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It is shown that there exist solutions for which the linear differential equations of physics are transformed into nonlinear equations. The corresponding diffusion Maxwellian solution of the equation of magnetic induction in a moving medium can be used to describe the emergence and subsequent evolution of the magnetic fields of the Earth, Sun, and other planets and stars. If the magnetic viscosity is complex, the evolution of the magnetic induction is cyclic, in which case the magnetic induction can change sign.

Supernova remnants (SNRs) are one of the most energetic astrophysical events and are thought to be the dominant source of Galactic cosmic rays (CRs). A recent report on observations from the Fermi satellite has shown a signature of pion decay in the gamma-ray spectra of SNRs. This provides strong evidence that high-energy protons are accelerated in SNRs. The actual gamma-ray emission from pion decay should depend on the diffusion of CRs in the interstellar medium. In order to quantitatively analyse the diffusion of high-energy CRs from acceleration sites, we have performed test particle numerical simulations of CR protons using a three-dimensional magnetohydrodynamics (MHD) simulation of an interstellar medium swept-up by a blast wave. We analyse the diffusion of CRs at a length scale of order a few pc in our simulated SNR, and find the diffusion of CRs is precisely described by a Bohm diffusion, which is required for efficient acceleration at least for particles with energies above 30 TeV for a realistic interstellar medium. Although we find the possibility of a superdiffusive process (travel distance proportional to t^0.75) in our simulations, its effect on CR diffusion at the length scale of the turbulence in the SNR is limited., Comment: 20 pages, 4 tables, 10 figures

A fundamental problem in plasma physics, space science, and astrophysics is the transport of energetic particles interacting with stochastic magnetic fields. In particular the motion of particles across a large scale magnetic field is difficult to describe analytically. However, progress has been achieved in the recent years due to the development of the unified non-linear transport theory which can be used to describe magnetic field line diffusion as well as perpendicular diffusion of energetic particles. The latter theory agrees very well with different independently performed test-particle simulations. However, the theory is still based on different approximations and assumptions. In the current article we extend the theory by taking into account the finite gyroradius of the particle motion and calculate corrections in different asymptotic limits. We consider different turbulence models as examples such as the slab model, noisy slab turbulence, and the two-dimensional model. Whereas there are no finite gyroradius corrections for slab turbulence, the perpendicular diffusion coefficient is reduced in the other two cases. The matter investigated in this article is also related to the parameter a^2 occurring in non-linear diffusion theories., Paper accepted by Advances in Space Research

Recently an advanced nonlinear diffusion theory for particle transport across the mean magnetic field has been developed. The method used in the derivation of the latter theory is based on the cosmic ray Fokker-Planck equation. In the present article we use the same approach to describe pitch-angle scattering and parallel spatial diffusion nonlinearly. Furthermore, we derive the quasilinear transport theory, the weakly nonlinear theory as well as the Bohm limit as special cases from our more general approach.

The self-consistent interaction between energetic particles and self-generated hydromagnetic waves in a cosmic-ray pressure dominated plasma is considered. Using a three-dimensional hybrid MHD-kinetic code, which utilises a spherical harmonic expansion of the Vlasov-Fokker-Planck equation, high resolution simulations of the magnetic field growth including feedback on the cosmic rays are carried out. It is found that for shocks with high cosmic-ray acceleration efficiency, the magnetic fields become highly disorganised, resulting in near isotropic diffusion, independent of the initial orientation of the ambient magnetic field. The possibility of sub-Bohm diffusion is demonstrated for parallel shocks, while the diffusion coefficient approaches the Bohm limit from below for oblique shocks. This universal behaviour suggests that Bohm diffusion in the root mean squared field inferred from observation may provide a realistic estimate for the maximum energy acceleration timescale in young supernova remnants. Although disordered, the magnetic field is not self-similar suggesting non-uniform energy dependent behaviour of the energetic particle transport in the precursor. Possible indirect radiative signatures of cosmic-ray driven magnetic field amplification are discussed., Comment: Accepted for publication in MNRAS

Astronomy and astrophysics 593, A20(2016). doi:10.1051/0004-6361/201527345, Supernova remnants are known as sources of Galactic cosmic rays for their nonthermal emission of radio waves, X-rays, and gamma rays. However, the observed soft broken power-law spectra are hard to reproduce within standard acceleration theory based on the assumption of Bohm diffusion and steady-state calculations.Aims. We point out that a time-dependent treatment of the acceleration process together with a self-consistent treatment of the scattering turbulence amplification is necessary.Methods. We numerically solve the coupled system of transport equations for cosmic rays and isotropic Alfvénic turbulence. The equations are coupled through the growth rate of turbulence determined by the cosmic-ray gradient and the spatial diffusion coefficient of cosmic rays determined by the energy density of the turbulence. The system is solved on a comoving expanding grid extending upstream for dozens of shock radii, allowing for the self-consistent study of cosmic-ray diffusion in the vicinity of their acceleration site. The transport equation for cosmic rays is solved in a test-particle approach.Results. We demonstrate that the system is typically not in a steady state. In fact, even after several thousand years of evolution, no equilibrium situation is reached. The resulting time-dependent particle spectra strongly differ from those derived assuming a steady state and Bohm diffusion. Our results indicate that proper accounting for the evolution of the scattering turbulence and hence the particle diffusion coefficient is crucial for the formation of the observed soft spectra. In any case, the need to continuously develop magnetic turbulence upstream of the shock introduces nonlinearity in addition to that imposed by cosmic-ray feedback., Published by EDP Sciences, Les Ulis

The research reported in an article previously published in this journal is pursued here further on. A staircase profile of the graphical representation of the absolute value of the expression for Bohm-type diffusion in two dimensions is analyzed allowing the suggestion that its shape could be related to the well-known structure of levels of the quantized square of the guiding center radius vector and that this structure could be responsible for the appearance of the successive steps in such a profile. When these considerations are taken into account, the expression for Bohm-type diffusion in two dimensions is normalized according to the formula for the quantized square of the guiding center radius vector and a diffusion coefficient whose value is 4 π times the Bohm diffusion coefficient is obtained for large values of the independent variable.

A lot of theoretical effort has been achieved in cosmic ray scattering theory during the previous years. On the other hand several authors employed the so-called Bohm limit to replace cosmic ray diffusion coefficients in the diffusive transport equation for describing particle acceleration in supernove remnants and in other environments. In this article it is shown how the Bohm limit can be derived from cosmic ray diffusion theory by assuming a strong turbulent magnetic field component. Also a test-particle code is employed to explore the regimes for which the Bohm limit is valid and for which not. These results are important to distinguish between the parameter regimes for which the Bohm limit is valid and for which traditional diffusion theories have to be applied.

A two-dimensional numerical modeling is carried out to simulate argon plasma-neutral transport in a linear divertor simulator with an axisymmetric cylindrical geometry. A pure argon plasma flow is introduced from the source region into the transport region, and pumped out near the target plate. This numerical modeling is based on a time-dependent Braginskii's fluid formulation for plasma transport and a simple diffusion model for neutral transport. The Bohm diffusion model is adopted for calculation of radial diffusion coefficients across the parallel magnetic field in the simulator. Using the design and operation parameters of the Multi-Purpose Plasma (MP 2 ) facility at the National Fusion Research Institute (NFRI) in Korea, argon plasma properties such as density and temperature distributions are calculated, and the formation of ionization front is found in the transport region. Plasma equilibrium profiles along the near axis turn out to be actually unaffected by the pumping positions along the cylindrical wall. Moreover, a gas target divertor concept is numerically simulated to find out puffing effects as well as pumping roles. As increasing the puffing rate at the target plate, not only the ionization front in the plasma density profile is gradually moving toward the entrance region, but also plasma density and electron temperature at the target are dramatically reduced. Two relatively peaked poles in the neutral density profile are resulted from puffing and recycling neutrals, respectively.

Equatorial radial distributions of plasma density in the 3 < L < 9 region of Saturn’s magnetosphere, obtained from measurements on the Cassini spacecraft, are considered on the basis of diffusion theory. The concentration of particles in the magnetic tubes is found to grow with L. The external source is located at L ≳ 9. The particles diffuse to Saturn. In the 5 < L < 9 interval the distribution is close to equilibrium. A relation between the diffusion coefficient and the densities of internal sources and losses is obtained in this interval. Prevalence of losses over sources is very probable. Estimates of the diffusion flux and its derivative are given. If the diffusion coefficient is expressed as D LL = D o L 3 and the contencentration of particles depends on L according to a power law, the diffusion rate is constant.

Three experimental cases of cross-field diffusions in the magnetized plasmas reported to be related with Bohm diffusion are investigated based on the ion current induced by the ion-neutral collisions. High diffusion coefficient for the original Bohm/Simon experiments and the recent experiments of strongly pulsed plasmas can be explained by the gyro-center shift current combined with the short circuit effect, which is different from the turbulence-induced transport of nuclear fusion devices. It can be deduced that Bohm’s interpretation of diffusion with $1/B$ dependence came from the fact that the short circuit effect of his experiment was limited by the parallel ion velocity. The ratio of azimuthal current density to the discharge current density measured in the pulsed magnetron experiments is analyzed to be constant and independent from the magnitude of magnetic field due to the maximum condition for the Pedersen conductivity.

Constraints on the diffusion and acceleration parameters in five young supernova remnants (SNRs) are derived from the observed thickness of their X-ray rims, as limited by the synchrotron losses of the highest energy electrons, assuming uniform and isotropic turbulence. It is shown that the magnetic field must be amplified up to values between 250 and 500 microGauss in the case of Cas A, Kepler, and Tycho, or ~ 100 microGauss in the case of SN 1006 and G347.3-0.5. The diffusion coefficient at the highest electron energy can also be derived from the data, by relating the X-ray energy cutoff to the acceleration timescale. Values typically between 1 and 10 times the Bohm diffusion coefficient are found to be required. We also find interesting constraints on the energy dependence of the diffusion coefficient. This favours diffusion regimes between the Kraichnan and the Bohm regime, and rejects turbulence spectrum indices larger than ~ 3/2. Finally, the maximum energy of the accelerated particles is found to lay between 10^13 and 5 10^13 eV for electrons, and around Z \times 8 10^14 eV at most for nuclei (or ~ 2.5 times less if a Bohm diffusion regime is assumed), roughly independently of the compression ratio assumed at the shock. Even by taking advantage of the uncertainties on the measured parameters, it appears very difficult for the considered SNRs in their current stage of evolution to produce protons up to the knee of the cosmic-ray spectrum, at ~ 3 10^15 eV, and essentially impossible to accelerate Fe nuclei up to either the ankle at ~ 3 10^18 eV or the second knee at ~ 5 10^17 eV.

The problem of normal and anomalous diffusion is formulated on the basis of integral master-type equations with various probability transition functions for diffusion in coordinate space (PTD functions). Grain diffusion in dusty plasmas has a normal character. The dependence of the diffusion coefficient as a function of the grain–grain interaction strength is investigated.

The magnetic induction equation for an axially symmetric magnetic field reveals an interesting feature, when the Bohm plasma diffusion is incorporated. The 1/B dependence of Bohm diffusion allows the induction equation to transform into a simple heat equation which admits an exact solution when the plasma temperature is constant. When the diffusion velocity satisfies a certain condition, the axially symmetric magnetic field can be significantly enhanced.

Density, temperature and potential fluctuations have been measured in the edge region and the scrape off layer (SOL) of the SINP tokamak. The triple probe technique has been used to obtain the instantaneous value of these quantities simultaneously and virtually at the same spatial position. The fluctuation levels thus found are significant (e/Te≈20–35% and n/n≈35–55%) and the spectra are broadband. The effect of temperature fluctuation on the turbulent transport has also been investigated and found to be considerable. The measured diffusion coefficient comes out to be about twice the Bohm diffusion coefficient. Radial profiles show sharp density and temperature gradients and there exists a self-generated Er×B velocity shear layer near the limiter. The results have been compared with the existing theories of edge turbulence in tokamaks and the rippling mode driven by the resistivity gradient has been identified as the most probable mechanism.

Cross field diffusion of energetic particles (cosmic rays) in a two-dimensional static magnetic field turbulence is studied performing test particle simulations. Qualitatively different diffusion processes are observed depending on the ratio of Larmor radius (ρ) to the correlation length (λ) of the magnetic field fluctuations. The diffusion is found to be composed of several regimes with distinct statistical properties, which can be characterized using Levy statistics.

The method of molecular dynamics is used to study behavior of a ultracold non-ideal ion-electron Be plasma in a uniform magnetic field. Our simulations yield an estimate for the rate of electron-ion collisions which is non-monotonicallydependent on the magnetic field magnitude. Also they explicitly show that there are two types of diffusion: classical one, corresponding to Brownian motion of particles, and Bohm diffusion when the trajectory of particles (guiding centers) includes substantial lengths of drift motion., Comment: 7 pages; 6 figures

Particle diffusion in a given electrostatic turbulence with a finite correlation length along the confining magnetic field is studied in the test particle approach. An anomalous diffusion regime with amplified diffusion coefficient is found under the conditions when trajectory trapping in the structure of the stochastic potential is effective.

We present the results of large hybrid (kinetic ions - fluid electrons) simulations of particle acceleration at non-relativistic collisionless shocks. Ion acceleration efficiency and magnetic field amplification are investigated in detail as a function of shock inclination and strength, and compared with predictions of diffusive shock acceleration theory, for shocks with Mach number up to 100. Moreover, we discuss the relative importance of resonant and Bell's instability in the shock precursor, and show that diffusion in the self-generated turbulence can be effectively parametrized as Bohm diffusion in the amplified magnetic field., 9 pages, 10 figures; Proceedings of the conference "Cosmic ray origin: beyond the standard models", San Vito di Cadore (Dolomites, Italy), March 2014. To appear in Nuclear Physics B Proceedings Supplement

In this study, the relationship between diffusion and the electrical conductivity tensor is investigated by using the real geometry of the Earth's magnetic field in the Northern Hemisphere for mid-latitudes. This relationship is derived from equation. Only in the elements of the diagonal of the tensor is an equal relationship found between the electrical conductivity called the longitudinal conductivity and the diffusion coefficient. The diagonal elements are equal to each other and do not depend on the Earth's magnetic field; however, the other elements of the tensor strongly depend on the Earth's magnetic field and they have characteristic of Bohm diffusion became a semi-empirical model (DB= (1/16)kT/eB) but they do not depend on the electrical conductivity or the classical diffusion coefficient. © 2014 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved.

The radial profiles of KT-1 tokamak (major radius of 27 cm, minor radius of 4.25 cm, two poloidal stainless-steel limiters) edge plasma parameters are measured using single and triple electric probes. The particle transport parameters are calculated from the measured edge plasma parameters, and the results are analyzed by the simple fluid approximations. The cross-field particle diffusion coefficient ( D ⊥ ) in the boundary plasma of the KT-1 is calculated from the density scrape-off length ( λ n ) measured by using a triple probe. The particle density and electron temperature fall exponentially in the radial direction with the e-folding length of λ n =0.13 cm and λ e =0.41 cm, respectively. From the scrape-off layer (SOL) model, the experimental values of scrape-off length ( λ n ) is used to calculate the cross-field diffusion coefficient ( D ⊥ =1.2×10 3 cm 2 /s), roughly corresponding to one third of the typical Bohm value. A simple SOL model with the contribution of recombination is introduced to evaluate the Bohm diffusion in the KT-1 tokamak edge plasma. Cross-field heat conductivity calculated from these deduced values is ∼5.2 D ⊥ in the SOL of KT-1 edge plasma. These results provide the finally certain information for edge particle transport in the KT-1 boundary plasmas.

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with low-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the relativistic quasilinear diffusion coefficients are calculated explicitly for magnetically-trapped particle distributions in axisymmetric magnetic geometry in terms of drift-bounce resonant contributions associated with low-frequency fluctuations which conserve the first adiabatic invariant.

We study transport in random undirectional wave-like velocity fields with nonlinear dispersion relations. For this simple model, we have several interesting findings: (1) In the absence of molecular diffusion the entire family of fractional Brownian motions (FBMs), persistent or anti-persistent, can arise in the scaling limit. (2) The infrared cutoff may alter the scaling limit depending on whether the cutoff exceeds certain critical value or not. (3) Small, but nonzero, molecular diffusion can drastically change the scaling limit. As a result, some regimes stay intact; some (persistent) FBM regimes become non-Gaussian and some other FBM regimes become Brownian motions with enhanced diffusion coefficients. Moreover, in the particular regime where the scaling limit is a Brownian motion in the absence of molecular diffusion, the vanishing molecular diffusion limit of the enhanced diffusion coefficient is strictly larger than the diffusion coefficient with zero molecular diffusion. This is the first such example that we are aware of to demonstrate rigorously a nonperturbative effect of vanishing molecular diffusion on turbulent diffusion coefficient.

A hollow-cathode planar magnetron (HCPM), built by surrounding a planar sputtering-magnetron cathode with a hollow-cathode structure (HCS) [Z. Wang and S. A. Cohen, J. Vac. Sci. Technol. A 17, 77 (1999)], is operable at substantially lower pressures than its planar-magnetron counterpart. HCPM operational parameters depend on the inner diameter D and length L of its cylindrical HCS. Only when L is greater than L0, a critical length, is the HCPM operable in the new low-pressure regime. The critical length varies with HCS inner diameter D. Explanations of the lower operational pressure regime, critical length, and plasma shape are proposed and compared with a one-dimension diffusion model for energetic electron transport. At pressures above 1 mTorr, Bohm diffusion (temperature≅primary electron energy), with an ambipolar constraint, can explain the ion–electron pair creation required to sustain the discharge. At the lowest pressure, ∼0.3 mTorr, collision-limited diffusion creates fewer ion–electron pairs than...

A variational method is used to obtain estimates of the effective particle transport coefficients in a random static magnetic field. The particle propagation is described by an anisotropic diffusion equation. The diffusion coefficient parallel to the local magnetic field is much greater than the transverse diffusion coefficient. For large-scale magnetic-field variations the diffusion is described by effective coefficients. The variational approach can be used to find the effective parallel and perpendicular diffusion coefficients. It was shown that the instability growth rate of the magnetic field lines determines the upper estimate of the effective transverse diffusion coefficient.

A technique is presented to solve analytically the turbulent diffusion equation for the concentration of a passive contaminant emitted from an elevated continuous source into the atmosphere. A generalized method of solution using Sturm–Liouville and WKB theories is developed to overcome difficulties due to the height‐dependent wind velocity and diffusion coefficient appearing in the diffusion equation. The method presented in this paper is able to derive an asymptotic expression for the concentration obtained from the solution of the atmospheric diffusion equation which involves explicitly inhomogeneous wind velocity and diffusion coefficient. The diffusion equation model derived from this method can be applied in a practical prediction of contaminant concentration in a turbulent atmosphere.

We numerically simulated the diffusion of a charged Brownian particle confined to a plane under the action of an orthogonal magnetic field with intensity depending on the distance from a center. Despite its apparent simplicity, this system exhibits anomalous diffusion. For positive field gradients, radial and angular dynamics are asymptotically subdiffusive, with exponents given by simple analytical expressions. In contrast, when driven by a weakly decaying field, the particle attains normal diffusion only after exceedingly long superdiffusive transients. These mechanisms can be related to Bohm diffusion in magnetized plasmas.

One- and two-dimensional particle simulations have been carried out to study electrostatic ion cyclotron instabilities for a hydrogen plasma in a strong magnetic field. It is found that strong ion heating and anomalous cross-field diffusion comparable to Bohm diffusion take place associated with the instability. Implications of the instability to the recent observations in fusion devices and space plasmas are discussed.

We describe a charged-particle diffusion in unbounded plasma, which is controlled by the temperature gradients of the charged particles. The obtained diffusion coefficient can be negative if the temperature of the electrons is greater than the temperature of the ions. We show that this charged-particle diffusion can cause plasma self-constriction, presented by a bell soliton.

This article describes the theory and numerical modeling of the cathode sheath region near the target of a magnetron. Since electrons are assumed to be confined by the magnetic field, a fluid model is appropriate. Collisionless and fluid models for ion motion are considered and the sheath properties are compared for each of the models considered. It is shown that, if electron diffusion in the sheath is classical, the magnetized electrons have a strong effect on the sheath, whereas for the case of Bohm diffusion this effect is negligible.

In a new toroidal laboratory plasma device including a poloidal magnetic field created by an internal circular conductor, the confinement efficiency of the magnetized plasma and the turbulence level are studied in different situations. The plasma density is greatly enhanced when a sufficiently large poloidal magnetic field is established. Moreover, the instabilities and the turbulence usually found in toroidal devices without sheared magnetic field lines are suppressed by the finite rotational transform. The particle confinement time is estimated from the measurement of the plasma decay time. It is compared to the Bohm diffusion time and to the value predicted by different diffusion models, in particular neoclassical diffusion involving trapped particles.

A database consisting of edge equilibrium, turbulence and transport related plasma parameters has been compiled. Scaling laws for edge density, electron temperature, and radial particle flux are derived in an initial study using a subset of data obtained from tokamaks Phaedrus-T, Tokamak de Varennes, TEXT and TEXT-U. A comparison of edge particle transport in divertor and limiter plasmas shows that the magnetic topology of a separatrix or a divertor improves particle confinement. The particle diffusion coefficient varies radially in a manner opposite to that of Bohm diffusion.

[1] The Sweet-Parker analysis of the inner electron diffusion region of collisionless magnetic reconnection is presented. The study includes charged particles motion near the X-line and an appropriate approximation of the off-diagonal term for the electron pressure tensor. The obtained scaling shows that the width of the inner electron diffusion region is equal to the electron inertial length, and that electrons are accelerated up to the electron Alfven velocity in X-line direction. The estimated effective plasma conductivity is based on the electron gyrofrequency rather than the binary collision frequency, and gives the extreme (minimal) value of the plasma conductivity similar to Bohm diffusion. The scaling properties are verified by means of Particle-in-Cell simulations. An ad hoc parameter needs to be introduced to the scaling relations in order to better match the theory and simulations.

We develop an approach, by calculating the autocorrelation function of spins, to derive the magnetic field gradient induced transverse ($T_2$) relaxation of spins undergoing restricted diffusion. This approach is an extension to the method adopted by McGregor. McGregor's approach solves the problem only in the fast diffusion limit; however, our approach yields a single analytical solution suitable in all diffusion regimes, including the intermediate regime. This establishes a direct connection between the well-known Torrey's slow diffusion result and the fast diffusion result. We also perform free induction decay measurements on spin-exchange optically polarized $^3$He gas with different diffusion constants. The transverse relaxation profiles are compared with the theory and satisfactory agreement has been found throughout all diffusion regimes. In addition to the transverse relaxation, this approach is also applicable to solving the longitudinal relaxation ($T_1$) regardless of the diffusion limits. It turns out that the longitudinal relaxation in the slow diffusion limit differs by a factor of two, compared with that in the fast diffusion limit.

We show that puzzling recent experimental results on spin diffusion in a strongly interacting atomic gas may be understood in terms of the predicted spin diffusion coefficient for a generic strongly interacting system. Three important features play a central role: (a) Fick's law for diffusion must be modified to allow for the trapping potential; (b) the diffusion coefficient is inhomogeneous, due to the density variations in the cloud; and (c) the diffusion approximation fails in the outer parts of the cloud, where the mean free path is long.

The one-dimensional L\'evy flight in a composite medium consisting of two layers in contact, with arbitrary L\'evy indices, is investigated. Such systems are of much interest in the field of organic electronics, where diffusional transport between two materials profoundly influences the device performance. Using the jump-length probability density function for a particular L\'evy index as a starting point, equations are derived that describe anomalous diffusion in a composite two-layer medium. Moreover, expressions for the current density are given, and the steady-state distribution for the special case of one dominating diffusion coefficient is illustrated.

International audience; " Bohm diffusion " causes the electrons to diffuse perpendicular to the magnetic field lines. However, its origin is not yet completely understood: low and high frequency electric field fluctuations are both named to cause Bohm diffusion. The importance of including this process in a Monte Carlo (MC) model is demonstrated by comparing calculated ionization rates with particlein-cell/Monte Carlo collisions (PIC/MCC) simulations. A good agreement is found with a Bohm diffusion parameter of 0.05, which corresponds well with experiments. Since the PIC/MCC method accounts for fast electric field fluctuations, we conclude that Bohm diffusion is caused by fast electric field phenomena.

The current state of anomalous diffusion research at the magnetopause and its responsibility for the formation of the magnetopause boundary layer (MPBL) are reviewed. Most of the relevant unstable wave modes contribute negligibly to the diffusion process at the magnetopause under magnetically undisturbed southward IMF conditions. Global stationary diffusion due to wave-particle interactions does not take place at the magnetopause. Resonant diffusion due to electrostatic ion cyclotron waves is probably also unlikely to explain the existence of the boundary layer. There is a relation between phase space diffusion and spatial diffusion due to resonant interactions and the diffusion coefficients may be high, but diffusion affects only a narrow velocity interval of resonant particles injecting mainly monochromatic particles into the magnetosphere. Bulk diffusion can probably not be caused by this mechanism. Eddy diffusion or time-dependent processes to feed the MPBL are favored. Microscopic wave-particle interactions and anomalous diffusion may contribute to locally break the MHD frozen-in conditions and help in transporting large amounts of magnetosheath plasma across the magnetospheric boundary. >

Progress in the theory of anomalous diffusion in weakly turbulent cold magnetized plasmas is explained. Several proposed models advanced in the literature are discussed. Emphasis is put on a new proposed mechanism for anomalous diffusion transport mechanism based on the coupled action of conductive walls (excluding electrodes) bounding the plasma drain current (edge diffusion) together with the magnetic field flux "cutting" the area traced by the charged particles in their orbital motion. The same reasoning is shown to apply to the plasma core anomalous diffusion. The proposed mechanism is expected to be valid in regimes when plasma diffusion scales as Bohm diffusion and at high $B/N$, when collisions are of secondary importance., Comment: 9 pages, 4 figures

This paper considers the question of whether the distribution of mass in the Io plasma torus is consistent with the concept of interchange eddy transport. Specifically, the flux tube content exhibits a gradual decrease with increasing radial distance from the source near Io without any evidence for substantial density irregularity associated with the plasma source or loss. Using a simple one-dimensional numerical model to simulate macroscopic interchange eddy transport, it is demonstrated that this smooth equilibrium distribution of mass can occur but only with the inclusion of a minimal level of small scale microscopic mixing at a rate approaching Bohm diffusion. Otherwise, the system exhibits a chaotic appearance which never approaches an equilibrium distribution. Various physical mechanisms for the microscopic diffusion process which is required to provide a sufficiently rapid mixing of material between the macroscopic eddies are discussed.

Diffusion of stochastic magnetic field lines is studied in a toroidal geometry. General expressions for the radial diffusion coefficient are obtained in various physically important situations. The Poincare representation of magnetic field lines is reduced to discrete mappings and the corresponding diffusion coefficients are derived. The diffusion processes taking place near the threshold to global stochasticity are also discussed.

We calculate the yield of high energy neutrinos produced in astrophysical sources for arbitrary interaction depths τ0 and magnetic field strengths B. We take into account energy loss processes like synchrotron radiation and diffusion of charged particles in turbulent magnetic fields as well as the scattering of secondaries on background photons and the direct production of charm neutrinos. Meson‐photon interactions are simulated with an extended version of the SOPHIA model. Diffusion leads to an increased path‐length before protons leave the source of size Rs and therefore magnetized sources lose their transparency below the energy E∼1018 eV(.Rs/pc) (B/mG)τ01/α, with α = 1/3 and 1 for Kolmogorov and Bohm diffusion, respectively. Moreover, the neutrino flux is suppressed above the energy where synchrotron energy losses become important for charged particles. As a consequence, the energy spectrum and the flavor composition of neutrinos are strongly modified both at low and high energies even for sources wit...

We consider diffusion of outer zone radiation belt electrons by chorus waves. Quasi-linear diffusion coefficients valid outside the plasmasphere have only been calculated recently, and indicate that the energy and cross diffusion rates can be comparable to that for pitch angle diffusion. Proper solution of the diffusion equation for phase space density must therefore be based on the full diffusion tensor, but this has been plagued by numerical problems associated with the large and rapidly varying cross terms. To circumvent this, techniques are developed for transforming to variables in which the cross diffusion term vanishes. A model calculation shows significant diffusion of phase space density at L = 4.5 from 0.2 MeV up to a few MeV in less than a day.

The acceleration of interstellar pick-up ions as well as solar wind species has been observed at a multitude of interplanetary (IP) shocks by different spacecraft. The efficiency of injection of the pick-up ion component differs from that of the solar wind, and is expected to be strongly enhanced at highly oblique and quasi-perpendicular shock events, in accord with inferences from {\it in situ} observations. This paper explores theoretical modeling of the phase space distributions of accelerated ions obtained by the Ulysses mission for the Day 292, 1991 shock associated with a corotating interaction region, encountered before Ulysses' fly-by of Jupiter. A Monte Carlo simulation is used to model the acceleration process, adapting a technique that has been successfully tested on earlier IP shocks possessing minimal pick-up ion presence. Phase space distributions from the simulation technique for various low mass ions are compared with SWICS and HI-SCALE data to deduce values of a ``turbulence parameter'' that controls the efficiency of injection, and the degree of cross-field diffusion. Acceptable fits are obtained for the $H^+$ and $He^+$ populations using standard prescriptions for the pick-up ion distribution; $He^{++}$ spectral data was only fit well for scenarios very close to the Bohm diffusion limit. It is also found that the simulation successfully accounts for the observation of energetic protons farther upstream of the forward shock than lower energy pick-up protons, using the same turbulence parameter that is required to achieve reasonable spectral fits., Comment: 15 pages, 2 embedded figures, Advances Space Research, in press

[1] Magnetic field turbulence in the heliosphere is modeled by two-dimensional coherent vortex structures and random-phase linear wave fields added to a background magnetic field. Energetic particle trapping and acceleration by interaction with the turbulent fields are studied numerically. The corresponding radial and field-aligned diffusion coefficients are estimated. Different diffusion regimes (subdiffusion, superdiffusion, classical diffusion) are controlled by the following parameters: the ratio between amplitudes of the random component and the regular vortex field, e1, and the ratio between the average particle gyroradius and the magnetic field correlation length, e2. The anomalous diffusion regime occurs when the correlation length of magnetic field disturbances is about the same or larger than the particle gyroradius (e2 ≤ 1). Applications of our results to cosmic ray transport are discussed.

Conventional annular Hall thrusters become inefficient when scaled to low power. Cylindrical Hall thrusters, which have lower surface-to-volume ratio, are therefore more promising for scaling down. They presently exhibit performance comparable with conventional annular Hall thrusters. Electron cross-field transport in a 2.6 cm miniaturized cylindrical Hall thruster (100 W power level) has been studied through the analysis of experimental data and Monte Carlo simulations of electron dynamics in the thruster channel. The numerical model takes into account elastic and inelastic electron collisions with atoms, electron-wall collisions, including secondary electron emission, and Bohm diffusion. We show that in order to explain the observed discharge current, the electron anomalous collision frequency {nu}{sub B} has to be on the order of the Bohm value, {nu}{sub B} {approx} {omega}{sub c}/16. The contribution of electron-wall collisions to cross-field transport is found to be insignificant.

We present numerical results that show, first, conditions under which parallel scattering reduces the effectiveness of perpendicular scattering, leading to the phenomenon of subdiffusion (“compound diffusion”), and second, that when sufficiently strong three dimensional effects are present, true diffusion is restored, with a suppressed perpendicular diffusion coefficient that depends upon the parallel mean free path.