Hydromagnetic Turbulence Research Articles

Low-frequency plasma turbulence during solar wind-comet interaction

The pick up cometary ion distributions are shown to excite Alfvenic mode instabilities, slow ion-acoustic mode instability and a lower hybrid instability during solar wind-comet interaction. The growth rates of all these instabilities become larger as the comet is approached. The lower hybrid instability is shown to account for the low-frequency 0–300 Hz electrostatic turbulence observed near comet Halley. The Alfven modes can grow to large amplitudes and become modulationally unstable, in the presence of low-frequency density fluctuations, going over to envelope Alfven solitons. A model consisting of a gas of Alfven solitons is suggested to explain the hydromagnetic turbulence observed near comet Halley and comet Giacobini-Zinner.

Nonlinear propagation of Alfv�n waves in cometary plasmas

Large-amplitude Alfven waves propagating along the guide magnetic field in a three-component plasma are shown to be spatially localized due to their nonlinear interaction with nonresonant electrostatic density fluctuations. A new class of subsonic Alfven soliton solutions are found to exist in the three-component plasma. The Alfven solitons can be relevant in explaining the properties of hydromagnetic turbulence near the comets.

Hydromagnetic waves and instabilities associated with cometary ion pickup: ICE observations

The hydromagnetic turbulence surrounding comet Giacobini‐Zinner is characterized by two dominent components: large amplitude, linearly polarized waves with periods near 10² s and circularly polarized wave packets with periods near 3 s. The latter appear in association with variations in field magnitude produced by the long period waves. A third, commonly observed feature is identified, consisting of a partial rotation of the magnetic field (a hook‐like structure) which also appears to be triggered by the long period waves. The possibility that the long period waves are generated by the pickup of freshly ionized cometary neutrals has been investigated. A resonant instability identified by Wu and Davidson (1972) appears able to account for the long period waves in terms of the pickup of cometary ions of the water group. Application of the theory also indicates that the growth rate of proton cyclotron waves, as a consequence of hydrogen ion pickup, is somewhat lower, due to both higher neutral velocities and longer ionization times. Several significant features of the wave packets and hooks are presently unexplained and will require further study.

Strong hydromagnetic turbulence associated with comet Giacobini‐Zinner

The turbulence surrounding comet Giacobini‐Zinner reached intensities three orders of magnitudes above that of “intermediate” solar wind conditions, was characterized by Δ B/Bo almost equal to one, and extended to cometocentric distances beyond 106 km. The strong spectral peak at f ∼ 10−2 Hz and the general intensity profile of the turbulence (a lack of emissions close to the nucleus [< 2.5 × 104 km], peak intensities near the bow wave, and a spatial extend > 106 km) are in excellent agreement with generation by plasma instabilities associated with the pickup of H2O+ group ions.The total energy of the magnetic turbulence near f ∼ 10−2 Hz is estimated to be ∼ 5 × 1015 joules and that of ion energization due to solar wind pickup ∼6 × 1013 watts. It thus takes a minimum of ∼ 100 s to build up the magnetic turbulence. This scale is approximately the linear growth rate of the ion pickup instability, giving a consistent picture of the energy source of the turbulence.

Comet‐solar wind interaction: Dynamical length scales and models

While the ICE magnetometer measurements at Comet Giacobini‐Zinner led to a number of unexpected discoveries such as the intense hydromagnetic turbulence, the large‐scale structure of the induced cometary magnetosphere that it delineated was close to theoretical predictions. While the strong draping of the magnetic field lines to form a magnetotail was anticipated, the structure of this magnetotail also indicated the existence of other predicted features. These included a weak shock or compression wave, an ionopause which at least partially impeded the penetration of the solar wind into the cometary ionosphere, and a magnetic barrier region where the magnetic field was piled up ahead of the ionopause. The inferred positions of these features enabled the estimation of the production rate of the neutrals from the nucleus (≈ 4×1028 mols/sec), as well as the strength of the coupling between the inflowing solar wind ions and the outflowing cometary neutrals.

Shock formation time and the viability of prompt MeV proton shock acceleration in solar flares

A critical analysis is made of a proposed mechanism to explain the ≲2‐ to 100‐s delays observed in some flares between γ rays due to several MeV protons and hard X rays due to ∼100‐keV electrons. The proposed mechanism is first‐order Fermi acceleration of protons bouncing between two shocks formed by the electrons causing the hard X rays. For the maximum possible flux for stable beam propagation the shock formation time is found to be ≳2 s and the shock velocity ≲1800 km s−1. The mechanism as proposed produces protons which gain only ∼3 MeV before they are transmitted through the shocks. The mechanism will work with additional pitch angle scattering, which also raises the possibility of multiple encounters with a single shock, a case not analyzed. For this reason the final energy gains of the proposed mechanism may be altered. The times during which this type of shock acceleration could be important and thus the range of observed delays which could be explained are given for a range of loop lengths and injected electron spectra. Alternate possibilities such as stochastic acceleration by hydromagnetic turbulence must be invoked to explain the shortest delays associated with this prompt proton acceleration.

The evolution of supernova remnants as radio sources

The acceleration of relativistic electrons by hydromagnetic turbulence in shell-type supernova remnants (SNRs) is examined within the framework of previous studies of their structural evolution through interaction with the interstellar medium. The predicted evolution of the synchrotron radio emission by the electrons is in agreement with a wide variety of observations.

Statistical theory of the decay-process of weak homogeneous hydromagnetic turbulence

A statistical model for the spectral analysis of one dimensional hydromagnetic turbulence is presented for the purpose of gaining insight into the nonlinear relaxation in the decay-process. The random fluctuations of velocity and magnetic fields have been considered on the basis of wavenumbers in Fourier-space together with linearized mode approximation. Finally, with the aid of Bogoliubov expansion method, the dynamical equations for the decay of kinetic and magnetic energy have been derived for weak homogeneous hydromagnetic turbulence.

Prompt acceleration of ? 30 MeV per nucleon ions in solar flares

Observation of prompt γ-rays in solar flares requires that ions be accelerated to >30 MeV nucl-1 in ≲ 2 s. A model for prompt acceleration is developed. The energy release is assumed to occur in a flaring loop with the energy release region being ≲ 104 km in dimensions and with an Alfven speed υ A ≃ 3 × 103 km s-1. The acceleration is assumed to occur in two steps. The second-step acceleration from ≃ ɛ T = 1/2m p υA 2 nucl-1 to ≳ 30 MeV nucl-1 is attributed to stochastic acceleration by hydromagnetic turbulence which is found to be fast enough under conditions which are not extreme. Main emphasis is placed on the first step, called preacceleration, to ɛ T ≃ 100 keV nucl-1. Preacceleration mechanisms which involve accelerating a small fraction of ions from the tail of a Maxwellian distribution are unacceptable because they would lead to enormous abundance anomalies. Preacceleration is attributed either to localized heating of ions to ≃ 109 K or to acceleration by potential electric fields. The latter mechanism is favoured and some theoretical ideas are outlined based on observations of reconnection in the Earth's magnetotail. Whether energetic ions are prompt, delayed or unobservable depends only on the rate at which the stochastic acceleration proceeds. The second-step acceleration of electrons, invoked to account for a harder microwave component, is predicted to be slower by a factor ≃ 3 than for ≃ 30 MeV nucl-1 ions.

Hydromagnetic turbulence, shock waves and particle acceleration in supernova remnants

A number of mechanisms for generation of the small-scale hydromagnetic turbulence in Supernova remnants is investigated. It is shown that the mechanisms of particle acceleration on the shock waves and on the large-scale turbulence face considerable difficulties.

The Evolution of Supernova Remnants as Radio Sources

The acceleration of relativistic electrons by hydromagnetic turbulence in shell-type supernova remnants (SNRs) is examined within the framework of previous studies of their structural evolution through interaction with the interstellar medium. The predicted evolution of the synchrotron radio emission by the electrons is in agreement with a wide variety of observations.

Radial evolution of power spectra of interplanetary Alfvénic turbulence

The radial evolution of the power spectra of the MHD turbulence within the trailing edge of high‐speed streams in the solar wind has been investigated with the magnetic field data of HELIOS 1 and 2 for heliocentric distances between 0.3 and 0.9 AU. In the analyzed frequency range 2.8 · 10−4 ‐ 8.3 · 10−2 Hz the computed spectra have, near the earth, values of the spectral index close to that predicted for an incompressible hydromagnetic turbulence in a stationary state. Approaching the sun, the spectral slope remains unchanged for frequencies f ≳ 10−2 Hz, whereas at lower frequencies we find a clear evolution toward a less steep falloff with frequency. The radial gradient of the power in Alfvénic fluctuations depends on frequency and it increases upon increasing frequency. For frequencies f ≳ 10−2 Hz, however, the radial gradient remains approximately the same. A discussion of possible theoretical implications of the observational features pointed out is given.

Acceleration of relativistic charged particles by supersonic hydromagnetic turbulence

The acceleration of relativistic particles is considered during their intersection with hydromagnetic shock fronts in the presence of randomly distributed large-scale magnetic fields. In a series of astronomical objects, the Larmor radius of the relativistic particles exceeds the width of the shock front. In this case there is a change in the adiabatic invariant which results in an increase in the energy of the particle when it crosses the front in any direction. We have proved that the adiabatic part of the energy change will be partially or completely compensated by its reverse change in the weaker regions of the magnetic field. The acceleration mechanism considered is found to be more effective than the Fermi mechanism.

Hydromagnetic waves in high Beta plasmas

We have determined the wave propagation and damping properties in a collisionless thermal plasma for which ..beta.., the ratio of the plasma pressure to the magnetic pressure, is much greater than unity. We achieve this by solving the full collisionless dispersion relation as an expansion in 1/..beta... To do this we develop a set of iteration methods which converge to this solution. We illustrate these results with two applications, the trapping of cosmic rays in supernovae remnants and the collisionless damping of hydromagnetic turbulence.

An Application of Karman’s Energy Transfer Process in Hydromagnetic Turbulence

Abstract A modified version of Chandrasekhar’s equation is derived with the aid of Karman’s energy transfer process for the decay of hydromagnetic turbulence in the limiting case of zero viscosity and infinite electrical conductivity. It is found that the asymptotic behaviour of self-preserving solutions of the aforesaid equations leads to F(k, t)≈k4 , (c = 2/7), G(k, t)≈k6 , (c = 2/9) as k→0 and F(k,t)≈k-5/3 ,G(k,t)≈k-5/3 for k→∞.

Plasma irregularities in the comet's tail

Scintillation theory is invoked to explain fluctuations in radio intensity observed during occultation of the extragalactic radio source PKS 2025-15 by the plasma tail of comet 1973 XII on Jan. 5, 1975. Plasma irregularities and turbulence in the tail of the comet (Kohoutek 1973f) are fitted to a Gaussian spectrum and to a Kolmogorov power-law spectrum in analyzing the scintillation data. The rms fluctuation of electron density in the cometary tail is reported at 80 electrons per cu mm, the inner scale of the fluctuation at 800 km, and the largest scale of fluctuation at possibly 400,000 km. A hump in the comet power-law spectrum is noted. Use of the power spectrum of electron density fluctuations to predict the power spectrum of magnetic field fluctuations for irregularities associated with hydromagnetic turbulence is recommended.

Can Precession Power the Geomagnetic Dynamo?

The power requirement of a stationary geomagnetic dynamo driven by some agency external to the core (e. g. precession) is equal to the ohmic dissipation in the core, Q1. For a dynamo in which differential rotation is important we show that Q1ασ1−2, where σ1≃ 5 × 105 ohm−1 m−1 is the electrical conductivity of the core. Estimates of Q1 for kinematic dynamo models range from 109 to over 1012 Watts, depending on the particular regenerative scheme characterizing the dynamo. Precessional power input to the magnetic field can be estimated in terms of the electromagnetic part of the core-mantle coupling and the tiltover angle (inclination of the core angular momentum vector to that of the mantle). We correct Stacey's estimate of core-mantle coupling to take into account the diurnal frequency of precession-induced flow relative to the mantle, and show that the power available from precession to stir the core cannot exceed 108 W if the core flow remains stable. As a caution against the widespread uncritical acceptance of Malkus’ claims to have demonstrated the energetic adequacy of precession-driven hydromagnetic turbulence, we enumerate the mathematical and physical errors which cast doubt on his theoretical arguments.

Low-frequency fluctuations in the solar wind. I - Theory

Several simple relationships between the power spectra of density and velocity fluctuations and the power spectrum of magnetic field fluctuations are derived within the context of plasma kinetic theory. The theory is restricted to the low-frequency regime (less than the proton cyclotron frequency) where hydromagnetic turbulence is expected to play the most important role. The affects of Alfven and magnetosonic waves upon the plasma fluctuations are discussed separately. The results are then applied to proton fluctuations in the solar wind, demonstrating a connection between plasma and field fluctuations.

Resonant scattering of particles and second phase acceleration in the solar corona

Effective acceleration of particles by hydromagnetic turbulence requires that the particles be scattered at a rate ν comparable with the frequency ω of the turbulence. The only effective scattering process is due to resonant wave-particle interactions. The resonant waves are HM waves for ions with β≫βA(βc = particle speed, βAc = Alfven speed) and for electrons with γβ ⩾ 43β0(β0 ≈ 43βA), and are whistlers for electrons with β0 ≪ γβ≲ 43β0. The resonant waves can be generated by an anisotropic distribution of particles provided that the anisotropy factor A exceeds a threshold anisotropy A0 ≈ βA/β for HM waves and A0 ≈ β02/β2γ for whistlers. Turbulence with relative magnetic amplitude ɛ causes acceleration at a rate {ie0353-02} provided the following conditions are satisfied: (a) β ≫ βA for ions, β ≫ β0 for electrons; (b) ɛ ≫ A0; (c) n1/ne≲ω/gWi or n1/ne ≫(ω/Ωi) (γβ/43β0)2 for scattering by HM waves or whistlers respectively (n1 = number density of accelerated particles, Ωi = ion gyrofrequency).

On the evolution of turbulent magnetic fields in a collision dominated plasma

In a weakly ionized plasma, in which collisions with the neutral background control the velocity fields of the ions and electrons against pressure gradients and the Lorentz force, it is demonstrated that: (1) The energy density in the turbulent magnetic field declines as time progresses. (2) The rate of decline depends on the amount of 'helicity' present in the turbulent magnetic field. (3) The 'helicity' must either be zero or must take on one of its two possible equipartition values, which are equal and opposite. (4) The effect of helicity is to increase the rate of decay of the long wavelength modes of the turbulent field over the decay rate obtained in its absence. This calculation was done both to illustrate the way in which the non-linear interaction of fluid velocities and magnetic fields influences the temporal evolution of the turbulent magnetic field, and as a directional guide which may, perhaps, eventually indicate a self-consistent method of handling the problem of hydromagnetic turbulence in conducting fluids.