Magnetic Turbulence Spectra Research Articles

Jitter Radiation as an Alternative Mechanism for the Nonthermal X-Ray Emission of Cassiopeia A

Synchrotron radiation from relativistic electrons is usually invoked as responsible for the nonthermal emission observed in supernova remnants. Diffusive shock acceleration is the most popular mechanism to explain the process of particles acceleration and within its framework a crucial role is played by the turbulent magnetic field. However, the standard models commonly used to fit X-ray synchrotron emission do not take into account the effects of turbulence in the shape of the resulting photon spectra. An alternative mechanism that properly includes such effects is the jitter radiation, which provides for an additional power law beyond the classical synchrotron cutoff. We fitted a jitter spectral model to Chandra, NuSTAR, SWIFT/BAT, and INTEGRAL/ISGRI spectra of Cassiopeia A (Cas A) and found that it describes the X-ray soft-to-hard range better than any of the standard cutoff models. The jitter radiation allows us to measure the index of the magnetic turbulence spectrum ν B and the minimum scale of the turbulence across several regions of Cas A, with best-fit values ν B ∼ 2 − 2.4 and km.

Dispersive Fast Magnetosonic Waves and Shock‐Driven Compressible Turbulence in the Inner Heliosheath

AbstractThe solar wind in the inner heliosheath beyond the termination shock (TS) is a nonequilibrium collisionless plasma consisting of thermal solar wind ions, suprathermal pickup ions, and electrons. In such multi‐ion plasma, two fast magnetosonic wave modes exist, the low‐frequency fast mode and the high‐frequency fast mode. Both fast modes are dispersive on fluid and ion scales, which results in nonlinear dispersive shock waves. We present high‐resolution three‐fluid simulations of the TS and the inner heliosheath up to a few astronomical units (AU) downstream of the TS. We show that downstream propagating nonlinear fast magnetosonic waves grow until they steepen into shocklets, overturn, and start to propagate backward in the frame of the downstream propagating wave. The counterpropagating nonlinear waves result in 2‐D fast magnetosonic turbulence, which is driven by the ion‐ion hybrid resonance instability. Energy is transferred from small scales to large scales in the inverse cascade range, and enstrophy is transferred from large scales to small scales in the direct cascade range. We validate our three‐fluid simulations with in situ high‐resolution Voyager 2 magnetic field observations in the inner heliosheath. Our simulations reproduce the observed magnetic turbulence spectrum with a spectral slope of −5/3 in frequency domain. However, the fluid‐scale turbulence spectrum is not a Kolmogorov spectrum in wave number domain because Taylor's hypothesis breaks down in the inner heliosheath. The magnetic structure functions of the simulated and observed turbulence follow the Kolmogorov‐Kraichnan scaling, which implies self‐similarity.

Implication of kinetic Alfvén waves to magnetic field turbulence spectra: Earth’s magnetosheath

In the present paper, we investigate the power-law behaviour of the magnetic field spectra in the Earth’s magnetosheath region using Cluster spacecraft data under solar minimum condition. The power spectral density of the magnetic field data and spectral slopes at various frequencies are analysed. Propagation angle, $\theta_{kB}$ , and compressibility, $R_{\|}$ , are used to test the nature of turbulent fluctuations. The magnetic field spectra have the spectral slopes, $\alpha$ , between −1.5 to 0 down to spatial scales of $20\rho_{i}$ (where $\rho_{i}$ is ion gyroradius), and show clear evidence of a transition to steeper spectra for small scales with a second power-law, having $\alpha$ between −2.6 to −1.8. At low frequencies, $f_{sc} <0.3 f_{ci}$ (where $f_{ci}$ is ion gyro-frequency), $\theta_{kB}\sim 90^{ \circ} $ to the mean magnetic field, $B_{0}$ , and $R_{\|}$ shows a broad distribution, $0.1 \le R_{\|} \le 0.9$ . On the other hand at $f_{sc} >10 f_{ci}$ , $\theta_{kB}$ exhibits a broad range, $30^{ \circ} \le \theta_{kB} \le 90^{ \circ} $ , while $R_{\|}$ has a small variation: $0.2 \le R_{\|} \le 0.5$ . We conjecture that at high frequencies, the perpendicularly propagating Alfven waves could partly explain the statistical analysis of spectra. To support our prediction of kinetic Alfven wave dominated spectral slope behaviour at high frequency, we also present a theoretical model and simulate the magnetic field turbulence spectra due to nonlinear evolution of kinetic Alfven waves. The present study also shows the analogy between the observational and simulated spectra.

On the ion-inertial-range density-power spectra in solar wind turbulence

Abstract. A model-independent first-principle first-order investigation of the shape of turbulent density-power spectra in the ion-inertial range of the solar wind at 1 AU is presented. Demagnetised ions in the ion-inertial range of quasi-neutral plasmas respond to Kolmogorov (K) or Iroshnikov–Kraichnan (IK) inertial-range velocity–turbulence power spectra via the spectrum of the velocity–turbulence-related random-mean-square induction–electric field. Maintenance of electrical quasi-neutrality by the ions causes deformations in the power spectral density of the turbulent density fluctuations. Assuming inertial-range K (IK) spectra in solar wind velocity turbulence and referring to observations of density-power spectra suggest that the occasionally observed scale-limited bumps in the density-power spectrum may be traced back to the electric ion response. Magnetic power spectra react passively to the density spectrum by warranting pressure balance. This approach still neglects contribution of Hall currents and is restricted to the ion-inertial-range scale. While both density and magnetic turbulence spectra in the affected range of ion-inertial scales deviate from K or IK power law shapes, the velocity turbulence preserves its inertial-range shape in the process to which spectral advection turns out to be secondary but may become observable under special external conditions. One such case observed by WIND is analysed. We discuss various aspects of this effect, including the affected wave-number scale range, dependence on the angle between mean flow velocity and wave numbers, and, for a radially expanding solar wind flow, assuming adiabatic expansion at fast solar wind speeds and a Parker dependence of the solar wind magnetic field on radius, also the presumable limitations on the radial location of the turbulent source region.

Magnetic Turbulence Spectra and Intermittency in the Heliosheath and in the Local Interstellar Medium

Abstract The understanding of inertial-scale dynamics in the heliosheath is not yet thorough. Magnetic field fluctuations across the inner heliosheath (IHS) and the local interstellar medium (LISM) are here considered to provide accurate and highly resolved statistics over different plasma conditions between 88 and 136 au. By using the unique in situ 48 s measurements from the Voyager Interstellar Mission, we investigate different fluctuation regimes at the magnetohydrodynamic (MHD) scales, down to the MHD-to-kinetic transition. We focus on a range of scales exceeding five frequency decades (5 × 10−8 &lt; f &lt; 10−2 Hz), which is unprecedented in literature analysis. A set of magnetic field data for eight intervals in the IHS, in both unipolar and sector regions, and four intervals in the LISM is used for the analysis. Results are set forth in terms of the power spectral density, spectral compressibility, structure functions, and intermittency of magnetic field increments. In the heliosheath, we identify the energy-injection regime displaying a ∼1/f energy decay, and the inertial-cascade regime. Here, the power spectrum is anisotropic and dominated by compressive modes, with intermittency that can reach kurtosis values of up to 10. In the interstellar medium the structure of turbulence is anisotropic as well, with transverse fluctuations clearly prevailing after 2015 May. Here, we show that intermittent features occur only at scales smaller than 10−6 Hz.

Interplanetary Magnetic Field Turbulence and Rigidity Spectrum of the Galactic Cosmic Rays Intensity Variation (1969–2011)

AbstractThe present study investigates the relation between the rigidity R spectrum exponent γ of the galactic cosmic rays (GCR) flux changes (δD(R)/D(R) ∝ R−γ) and the exponents νy and νz of the power spectral density of the By and Bz components of the heliospheric magnetic field (HMF) fluctuations. Two parameters have been introduced: (1) the exponent γ demonstrating the rigidity dependence of long‐term changes of GCR flux on solar activity (SA) and (2) the exponents νy and νz signifying the state of turbulence which is divided of the By and Bz components. This study considers the period of time between 1969 and 2011 divided into four subperiods, according to the solar global magnetic field polarities: (I) 1969–1979, (A &gt; 0) (positive polarity magnetic field lines are directed away from the Sun's northern hemisphere); (II) 1980–1988, (A &lt; 0) (negative polarity magnetic field lines are directed toward the Sun's northern hemisphere); (III) 1991–2001, (A &gt; 0); and (IV) 2002–2011, (A &lt; 0). The paper finds that temporal changes of the resonant frequency (fres) of GCR protons in heliospheric magnetic field turbulence in relation to SA are mainly caused by variations of the induction of B components from year to year, while the contribution of the solar wind speed remains insignificant. The analyses of the four subperiods show that γ increases and νy and νz decrease in the periods of increased SA, and conversely, the γ decreases and νy and νz increase in the periods of reduced SA. The study concludes that the exponents γ, and νy and νz can be considered as important indices (proxies) for research on GCR transport in the heliosphere.

Inferring morphology and strength of magnetic fields from proton radiographs.

Proton radiography is an important diagnostic method for laser plasma experiments and is particularly important in the analysis of magnetized plasmas. The theory of radiographic image analysis has heretofore only permitted somewhat limited analysis of the radiographs of such plasmas. We furnish here a theory that remedies this deficiency. We show that to linear order in magnetic field gradients, proton radiographs are projection images of the MHD current along the proton trajectories. We demonstrate that in the linear regime (i.e., the small image contrast regime), the full structure of the projected perpendicular magnetic field can be reconstructed by solving a steady-state inhomogeneous 2-dimensional diffusion equation sourced by the radiograph fluence contrast data. We explore the validity of the scheme with increasing image contrast, as well as limitations of the inversion method due to the Poisson noise, discretization errors, radiograph edge effects, and obstruction by laser target structures. We also provide a separate analysis that is suited to the inference of isotropic-homogeneous magnetic turbulence spectra. Finally, we discuss extension of these results to the nonlinear regime (i.e., the order unity image contrast regime).

Nonlinear whistler wave model for lion roars in the Earth’s magnetosheath

In the present paper, we investigate the power-law behaviour of the magnetic field spectra in the Earths magnetosheath region using Cluster spacecraft data under solar minimum condition. The power spectral density of the magnetic field data and spectral slopes at various frequencies are analysed. Propagation angle and compressibility are used to test the nature of turbulent fluctuations. The magnetic field spectra have the spectral slopes between -1.5 to 0 down to spatial scales of 20 ion gyroradius and show clear evidence of a transition to steeper spectra for small scales with a second power-law, having slopes between -2.6 to -1.8. At low frequencies, f_sc<0.3f_ci(where f_ci is ion gyro-frequency), propagation angle approximately 90 degrees to the mean magnetic field, B_0, and compressibility shows a broad distribution, 0.1 < R > 0.9. On the other hand at f_sc>10f_ci, the propagation angle exhibits a broad range between 30-90 degree while 'R' has a small variation: 0.2 < R > 0.5. We conjecture that at high frequencies, the perpendicularly propagating Alfven waves could partly explain the statistical analysis of spectra. To support our prediction of kinetic Alfven wave-dominated spectral slope behaviour at high frequency, we also present a theoretical model and simulate the magnetic field turbulence spectra due to the nonlinear evolution of kinetic Alfven waves. The present study also shows the analogy between the observational and simulated spectra.

The connection of the interplanetary magnetic field turbulence and rigidity spectrum of Forbush decrease of the galactic cosmic ray intensity

We analyze the temporal changes in the rigidity spectrum of Forbush decrease (Fd) of the galactic cosmic ray (GCR) intensity observed in November 2004. We compute the rigidity spectrum in two energy ranges based on the daily data from the worldwide network of neutron monitors and Nagoya ground muon telescope. We demonstrate that the changes in the rigidity spectrum of Fd are linked to the evolution/decay of the interplanetary magnetic field (IMF) turbulence during various phases of the Fd. We analyze the time-evolution of the state of the turbulence of the IMF in various frequency ranges during the Fd. Performed analysis show that the decrease of the exponent ν of the Power Spectral Density (PSD ∝ f−ν, where f is frequency) of the IMF turbulence with decreasing frequency lead to the soft rigidity spectrum of Fd for GCR particles with relatively higher energies.

Empirical power law for magnetic turbulence spectra of an anisotropic plasma

Three-dimensional dynamic distributions of oscillations of the magnetic field over wave vectors k have been obtained from the plasma and magnetic measurements on four satellites in the Cluster experiment in a turbulent plasma in the outer Earth’s cusp and near it. The resulting k spectra exhibit strong inhomogeneous anisotropy. The dependences of the energy of magnetic oscillations on the wavenumber have been analyzed for 288 three-dimensional spectra in the wavelength interval covering the magnetohydrodynamic and ion scales. It has been shown that the energy density of magnetic fluctuations per unit volume in the wave vector space that is averaged over the total solid angle decreases in the wavelength interval from ∼2000 to ∼10 km with an increase in according to a power law with an exponent of α = -5.0 ± 0.3 for any magnitude and character of anisotropy.

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: II. Isotropic turbulence

AbstractThe random walk of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. An isotropic model is employed for the magnetic turbulence spectrum. An analytical investigation of the asymptotic behavior of the field-line mean-square displacement 〈(Δx)2〉 is carried out, in terms of the position variable z. It is shown that 〈(Δx)2〉 varies as ~z ln z for large distance z. This result corresponds to a superdiffusive behavior of field line wandering. This investigation complements previous work, which relied on a two-component model for the turbulence spectrum. Contrary to that model, quasilinear theory appears to provide an adequate description of the field-line random walk for isotropic turbulence.

Magnetic turbulence in cool cores of galaxy clusters

We argue that the recently reported Kolmogorov-like magnetic turbulence spectrum in the cool core of the Hydra A galaxy cluster can be understood by kinetic energy injection by active galaxies that drives a turbulent non-helical magnetic dynamo into its saturated state. Although dramatic differences exist between small-scale dynamo scenarios, their saturated state is expected to be similar, as we show for three scenarios: the flux rope dynamo, the fluctuation dynamo, and the explosive dynamo. Based on those scenarios, we develop an analytical model of the hydrodynamic and magnetic turbulence in cool cores. The model implies magnetic field strengths that fit well with Faraday rotation measurements and minimum energy estimates for the sample of cool core clusters having such data available. Predictions for magnetic fields in clusters for which the appropriate observational information is still missing, and for yet unobserved quantities like the hydrodynamical turbulence velocity and characteristic length-scale are provided. The underlying dynamo models suggest magnetic intermittency and possibly a large-scale hydrodynamic viscosity. We conclude that the success of the model to explain the field strength in cool core clusters indicates that in general cluster magnetic fields directly reflect hydrodynamical turbulence, also in clusters without cool cores.

Pickup protons and water ions at comet Halley: Comparisons with Giotto observations

A quasi‐linear diffusion model including both pitch angle and energy diffusion, adiabatic compression and convective motion with the solar wind flow has been used to investigate the cometary ion pickup process along the Sun‐comet line at comet Halley. The total pickup ion densities and magnetic turbulence spectrum levels observed by Giotto were used to constrain the quasi‐linear model. Comparisons of the model results were made with energetic ion distributions observed by instruments onboard the Giotto spacecraft. The observed power spectrum index of magnetic turbulence γ is about 2–2.5. However, our simulation shows that when γ was 2, the calculated proton distributions were much more isotropic than the observed ones; hence we have chosen γ = 2.5 in our study. Furthermore, we assumed that only about 5% of the total low frequency wave power propagates away from the comet. The numerical solutions of the quasi‐linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock (but upstream), which agrees with the observations. The calculated and observed proton distributions are somewhat more isotropic than the water group ion distributions in the region far upstream of the shock, but the opposite is true near the bow shock. We find that given the observed turbulence level, quasi‐linear theory gives pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.

The interplanetary scattering mean free path - Collisionless wave-damping effects

The role of dissipation in the scattering of charged particles in the interplanetary medium (IPM) is analyzed to obtain a model for the interplanetary magnetic turbulence spectrum that yields particle free paths (PEP) which agree with observational data. The scattering processes are attributed to waves with small wavelengths intersected by particles with zero pitch angles. The waves, being strongly damped by collisionless cyclotron damping in the ambient thermal plasma, produce reduced scattering and longer MFPs. The model, which includes the damping factor, was used to generate proton propagation maps at kinetic energy levels of under, over, and within the 5 MeV-2 GeV range. The results, when compared with observational data, displayed good agreement. The same held true for the MFP propagation of energetic electrons.