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The fluid model for positive ions is used together with the assumption of a constant ion mean free path to examine the structure of the plasma-wall sheath at low and medium pressures in plasmas where ionization is by electron impact and the ion temperature is set to zero. It is shown that in the near collisionless regime there is the same structure as was found with the constant collision frequency for momentum transfer model with the Bohm speed playing the same role and similar scaling of the transitional layer. At higher pressures there is again no transitional layer, only plasma joining smoothly to a collisional sheath, thus the Bohm criterion has no significance, but the scaling is with a different exponent than for the mobility case. No fundamental differences are found between the two models. An expression is derived to describe the boundary between the parameter region where the Bohm criterion applies and that where it does not.

In this paper, the stochastic magnetic field lines diffusion is studied. The stochastic behavior of the magnetic field lines is described by the generalized mapping to the second order which is derived from the magnetic field lines equations. The diffusion coefficient is calculated analytically using the Fourier paths technique and the characteristic function formalism. Both, they give exactly the same result of the diffusion coefficient. A numerical determination of the diffusion coefficient is also done.

The effect of a weak rotating magnetic field on an ECR discharge plasma in argon has been investigated. The field was produced by an arrangement of bars surrounding the discharge vessel and carrying harmonic currents appropriately shifted in phase. Optical probes, Thomson scattering, Li?beam diagnostics and a fast CCD camera were used for the investigations. A significant modulation of the electron density and temperature at the plasma edge was observed. This can be assigned to an increase of the transport of electrons to the discharge vessel walls where the lines of the total B field cross them. Alteration of the transport conditions results in perturbations, which diffuse radially inwards at a velocity corresponding to that of the Bohm diffusion. A pattern of light emission develops, which rotates synchronously with the rotating field. Correlation between the total light emission from different plasma volumes was determined based on measurements made with optical probes. This shows fluctuations propagating azimuthally, anticlockwise with respect to the direction of the main B field, with a wavelength of about (7-10) ? 10-2?m. These fluctuations exist independently of the presence of the rotating magnetic field. Further investigations are still needed to answer two key questions: does the plasma rotate as a whole or is the observed effect a rotation of the plasma state only, and how does the rotating field affect fluctuations at the plasma edge?

We consider the transport of charged particles in a stochastic magnetic field using a method based on the velocity correlation function vi(0)vj(t) developed by R. Kubo. This can be used under very general conditions to evaluate the corresponding spatial diffusion coefficients, if the fluctuations are statistically homogeneous in space and time. Although Kubo's theory is quite general, it is not obvious how it can be applied to describe compound diffusion when particles are strictly tied to the magnetic field lines and perpendicular transport results solely from the random walk of the field lines. This motion is non-Markovian and leads to a slower Δx2 ∝ t1/2 diffusion in contrast to the Δx2 ∝ t dependence of the standard diffusion. We demonstrate how compound diffusion fits into Kubo's formalism. As intuitively as can be anticipated, the non-Markovian nature of the motion results in a long-term anticorrelation in vj(0)vi(t), which causes the ordinary spatial diffusion coefficient to vanish identically. The Δx2 ∝ t1/2 dependence of the compound diffusion can also be recovered from the Laplace transform of the velocity correlation function. Some implications of the long-term anticorrelation are discussed.

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 collision-free space-charge sheath formed by cold ions at a negative surface is considered. The method of matched asymptotic expansions is applied, small parameter being the ratio of the electron temperature to the sheath voltage. Two expansions are considered, one describing bulk of the sheath where the electron density is exponentially small as compared to the ion density, and another describing the outer section of the sheath in which the densities are comparable. Boundary conditions for equations describing the bulk are found such that the model have exponential accuracy. A physical meaning of these conditions is that the ions are accelerated in the outer section from the Bohm velocity to twice the Bohm velocity and that the voltage drop, in the outer section equals (3/2)(kT/sub e//e). The model predicts the electric field and ion velocity at the surface and the thickness of the ion layer to the accuracy of several percent for sheath voltages exceeding 3(kT/sub e//e).

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 simple two-point representation of the tokamak scrape-off layer (SOL), based on the parallel and perpendicular energy balance equations, has been used to develop heat flux width scalings for a wide variety of χ ⊥ models in terms of B φ , n sep , q 95 , P SOL , R and a . These scalings have been tested against databases of SOL parameters established on COMPASS-D (which exhibits a collisionless SOL), JET Mk IIa divertor and Alcator C-MOD (both of which exhibit strongly collisional SOLs). The better fit scalings to the collisionless dataset all show a positive dependence of SOL width on q 95 and an inverse dependence on n sep . Four of the better fit scalings also show a positive dependence on P SOL and a strong inverse dependance on B φ . In the collisional case a group of 5 models, each with a χ ⊥ ∝ T 1/2 / n dependence, provide the better fit scalings to both collisional datasets. The derived scalings exhibit a strong inverse dependence on P SOL but are independent of B φ , unlike scalings derived from the commonly used Bohm diffusion model, and four of the five are also independent of n sep .

The widely used Child-Langmuir law for sheath thickness evaluation in semi-infinite collisionless plasmas makes the assumptions of quasi-neutrality (n/sub e/=n/sub i/) and zero electric field intensity E=0 at the sheath edge, as well as applying the Bohm criterion for ions entering the sheath. However, through a whole region fluid model, Poisson's equation has been solved numerically for the steady-state solution through the sheath and presheath without these assumptions. With the sheath edge defined, as in the Child-Langmuir law, at the place where the ion velocity is equal to the Bohm velocity, the sheath thickness of a bounded collisionless or weakly collisional plasma has been found with this model in some cases to be much larger than that obtained with the Child-Langmuir Law. The sheath thickness discrepancy is significant under conditions found in low pressure high density plasma (HDP) tools for plasma processing. Results presented indicate that the sheath thickness is very sensitive to the electric field and space charge density at the sheath edge. The electric field and space charge density can be successfully estimated by an intermediate scale matching method, and are used to derive a modified expression for the potential in the sheath that can be solved numerically for sheath thickness. With these results, the matching problem, arising when sheath and plasma are modeled separately, can be overcome.

This paper seeks to extend and improve upon an existing 1D isothermal model [1] for the cathode plasma boundary in magnetron discharges. Using an electron energy balance equation and treating the sheath as a source of electron heat flux, the plasma parameter profiles are solved in the pre-sheath, above the sputter trench. The cross-field transport of electrons is assumed to be dominated by Bohm diffusion (and mobility) in the mutually perpendicular electric and magnetic fields, while ions created by electron impact ionization fall directly to the cathode. Solutions show a fall in electron temperature with distance from the sheath-edge, with plasma densities rising by a factor of typically three or four from sheath-edge to plasma. This latter result is a departure from the normal prescription for Bohm sheath formation. Reasonable agreement between the model predictions and Langmuir probe measurements made in the region directly above the `race-track' sputter trench in a commercial magnetron show the usefulness of such simple models.

A spatially three-dimensional two-fluid model for electrons and ions has been developed in order to describe the plasma state of a magnetized hollow cathode arc burning in hydrogen at low pressure. In this direct current (DC) supplied discharge strong self-excited periodical oscillations have been observed previously, where a helically shaped plasma column rotates eccentrically around the magnetic field axis. The theoretical description of this plasma is based on the system of two-fluid equations formulated by Braginskii. After some estimations and approximations derived from the experimental results and by limiting the discussion to stationary and low-frequency phenomena, the system of equations can be reduced and a second-order differential equation of elliptic type for the plasma potential is derived. Using the measured spatial distributions of time resolved electron density and temperature as input data, this differential equation is solved numerically and the spatial distributions of the electric field, drift velocities, current densities and other quantities can be calculated. The results of our calculations show that an eccentrically rotating minimum of the plasma potential exists, while the arc current is concentrated in an annular region of maximum electron temperature. The magnitude of the radial particle transport coefficient is found to be in the order of the Bohm diffusion coefficient, which is about one order of magnitude larger than the classical diffusion coefficient. The measured oscillation frequencies can be explained by the drift frequency.

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.

The MagLIF approach to inertial confinement fusion involves subsonic/isobaric compression and heating of a DT plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstrates that the heat loss from the hot plasma to the cold liner is dominated by the transverse heat conduction and advection, and the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter ω{sub e}τ{sub e} effective diffusion coefficients determining the losses of heat and magnetic flux are both shown to decrease with ω{sub e}τ{sub e} as does the Bohm diffusion coefficient, which is commonly associated with low collisionality and two-dimensional transport. This family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.

The efficiency and uniqueness of the diffusive shock acceleration is studied on the basis of the novel kinetic solutions. These solutions obtained earlier (paper I, astro-ph/9707152) selfconsistently describe a strong coupling of cosmic rays with the gas flow. They show that the dependence of the acceleration efficiency upon physical parameters is critical in nature. In this paper we investigate a steady acceleration in the parameter space formed by the injection rate (\nu ), the upper cut-off momentum p_1 and the Mach number M while the flow compression R serves as an order parameter. We determine a manifold of all possible solutions in this parameter space., Comment: 24 pages, 8 PostScript figures, uses aasms4.sty, to appear in Dec. 20, 1997 issue ApJ, vol. 491

Measurements of radiofrequency (RF) loading on the Doubler III D shape (DIII-D) tokamak using a fast wave ion cyclotron antenna with and without a Faraday shield present indicate that the loading resistance seen by the antenna is significantly higher at low values of RF power (P ≤ 20 kW with no Faraday shield) than is predicted by standard fast wave antenna coupling theory. Measurements of the density profile in the plasma edge region allow a direct comparison of calculated and measured loading. At high power, the calculated fast wave loading agrees with the measurements. The high loading observed at low power can be explained by direct losses in an RF enhanced sheath. The density value at the current strap of approximately=4*1010 cm-3 needed to give the observed loading behaviour is in agreement with the measured density values in the plasma scrape-off region, extrapolated to the current strap location using a simple Bohm diffusion model

The effect of two-temperature electron distribution on the Bohm sheath criterion is studied in a collisionless sheath layer in contact with a perfectly absorbing wall. A modified Maxwell-Boltzmann model is used for the electron distribution functions, which considers the effect that the electrons above the sheath potential energy do not reflect back into the plasma. The present model shows that the Bohm velocity at the sheath edge is much more independent of the hotter species than what was understood previously with a simple Maxwell-Boltzmann electron model. {copyright} {ital 1996} {ital The American Physical Society}

Transport is the outstanding physics issue in the quest for fusion by magnetic confinement. In spite of the intrinsic difficulty, a great deal of progress has been made in the past 25 years. Experiments have gone from being dominated by high anomalous losses, of the order of Bohm diffusion losses, to operation with no anomalous transport. This success is due to a combination of improved experimental infrastructure and the high degree of knowledge on how to control plasma discharges, Both have made it possible to access enhanced confinement regimes and to unravel new effects in confinement physics. Although there is not yet a complete understanding of the dynamical mechanisms underlying the anomalous transport process, there is some understanding of important components such as the ion transport loss mechanism at the plasma core and of the main mechanism for turbulence suppression in the enhanced confinement regimes.

We consider two-dimensional Yukawa systems in a perpendicular magnetic field. Computer simulations of both one-component and binary systems are used to explore the equilibrium particle dynamics in the fluid state. The mobility is found to scale with the inverse of the magnetic field strength (Bohm diffusion), for strong fields (ωc/ωp≳1). For bidisperse mixtures, the magnetic field dependence of the long-time mobility depends on the particle species, providing an external control of their mobility ratio. At large magnetic fields, the highly charged particles are almost immobilized by the magnetic field and form a porous matrix of obstacles for the mobile low-charge particles.

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.

A model is developed to describe the electrostatic boundary layer in a positively biased magnetic filter in filtered arcs with low collisionality. The set of equations used includes the electron momentum equation, with an anomalous collision term due to micro-instabilities leading to Bohm diffusion, electron mass conservation, and Poisson equation. Analytical solutions are obtained, valid for the regimes of interest, leading to an explicit expression to determine the electron density current to the filter wall as a function of the potential of the filter and the ratio of electron density at the plasma to that at the filter wall. Using a set of planar and cylindrical probes it is verified experimentally that the mentioned ratio of electron densities remains reasonably constant for different magnetic field values and probe bias, which allows to obtain a closed expression for the current. Comparisons are made with the experimentally determined current collected at different sections of a positively biased straight filter. Fil: Minotti, Fernando Oscar. Consejo Nacional de Invest.cientif.y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Fisica del Plasma; Argentina; Fil: Giuliani, Leandro Estanislao. Consejo Nacional de Invest.cientif.y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Fisica del Plasma; Argentina; Fil: Grondona, Diana Elena. Consejo Nacional de Invest.cientif.y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Fisica del Plasma; Argentina; Fil: Della Torre, H.. Consejo Nacional de Invest.cientif.y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Fisica del Plasma; Argentina; Fil: Kelly, Hector Juan. Consejo Nacional de Invest.cientif.y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Fisica del Plasma; Argentina

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.

If shock acceleration of protons is responsible for an appreciable fraction of the non-thermal emission from AGN central engines, they are probably also powerful sources of high energy neutrinos. The neutrino background intensity at the Earth has been predicted by several authors on that basis. This paper describes a calculation of the neutrino spectrum, starting from assumptions about the state of accreting plasma near the central black hole. Our assumptions are closest to those of Stecker and Salamon. where the protons cool by photo-pion production, and neutrino emission is normalised to X-ray emission. However, rather than using the non-relativistic test-particle analytic results for proton acceleration rate and spectral index, we use the results of a numerical code developed at Imperial College, which takes into account aspects of the non-linear shock regime, and shows that relativistic shocks produce a harder spectrum with a faster acceleration time. Also, because of the narrow ranges of plasma properties which permit steady shocks, and doubts about shock stability, we believe that particle acceleration in AGN central engines occurs at transient shocks, small compared with the overall source size, and at a wide range of radii, rather than a single steady shock at a fixed distance from the central black hole, as is usually assumed. Observations of rapid X-ray variability in Seyferts are also suggestive of such a picture. We calculate neutrino spectra for 3C 273, and more importantly, overall background spectra from unresolved AGN, which are compared with other model predictions. We show that with a realistic correction to the Bohm diffusion limit for protons, parallel shocks are unlikely to produce an observable neutrino flux, and quasi-perpendicular relativistic shocks are necessary.

Bohm criterion, originally derived for an isothermal-electron and cold-ion plasma, is often used as a rule of thumb for more general plasmas. Here, we establish a more precise determination of the Bohm criterion that are quantitatively useful for understanding and modeling collisional plasmas that still have collisional mean-free-path much greater than plasma Debye length. Specifically, it is shown that electron heat flux, rather than the isothermal electron assumption, is what sets the Bohm speed to be k B ( T e ∥ + 3 T i ∥ ) / m i with T e , i ∥ the electron and ion parallel temperature at the sheath entrance and mi the ion mass.

This paper presents the behavior of plasma profiles of a sheath in unmagnetized collisionless plasma in the presence of nonextensively distributed two-temperature electrons and isothermal ions. A theoretical model is developed where isothermal ions are described by the conventional hydrodynamic equations along with the effect of electron nonextensivity described by q-distribution function. The plasma sheath parameters like Bohm velocity, potential, and density profiles in the presence of nonextensively distributed two-temperature electrons and isothermal ions are investigated.

Bohm criterion is revisited in the framework of a one-dimensional stationary and unmagnetized low-pressure argon and helium plasma mixture containing non-thermal electrons and dust grains model. Dust grains, electron non-thermality, and ions density ratio effects on Bohm velocities along with dust grain charge number |Φd0|, are investigated. It is revealed that Bohm velocities are highly correlated, with their profiles exhibiting a moving peak. Mixing the two gases allowed the appearance of subsonic (argon) as well as supersonic (helium) Bohm velocities. The present model may be generalized to many ion species plasmas.

The time-dependent solution of diffusion equation by the Fourier integration provides the axial diffusion velocity of a plasma packet, which is a key element of the plasma propagation in a plasma jet operated by the several tens of kHz. The plasma diffusion velocity is higher than the order of un ∼ 10 m/s at a high electric-field region of plasma generation and it is about the order of un ∼ 10 m/s at the plasma column of a low field region in a jet-nozzle inside. Meanwhile, the diffusion velocity is slower than the order of un ∼ 10 m/s in the open-air space where the plasma density flattens due to its radial expansion. Using these diffusion velocity data, the group-velocity of plasma diffusion wave-packet is given by ug ∼ cs2/un, a combination of the diffusion velocity un and the acoustic velocity cs. The experimental results of the plasma propagation can be verified with the plasma propagation in a form of the wave-packet whose propagation velocity is 104 m/s in a tube inside and is as fast as 105 m/s in...

In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B0)(� � /� ⊥ )f or rms magnetic fluctuation b, large-scale mean field B0, and parallel and perpendicular coherence scales � � and � ⊥, respectively. Here we examine the FLRW when R →∞ by taking B0 → 0 for finite bz (fluctuation component along B0), which differs from the well-studied route with bz = 0o rbzB0 as the turbulence becomes quasi-two- dimensional (quasi-2D). Fluctuations with B0 = 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k −1 or k −2 moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B0 → 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.

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.

Localized light emission patterns observed during on time of a high power impulse magnetron sputtering (HiPIMS) discharge on a planar magnetron, known as spokes or ionization zones, have been identified as a potential source of anomalous cross-B field diffusion. In this paper experimental evidence is presented that anomalous diffusion is triggered by the appearance of spokes. The Hall parameter , product of the electron cyclotron frequency and the classical collision time, reduces from Bohm diffusion values ( and higher) down to the value of 3 as spokes appear, indicating anomalous cross-B field transport. A combination of intensified charge coupled device imaging and electric probe measurements reveals that the ions from the spokes are instantaneously diffusing away from the target. The ion diffusion coefficients calculated from a sideways image of the spoke are six times higher than Bohm diffusion coefficients, which is consistent with the reduction of the Hall parameter.

Cosmic ray (CR) acceleration in supernova remnants (SNRs) has been studied for a wide range of interstellar medium (ISM) parameters. The CR transport equation with Bohm diffusion coefficient has been numerically solved self-consistently with gas dynamic equations for the underlying flow. It is shown that CRs are accelerated in SNRs very efficiently, up to 90% of the explosion energy can be absorbed by CRs. At the same time, contrary to the plane-wave and simplified model prediction, the SN shock cannot be completely modified: together with a smooth precursor, the shock front always includes a sufficiently strong subshock. The shock compression ratio σ ∼- M3/4 is an increasing function of the shock Mach number M, it can be much greater than 4, the compression ratio of strong classical shocks. Alfven wave dissipation restricts the shock compression ratio to about 7.3. Acceleration efficiency remains high, about 50% of the explosion energy is absorbed by CRs. The result fits very well with the requirements for the energy density of galactic CRs, and also with their spectral shape in the energy range up to 1015 eV.

[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.

A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as adiabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q = 5/3) and Kraichnan (q = 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of astrophysical environments., 14 pages, 4 figures; comments and references added; to appear in JCAP

In this work, we have generalized the computation of Bohm criterion for electronegative complex plasma. For this, we have established a one‐dimensional, unmagnetized and stationary theoretical model where the positive ions and dust particles are modeled by fluid equations. The electrons and negative ions are considered in thermodynamic equilibrium; therefore they obey to Boltzmann's statistic. In this case, the numerical results show that the generalized Bohm velocity is small compared to the classical value. For electronegative dusty plasma, the corrections are less important.

Electrostatic turbulence and various aspects of magnetic fluctuations have been investigated, in the edge region of the TBR-1 tokamak, by using a set of Langmuir and magnetic probes, and a triple probe. Measurements of plasma parameters such as plasma potential, density, temperature and magnetic field were taken in order to elucidate, the effect on transport of the electrostatic and magnetic fluctuations in the edge. The fluctuations levels are found to be higher than in most tokamaks. The particle flux is outward and slightly higher than that calculated from Bohm diffusion, and occurs in the frequency region typical of the macroscopic MHD oscillations. The Mirnov-oscillation frequencies in TBR-1 are higher than those observed in other tokamaks and, consequently, there is an uncommon superposition between the Mirnov and turbulent density fluctuations spectra. This fact and the presence of high MHD activity may contribute to elucidate the possible influence of the magnetic oscillations on the electrostatic transport observed in the plasma edge.

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.

Summary form only given. Recent experiments have shown that ions in plasmas containing two ion species reach a common velocity at the sheath-presheath boundary. A new theory suggests that collisional friction between the two ion species enhanced by two stream instability dominates the drift velocity of each ion species near the sheath edge but also suggest that there are differences in ion the velocity at the sheath-presheath boundary given by [2/α(v2th1 + v2th2)]½. This suggests that significant differences in velocity will occur as the relative concentration varies and that when the concentrations are very different, each species velocity approaches the individual Bohm velocities. We report the first experimental test of this model. We measure ion velocity distribution functions (ivdfs) near sheath edge in an Argon/Xenon plasma as a function of the concentration ratios. The relative concentration of the two ion species is determined by the Ion Acoustic Wave phrase velocity measurements, the ivdfs are determined by Laser Induced Florescence, the electron temperature is measured by Langmuir probe and the plasma potential is measured by emissive probe.

Recent experiments have shown that ions in weakly collisional plasmas containing two ion species of comparable densities nearly reach a common velocity at the sheath edge. A new theory suggests that collisional friction between the two ion species enhanced by two stream instability reduces the drift velocity of each ion species relative to each other near the sheath edge and finds that the difference in velocities at the sheath edge depends on the relative concentrations of the species. It is small when the concentrations are comparable and is large, with each species reaching its own Bohm velocity, when the relative concentration differences are large. To test these findings, ion drift velocities were measured with laser-induced fluorescence in argon-xenon plasmas. We show that the predictions are in excellent agreement with the first experimental tests of the new model.

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.

A one‐dimensional kinetic code is used to study the effect of ion‐neutral (charge exchange and elastic scattering) and ion‐ion collisions on plasma flow in the downstream region of an electron‐cyclotron‐resonance plasma etching system. Ions are assumed to leave the source region at the Bohm velocity. Argon, nitrogen, and CF4 plasmas are simulated, assuming that the dominant ion species are Ar+, N2+, and CF3+, respectively. Results show that charge exchange and elastic scattering collisions play a significant role in reducing the electrostatic potential variation in the downstream region. For neutral gas pressures above ∼1 mTorr, the potential drop in the downstream region is small, which means that most of the energy with which ions hit the substrate surface is gained while crossing the substrate sheath region. Although the effect of ion‐ion collisions on the plasma potential profile and on the ion distribution function is weak, ion‐ion collisions are responsible for transferring energy from the parallel ...

We have investigated the effect of a nonlinear localized structure obtained through the self-interaction of the interchange mode, on the diffusion in a plasma. The nonlinear localized structure is obtained with periodic boundary conditions in the density gradient direction and a modulation perturbation in the drift direction. We have obtained the expressions of the diffusion tensor in the plane perpendicular to the magnetic field using Fick's law. We have also discussed the nature of the diffusion coefficient's in two limits (i) far from and (ii) close to the linear instability region. It is found that the diffusion due to interchange mode both in the far from and close to linear instability regions far exceeds the diffusion generated by the drift mode.

The heating of the electrons in a plasma by radio frequency (rf) fields results in an electron distribution function that can be highly non‐Maxwellian. The response of these heated electrons can lead to a substantially larger total potential drop than that obtained by arbitrarily choosing a single‐temperature parameter to describe the electron distribution in a traditional Boltzmann approximation. Electromotively driven rf fields can have scale lengths along a static magnetic field line that are much larger than a Debye length and produce electron–sheath interactions that are best described as collisions. Estimates of the floating potential of a plasma that is excited by electromotively driven rf plasma currents parallel to a strong static magnetic field have been made using a Fermi acceleration heating model and linear estimates for the rf fields with plasma. When this non‐Maxwellian distribution function is used for estimates of the static potential, the results show that the total potential drop is proportional to the rf oscillation energy and the square root of the ion to electron mass ratio. Numerical solutions to Poisson’s equation are presented for non‐Boltzmann electrons. Analytic estimates of parasitic rf power absorption and edge profile modification using a Bohm diffusion model are presented. Estimates for a purely electrostatic heating operator with rf fields that are assumed to scale as the Debye length along static magnetic field lines are also made for comparison with the electromagnetic result.

A one-dimensional simulation of a low-pressure RF-driven discharge is used to verify the theoretical prediction of the Bohm velocity of ions at the sheath edge for a two-temperature electron distribution. Simulation results indicate that the Bohm velocity is geared to the cooler species, provided that it contains most of the electrons. A similar comparison is performed for an electronegative plasma. >