Stochastic aspects of magnetic lines of force with application to cosmic-ray propagation.
Stochastic and ergodic aspects of magnetic lines of force, discussing cosmic ray diffusion in interplanetary magnetic field
Jokipii, J. R.↗
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Soliton and strong Langmuir turbulence in solar flare processes
The occurrence of modulational instability in the current sheet of a solar flare is investigated. Special attention is given to the plasma microinstability in this sheet and its relation to the flare process. It is found that solitons or strong Langmuir turbulence are likely to occur in the diffusion region under solar flare conditions in which the electric resistivity could be enhanced by several orders of magnitude in the region, resulting in significant heating and stochastic acceleration of particles. A numerical example is used to demonstrate the transition of the magnetic field velocity and plasma density from the outer MHD region into the diffusive region and then back out again with the completion of the energy conversion process. This is all made possible by an increase in resistivity of four to five orders of magnitude over the classical value.
Song, M. T.↗
Ion acceleration in impulsive solar flares
Nonrelativistic spectra of protons and ions accelerated in impulsive solar flares are derived using more realistic turbulence power spectra. The calculation is based on a particle transport equation extracted from a second step acceleration model containing stochastic acceleration. The turbulence model is generalized to waves with a small angle to the magnetic field vector and to turbulence power spectra with spectral indices s smaller than 2. Due to the occurrence of impulsive flares at low coronal heights, Coulomb losses at the dense coronal plasma and diffusive particle escape are taken into account. The ion spectra show deviations from long-duration spectra near the Coulomb barrier, where the losses become maximal. The Z-squared/A-dependence of the Coulomb losses leads to spectral variations for different ions. We present a method to estimate the turbulence parameters and injection conditions of the flare particles using ion ratios like Fe/O of impulsive flares.
Steinacker, Jurgen↗
First Test of Stochastic Growth Theory for Langmuir Waves in Earth's Foreshock
This paper presents the first test of whether stochastic growth theory (SGT) can explain the detailed characteristics of Langmuir-like waves in Earth's foreshock. A period with unusually constant solar wind magnetic field is analyzed. The observed distributions P(logE) of wave fields E for two intervals with relatively constant spacecraft location (DIFF) are shown to agree well with the fundamental prediction of SGT, that P(logE) is Gaussian in log E. This stochastic growth can be accounted for semi-quantitatively in terms of standard foreshock beam parameters and a model developed for interplanetary type III bursts. Averaged over the entire period with large variations in DIFF, the P(logE) distribution is a power-law with index approximately -1; this is interpreted in terms of convolution of intrinsic, spatially varying P(logE) distributions with a probability function describing ISEE's residence time at a given DIFF. Wave data from this interval thus provide good observational evidence that SGT can sometimes explain the clumping, burstiness, persistence, and highly variable fields of the foreshock Langmuir-like waves.
Cairns, Iver H.↗
Observations of large transient magnetospheric electric fields
Transient electric field events were observed with the long, double probe instrumentation carried by the IMP-6 satellite. Nine, clearly defined, exceptionally large amplitude events are presented here. The events are observed in the midnight sector at geocentric distances 3.5 to .5.5 R sub e at middle latitudes within a magnetic L-shell range of 4.8 to 7.5. They usually have a total duration of one to several minutes, with peak power spectra amplitudes occurring at a frequency of about 0.3 Hz. The events occur under magnetically disturbed conditions, and in most cases they can be associated with negative dH/dt excursions at magnetic observatories located near the foot of the magnetic field line intersecting IMP-6. The magnetospheric motions calculated for these electric fields indicated a quasi-stochastical diffusive process rather than the general inward magnetospheric collapsing motion expected during the expansive phases of auroral substorm activity.
Aggson, T. L.↗
The Mechanism for the Energy Buildup Driving Solar Eruptive Events
The underlying origin of solar eruptive events (SEEs), ranging from giant coronal mass ejections to small coronalhole jets, is that the lowest-lying magnetic flux in the Sun's corona undergoes continual buildup of stress and free energy. This magnetic stress has long been observed as the phenomenon of "filament channels:" strongly sheared magnetic field localized around photospheric polarity inversion lines. However, the mechanism for the stress buildup-formation of filament channels-is still debated. We present magnetohydrodynamic simulations of a coronal volume that is driven by transient, cellular boundary flows designed to model the processes by which the photosphere drives the corona. The key feature of our simulations is that they accurately preserve magnetic helicity, the topological quantity that is conserved even in the presence of ubiquitous magnetic reconnection. Although small-scale random stress is injected everywhere at the photosphere, driving stochastic reconnection throughout the corona, the net result of the magnetic evolution is a coherent shearing of the lowest-lying field lines. This highly counterintuitive result-magnetic stress builds up locally rather than spreading out to attain a minimum energy state-explains the formation of filament channels and is the fundamental mechanism underlying SEEs. Furthermore, this process is likely to be relevant to other astrophysical and laboratory plasmas.
Knizhnik, K. J.↗
A review of transport theory
Ways in which energy change terms arise in the transport equation and how the various terms relate to the modes of energy exchange between the particles and plasma are shown. It is argued that the transport equation cannot be used to describe the initial acceleration of thermal particles by plasma shocks or relativistic shocks where the energetic particle speeds are never much greater than the flow speeds. In most other situations, it describes almost any acceleration process that can be caused by a moving plasma. It describes shock acceleration for both parallel shocks and oblique ones, and stochastic acceleration by the turbulent motion of the scatterers as well as by their motion across the magnetic field.
Jones, Frank C.↗
Reconnection and particle acceleration in 3D current sheet evolution in moderately-magnetized astrophysical pair plasma
Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially 2D) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in 3D, we conduct a comprehensive particle-in-cell simulation study comparing 2D and 3D evolution of long, thin current sheets in moderately-magnetized, collisionless, relativistically-hot electron- positron plasma, and find dramatic differences. We first systematically characterize this process in 2D, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths, and system sizes. We then show that 3D simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3D current-sheet evolution is not always fundamentally classical reconnection with perturbing 3D effects, but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details, and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in 2D. Intriguingly, nonthermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in 2D and 3D. Though the variety of underlying current-sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.
Gregory R. Werner↗
The Effect of Stochastic Acceleration on the Dynamics of Solar Energetic Particles in the Heliosphere
Solar Energetic Particles (SEPs) are crucial in space weather phenomena, impacting space-based technologies and human activities in space. Understanding the dynamics of SEPs, including their acceleration and transport mechanisms, is essential for improving predictive models and mitigating adverse effects. This study investigates the impact of stochastic acceleration (SA) on the dynamics of SEPs within the heliosphere. By integrating stochastic acceleration into a SEP transport model, we assess its impact relative to diffusive shock acceleration (DSA). The investigation utilizes the Adaptive Mesh Particle Simulator (AMPS) within the Space Weather Modeling Framework (SWMF) to simulate SEP dynamics, incorporating solar wind parameters and turbulence from the Alfven Wave Solar Model (AWSoM). To do this, we solve the focused transport equation to model the propagation of SEPs along magnetic field lines, extending these lines to 5 AU to incorporate the potential effects of pitch angle scattering beyond 1 AU. This aspect could notably impact the decay phase of a SEP event. Modeling the transport of SEPs is coupled with the simulation of solar wind dynamics, the interplanetary magnetic field, and the characteristics of Alfven wave turbulence. This presentation covers the modeling approach used in this research, the characterization of the impact of the stochastic acceleration, and the role of pitch angle scattering at various heliocentric distances on the dynamics of the SEP events' decay phase.
SEP↗
Generation of Kappa Distributions in Solar Wind at 1 au
We examine the generation of kappa distributions in the solar wind plasma near 1 au. Several mechanisms are mentioned in the literature, each characterized by a specific relationship between the solar wind plasma features, the interplanetary magnetic field (IMF), and the kappa index-the parameter that governs the kappa distributions. This relationship serves as a signature condition that helps the identification of the mechanism in the plasma. In general, a mechanism that generates kappa distributions involves a single or a series of stochastic or physical processes that induces local correlations among particles. We identify three fundamental solar wind plasma conditions that can generate kappa distributions, noted as (i) Debye shielding, (ii) frozen IMF, and (iii) temperature fluctuations, each one prevailing in different scales of solar wind plasma and magnetic field properties. Moreover, our findings show that the kappa distributions, and thus, their generating mechanisms, vary significantly with solar wind features: (i) the kappa index has different dependence on the solar wind speed for slow and fast modes, i.e., slow wind is characterized by a quasi-constant kappa index, K (is) approx. 4.3 +/- 0.7, while fast wind exhibits kappa indices that increase with bulk speed; (ii) the dispersion of magnetosonic waves is more effective for lower kappa indices (i.e., further from thermal equilibrium); and (iii) the kappa and polytropic indices are positively correlated, as it was anticipated by the theory.
Livadiotis, G.↗
Stochastic particle acceleration in flaring stars
The acceleration of electrons by the Fermi-Parker mechanisms in a quasistationary turbulent plasma of dimension l, mean magnetic field strength B, and mean number density n are considered. The electrons suffer radiative and ionization losses and have a scattering mean free path that increases linearly with their momentum. Analytic solutions for the steady-state electron energy spectra are presented. The spectra are characterized by an exponential cutoff above a given momentum determined by the synchrontron or the confinement time, depending on the physical characteristics of the accelerating region.
Bogdan, T. J.↗
Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
Khazanov, G. V.↗
Descriptions of the polarization states of vector processes - Applications to ULF magnetic fields
In recent years a wide variety of methods has been used to describe the polarization characteristics of ULF (.001 to 1 Hz) magnetic fields. This paper gives a detailed outline of some of the descriptions derived from the spectral matrices of n-variate stochastic processes. The matrices are expanded in three different, standard sets of matrices in order to add some simplification to the interpretation of the polarizations. One set is composed of n-squared trace-orthogonal, hermitean matrices and leads directly to a generalization of the Stokes parameters and the degree of polarization for n-variate processes. The second set is developed from the dyad expansion, which in particular cases is analogous to the spectral decomposition of the matrix. The third set is composed of n commuting idempotent matrices and proves to be the most useful set when the stochastic process is not strictly polarized.
Samson, J. C.↗
Observations of large transient magnetospheric electric fields
Transient electric field events were studied by means of the long double-probe instrumentation carried by the Imp 6 satellite, and nine clearly defined exceptionally large amplitude events are described. The events were observed in the midnight sector at geocentric distances of 3.5 to 5.5 earth radii at middle latitudes within a magnetic L shell range of 4.8 to 7.5; the duration is from one to several minutes with peak power spectra amplitudes occurring at a frequency of about 0.3 Hz. The events occur under magnetically disturbed conditions and are often associated with negative dH/dt excursions. The magnetospheric motions calculated for these electric fields indicate a quasi-stochastical diffusive process rather than the general inward magnetospheric collapsing motion expected during the expansive phases of auroral substorm activity. It is likely that the transient electric fields are responsible for the impulsive acceleration and injection of plasma to populate the outer radiation belt.
Aggson, T. L.↗
Time-Series Analysis of Supergranule Characterstics at Solar Minimum
Sixty days of Doppler images from the Solar and Heliospheric Observatory (SOHO) / Michelson Doppler Imager (MDI) investigation during the 1996 and 2008 solar minima have been analyzed to show that certain supergranule characteristics (size, size range, and horizontal velocity) exhibit fluctuations of three to five days. Cross-correlating parameters showed a good, positive correlation between supergranulation size and size range, and a moderate, negative correlation between size range and velocity. The size and velocity do exhibit a moderate, negative correlation, but with a small time lag (less than 12 hours). Supergranule sizes during five days of co-temporal data from MDI and the Solar Dynamics Observatory (SDO) / Helioseismic Magnetic Imager (HMI) exhibit similar fluctuations with a high level of correlation between them. This verifies the solar origin of the fluctuations, which cannot be caused by instrumental artifacts according to these observations. Similar fluctuations are also observed in data simulations that model the evolution of the MDI Doppler pattern over a 60-day period. Correlations between the supergranule size and size range time-series derived from the simulated data are similar to those seen in MDI data. A simple toy-model using cumulative, uncorrelated exponential growth and decay patterns at random emergence times produces a time-series similar to the data simulations. The qualitative similarities between the simulated and the observed time-series suggest that the fluctuations arise from stochastic processes occurring within the solar convection zone. This behavior, propagating to surface manifestations of supergranulation, may assist our understanding of magnetic-field-line advection, evolution, and interaction.
Dopplergrams↗
Bayesian inference in geomagnetism
The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.
Backus, George E.↗
Magnetic Field Strength Fluctuations in the Heliosheath: Voyager 1 Observations During 2009
We analyze the microscale fluctuations of the magnetic field strength B on a scale of several hours observed by Voyager1 (V1) in the heliosheath during 2009. The microscale fluctuations of B range from coherent to stochastic structures. The amplitude of microscale fluctuations of B during 1 day is measured by the standard deviation (SD) of 48 s averages of B. The distribution of the daily values of SD is lognormal. SD(t) from day of year (DOY) 1 to 331, 2009, is very intermittent. SD(t) has a 1/f or "pink noise" spectrum on scales from 1 to 100 days, and it has a broad multifractal spectrum f(alpha) with 0.57 less than or equal to alpha less than or equal to 1.39. The time series of increments SD(t + tau) -- SD(t) has a pink noise spectrum with alpha(1) = 0.88 plus or minus 0.14 on scales from 1 to 100 days. The increments have a Tsallis (q-Gaussian) distribution on scales from 1 to 165 days, with an average q = 1.75 plus or minus 0.12. The skewness S and kurtosis K have Gaussian and lognormal distributions, respectively. The largest spikes in K(t) and S(t) are often associated with a change in B across a data gap and with identifiable physical structures. The "turbulence" observed by V1 during 2009 was weakly compressible on average but still very intermittent, highly variable, and highly compressible at times. The turbulence observed just behind the termination shock by Voyager 2 was twice as strong. These observations place strong constraints on any model of turbulence in the heliosheath.
Brulaga, L. F.↗
Heating of coronal plasma by anomalous current dissipation
It is shown that there exist heating mechanisms which connect the observed radiative properties of the inner corona in a simple way to the underlying solar magnetic field. The mechanisms considered involve the generation and consequent dissipation of coronal currents. It is argued that the spatially and temporally inhomogeneous nature of the erupting solar magnetic field is an essential element of coronal heating. Unlike heating theories conceived in the context of the 'homogeneous' corona, this class of current heating models incorporates the observed stochastic coronal structuring at the onset, and does not view it as a complication of an otherwise straightforward model. Attention is given to the generation of coronal currents, the flux-tube emergence, the gradual growth and decay of active regions, the energetics of current dissipation, current sheath geometry and heat transport, and anomalous current dissipation.
Rosner, R.↗