an ion cyclotron resonant instability dominated the shock structure, in contrast to Parker's nonconvective fluid hose instability.…”

Section: Piibeam = Z M•n•u• 2 (2)mentioning

confidence: 99%

“…The long-wavelength modes should dominate in an unbounded system or in one where unstable group-standing solutions are not possible. Cipolla et al [1977] extended the cold beam analysis of Golden et al [1973] by including ion kinetic effects owing to the downstream heated plasma. They showed that unstable group-standing modes can be found for Alfv6n Mach numbers as low as 2.8.…”

Section: Piibeam = Z M•n•u• 2 (2)mentioning

confidence: 99%

“…In the Golden et al [1973] model the relative streaming speed of the two beams is defined as the difference in the flow speeds upstream and downstream from the shock. It follows that the relative speed is less than the shock speed and that the shock ramp must be broad enough that the waves have space to grow.…”

Section: Piibeam = Z M•n•u• 2 (2)mentioning

confidence: 99%

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Theory and simulation of collisionless parallel shocks

Quest¹

1988

J. Geophys. Res.

187

111

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A one‐dimensional theory of shocks propagating parallel to the ambient magnetic field in a collisionless plasma is presented. We show that shock formation and plasma heating can result from parallel propagating electromagnetic ion beam‐driven instabilities for a wide range of Mach numbers and upstream plasma conditions. The plasma upstream from a parallel shock overtakes the slower, downstream plasma in the absence of any electrostatic or electromagnetic wave fields. An interface region is created that is unstable to electromagnetic ion beam‐driven growth. The waves grow until they can scatter and couple the upstream and downstream plasma populations and can provide the necessary entropy increase for the shock. The marginal firehose state is reached downstream from the shock if the Alfvén Mach number MA is high enough (MA ≡ Uu/CA, where Uu is the upstream shock velocity and CA is the upstream Alfvén speed). A one‐dimensional compression of the ions along the magnetic field line direction results for weaker shocks. We solve a set of jump conditions and show that the marginal firehose state is first reached at a small magnetosonic Mach number (less than 2). We derive various conditions for creating and maintaining the shock via the ion beam‐driven instability and show that these conditions are roughly equal. The results from many one‐dimensional hybrid simulation runs are compared with the predictions of the theory and are shown to be in good agreement. At low Mach numbers, resonant group‐standing waves are the most strongly amplified and scatter the ions over several wavelengths. The transition in the ion pressure tensor is smooth, going from an isotropic upstream state to an anisotropic firehose state downstream in several wavelengths. The ions are compressed in one dimension at small Mach numbers, and there is little change in the perpendicular ion temperature across the shock. At high Mach numbers a small fraction of the upstream ions are backscattered by large‐amplitude magnetic waves at the shock front. The backscattered ions resonantly generate waves in the foreshock region, which are then convected downstream and are strongly compressed and amplified at the shock front. The bulk of the ion population passes through the shock and is nonresonantly scattered and heated by the amplified downstream waves. The change in the pressure tensor across the shock is abrupt; most of the entropy increase occurs within one or two wavelengths beyond where the waves are compressed and amplified. We compare the theoretical predictions with recently published observations of quasi‐parallel interplanetary shocks and the Earth's quasi‐parallel bow shock and find good agreement. Some theoretical limits on the fraction of ions that can be scattered back upstream are derived, and the implications for cosmic ray injection, particle acceleration, and astrophysical shocks are discussed.

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Section: Instabilitiessupporting

confidence: 69%

Section: Piibeam = Z M•n•u• 2 (2)mentioning

confidence: 99%

Section: Piibeam = Z M•n•u• 2 (2)mentioning

confidence: 99%

Section: Piibeam = Z M•n•u• 2 (2)mentioning

confidence: 99%

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Theory and simulation of collisionless parallel shocks

Quest¹

1988

J. Geophys. Res.

187

111

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“…A second instability mechanism is the cyclotron resonant mode, known as the resonant electromagnetic ion beam instability. Golden et al [1973] discussed the excitation of this mode, considering the interaction of the upstream and downstream states related by a Mott-Smith distribution in which the local parameters vary linearly from one state to the other. They showed from linear theory that resonant modes in a certain region of the transition can group stand in the flow and hence grow to large amplitudes over a short distance.…”

Section: Introductionmentioning

confidence: 99%

Re‐forming supercritical quasi‐parallel shocks: 2. Mechanism for wave generation and front re‐formation

Winske¹,

Omidi²,

Quest³

et al. 1990

J. Geophys. Res.

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One‐dimensional hybrid (particle ion, massless fluid electron) simulations of quasi‐parallel shocks and two stream interactions are carried out in order to study the mechanism by which large‐amplitude electromagnetic waves are generated at the shock and maintained in a quasi‐steady manner. It is concluded that a resonant interaction at the interface between the incoming ions and the heated downstream ions (“interface instability”) is the most likely source of the waves that ultimately comprise the quasi‐parallel shock. The effect of the generation of these waves at the shock transition results locally in a nonsteady shock ramp, which propagates downstream with respect to the average shock position and is then replaced by a new steepened ramp at the original front position. This process is complicated by several competing effects. First, backstreaming ions excite the beam cyclotron resonant instability at wavelengths longer than those generated at the shock interface which gives rise to compressive upstream perturbations that are then carried into the shock and interact with the shock‐generated waves. Second, the re‐formation process sometimes leads to the appearance of cold dense ion beams just upstream from the shock which gyrate in the upstream magnetic field to produce local density enhancements that have some effect on where the new shock front forms. Third, whistlers at wavelengths shorter than the waves associated with the re‐formation process are also present that can scatter the backstreaming ions into a hotter, more diffuse population. In order to separate these various processes, numerical experiments involving quasi‐parallel shocks and the interaction of two plasma streams have been carried out for various upstream parameters. In these studies the upstream conditions can be controlled to some extent by eliminating the backstreaming ions and suppressing the shorter wavelength modes, and in the case of the two stream interactions the upstream and downstream plasmas can also be distinguished. The interface instability that results from the interaction of the incident ion stream and a less dense population of heated downstream ions generates intermediate scale (kc/ωi ∼ 1) magnetosonic waves with group velocities pointing upstream, but phase fronts carried downstream, consistent with the waves observed in the shock simulations. A linear analysis indicates the wave numbers of the most unstable modes decrease with increasing upstream θBn and Mach number, in agreement with the simulations. Areas where further work is needed are also discussed.

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Microphysics of Quasi-parallel Shocks in Collisionless Plasmas

Burgess

Scholer

2013

Microphysics of Cosmic Plasmas

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Ion streaming instabilities with application to collisionless shock wave structure

Cited by 32 publications

References 12 publications

Theory and simulation of collisionless parallel shocks

Theory and simulation of collisionless parallel shocks

Re‐forming supercritical quasi‐parallel shocks: 2. Mechanism for wave generation and front re‐formation

Microphysics of Quasi-parallel Shocks in Collisionless Plasmas

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