Search

Hall Effect Thrusters (HETs) are nowadays widely used for satellite applications because of their efficiency and robustness compared to other electric propulsion devices. Computational modelling of plasma in HETs is interesting for several reasons: it can be used to predict thrusters’ operative life, moreover, it provides a better understanding of the physical behaviour of this device and can be used to optimize the next generation of thrusters. In this work, the discharge within the accelerating channel and near-plume of HETs has been modelled by means of an axisymmetric hybrid approach: a set of fluid equations for electrons has been solved to get electron temperatures, plasma potential and the discharge current, whereas a Particle-In-Cell (PIC) sub-model has been developed to capture the behaviour of neutrals and ions. A two-region electron mobility model has been incorporated. It includes electron–neutral/ion collisions and uses empirical constants, that vary as a continuous function of axial coordinates, to take into account electron–wall collisions and Bohm diffusion/SEE effects. An SPT-100 thruster has been selected for the verification of the model because of the availability of reliable numerical and experimental data. The results of the presented simulations show that the code is able to describe plasma discharge reproducing, with consistency, the physics within the accelerating channel of HETs. A small discrepancy in the experimental magnitude of ions’ expansion, due probably to boundary condition effects, has been found.

Multi-component active plasmas are modeled in the presence of a constant oblique magnetic field by using the hydrodynamics equations. Assuming the electrons and negative ions have Boltzmann distribution and the positive ions have finite temperature, the sheath formation criterion is derived by analyzing the Sagdeev potential. It is found that the Bohm velocity of positive ions depends sensitively on the plasma parameters such as ion-neutral collision frequency, electron impact ionization frequency, positive and negative ion temperatures, initial densities of the charged particles and direction of the applied magnetic field. Also, using our obtained Bohm criterion, the sheath properties of an active magnetized plasma consisting of electrons and positive and negative ion species are investigated numerically and the results are compared with the results of a similar quiescent plasma.

Hall thruster is a kind of plasma optics device, which is used in material surface treatment and space propulsion. To simulate the discharge process of plasma and the performance of a 5 kW hall thruster, a two-dimensional PIC-MCC model in the R-Z plane is built. In the model, the anomalous diffusion of the electrons including Bohm diffusion and near-wall conduction is modeled. The Bohm diffusion is modeled by using a Brownian motion instead of the Bohm collision method and the near-wall conduction is modeled by a secondary electron emission model. In addition to the elastic, excitation, and ionization collisions between electrons and neutral atoms, the Coulomb collisions are included. The plasma discharge process including the transient oscillation and steady state oscillation is well reproduced. First, the influence of the discharge voltage and magnetic field on the steady state oscillation is simulated. The oscillation amplitude increases as the discharge voltage gets larger at first, and then decreases. While the oscillation amplitude decreases as the magnetic field gets stronger at first, and then increases. Later, the influence of the discharge voltage and mass flow rate on the performance of the thruster is simulated. When the mass flow rate is constant, the total efficiency initially increases with the discharge voltage, reaches the maximum at 600 V, and then declined. When the discharge voltage is constant, the total efficiency increases as the mass flow rate rises from 10 to 15 mg/s. Finally, a comparison between simulated and experimental performance reveals that the largest deviation is within 15%, thereby indirectly validating the accuracy of the model.

Kinetic simulations of Sandia National Laboratories’ Z machine are conducted to understand particle transport in the highly magnetized environment of a multi-MA accelerator. Joule heating leads to the rapid formation of electrode surface plasmas. These plasmas are implicated in reducing accelerator efficiency by diverting current away from the load [M.R. Gomez et al., Phys. Rev. Accel. Beams 20, 010401 (2017)PRABCJ2469-988810.1103/PhysRevAccelBeams.20.010401, N. Bennett et al., Phys. Rev. Accel. Beams 22, 120401 (2019)PRABCJ2469-988810.1103/PhysRevAccelBeams.22.120401]. The fully-relativistic, electromagnetic simulations presented in this paper show that particles emitted in a space-charge-limited manner, in the absence of plasma, are magnetically insulated. However, in the presence of plasma, particles are transported across the magnetic field in spite of being only weakly collisional. The simulated cross-gap currents are well-approximated by the Hall current in the generalized Ohm’s law. The Hall conductivities are calculated using the simulated particle densities and energies, and the parameters that increase the Hall current are related to transmission line inductance. Analogous to the generalized Ohm’s law, we extend the derivation of the magnetized diffusion coefficients to include the coupling of perpendicular components. These yield a Hall diffusion rate, which is equivalent to the empirical Bohm diffusion.

The breakthrough of the tokamak with the Russian success in overcoming Bohm diffusion and plasma confinement problems, announced at the 1968 Novosibirsk conference, was the second pivotal moment. It ushered in a new optimistic era for fusion, forcing a drastic, but premature change of direction from purely scientific research (understanding how something works) to energy generation (making it work to a useful end). The fundamentals of tokamaks are introduced (design, fundamental parameters, bootstrap current, D-shape plasmas, divertor) in this chapter.

International audience; Magnetic cusps have been used for more than 50 years to limit charged particle losses to the walls and confine the plasma in a large variety of plasma sources or ion sources. Quantification of the effective loss area has been the subject of many experimental as well as theoretical investigations in the 1970-1990's. In spite of these efforts there is no fully reliable expression of the effective wall loss as a function of cusp magnetic field, electron temperature, ion mass, gas pressure, etc… We describe in this paper a first attempt at obtaining scaling laws for the effective loss width of magnetic cusps, based on two-dimensional PIC MCC (Particle-In-Cell Monte Carlo Collisions) simulations. The results show that the calculated leak width follows a 1/B scaling in the collisionless low B limit, is approximately proportional to the hybrid gyroradius with an ion velocity equal to the Bohm velocity and is proportional to the square root of gas pressure in the collisional limit.

A constant mean free path collisional plasma sheath model is investigated in the presence of two-temperature q-nonextensive electrons and fluid ions. By using Sagdeev potential technique, a modified Bohm sheath criterion is derived and also verified. It is shown that the density distribution of positive ions reduces monotonically when the Bohm velocity lies between the derived limits. The effect of collision on the plasma sheath profiles viz. density, potential, net space charge density and positive ion velocity in the sheath in presence of the proposed plasma configuration is investigated. It is also shown that the increasing values of ion-neutral collisionality leads to a decrease of sheath thickness, increase of sheath potential and net space charge density in the sheath region.

Plasma characteristics in the gap at lowered pressure in the presence of primary electrons are analyzed for the hydrodynamic model in the cold ion approximation. It is demonstrated that at a certain critical ionization level, the plasma state changes abruptly. The potential drop in the plasma can be not only more, but also less than ln(2)kTe/e, and hence the velocity of ions exiting from the plasma can be more or less than the Bohm velocity. For low ionization intensity and formation of the plasma with a high fraction of primary electrons, the velocity of secondary electron exiting from the plasma becomes equal to their thermal velocity, and their distribution differs significantly from the Boltzmann distribution.

The characteristics of sheath in a plasma system containing q-nonextensive electrons, cold fluid ions, and Boltzmann-distributed negative ions are investigated. A modified Bohm sheath criterion is derived by using the Sagdeev pseudopotential technique. It is found that the proposed Bohm velocity depends on the degree of nonextensivity (q), negative ion temperature to nonextensive electron temperature ratio (σ), and negative ion density (B). Using the modified Bohm sheath criterion, the sheath characteristics, such as the spatial distribution of the potential, positive ion velocity, and density profile, have been numerically investigated, which clearly shows the effect of negative ions, as well as the nonextensive distribution of electrons. It is found that, as the nonextensivity parameter and the electronegativity increases, the electrostatic sheath potential increases sharply and the sheath width decreases.

An analytical model for the anomalous electron collision frequency is proposed to predict the cross-field mobility of electrons in partially magnetized E × B plasma devices. The proposed model can be implemented through a dimensional analysis based on the electron momentum equations perpendicular to the magnetic field. To test the validity of the proposed method, it is applied to a 1D steady fluid analysis for a Hall thruster. The results show that compared to the Bohm diffusion model, the proposed model can yield more physically appropriate prediction results in terms of axial distributions for the anomalous electron collision frequency and azimuthal electron mean velocity.

From the static polarization function of electrons in the random phase approximation, the quantum Bohm potential for the quantum hydrodynamic description of electrons and the density gradient correction to the Thomas–Fermi free energy at a finite temperature for the two- and one-dimensional cases are derived. The behaviour of the Bohm potential and of the density gradient correction as a function of the degeneracy parameter is discussed. Based on recent developments in the fluid description of quantum plasmas, the Bohm potential for the high-frequency domain is presented.

The present paper deals with a particular case involving a magnetic field, namely that of a positive column situated in an axial magnetic field, and it is shown that the Bohm criterion still holds for the normal component of the ion velocity at the plasma boundary. This result is of considerable interest because the Boltzmann relation for the electron density has not been assumed. It can be recalled that the criterion was originally derived by Bohm using the Boltzmann relation for the electron density. In the present case a Boltzm ann gradient conditionhas been found at the plasma boundary which leads to the usual Bohm velocity. Some insight can be gained by considering the ion and electron densities plotted against potential, for both the plasma and the sheath regions. It would appear that the result is a general one applicable to other situations.

Transports of plasmas in the edge of fusion devices have similarities in terms of formation of a free presheath and unclear explanation on the transport process relating the diffusion coefficient ( D ⊥ ) to characteristic length of perturbing for flux tube ( L c ). D ⊥ and L c are investigated by generating perturbations in various free presheaths due to a perturbing object located at the axial center of a linear plasma device, called DiPS (Divertor Plasma Simulator). Free presheaths are generated due to a tungsten perturbing object by changing the magnetic flux density. Bounded presheaths are also formed due to a limiting structure of a magnetic nozzle and due to the given geometry of DiPS. In terms of plasma discharge currents, radial plasma profiles were measured by using a fast scanning probe system. D ⊥ and L c within the free presheath regions were calculated by using the measured plasma parameters and compared with those of bounded presheaths near the chamber walls. Decay length of plasma density was introduced to calculation of D ⊥ . To calculate the perturbation length (L) of free presheaths, a theoretical scale factor K was introduced as L = K L c using a fluid model. Normalized factor δ = D ⊥ / D B , where D B = Bohm diffusion coefficient, were obtained as 8 at free presheaths and 11 at bounded presheaths.

We find that hydromagnetic flux tubes in back-flows in the lobes of radio galaxies offer a suitable environment for the acceleration of cosmic rays (CR) to ultra-high energies. We show that CR can reach the Hillas (1984) energy even if the magnetised turbulence in the flux tube is not sufficiently strong for Bohm diffusion to apply. First-order Fermi acceleration by successive weak shocks in a hydromagnetic flux tube is shown to be equivalent to second-order Fermi acceleration by strong turbulence., Accepted for publication in the Monthly Notices of the Royal Astronomical Society on 31st May 2019

A 100 W radial scaled Hall Thruster has been designed and manufactured using as reference design the D-55 thruster with anode layer (TAL). The magnetic field required is provided by permanent magnets following a modular design in order to compare three different magnetic field configurations: A) nominal, B) orthogonal magnetic field and C) high magnetic field. In Hall Thrusters the magnetic field is used to confine the electrons and create highly ionized plasma. Configuration A and configuration B were chosen to compare two different topographies of the magnetic field with two different magnetic field gradients and to study their influence in the plasma discharge and thruster performance. Both configurations where derived assuming Bohm diffusion as the dominant process in the plasma discharge. If instead of Bohm diffusion it is considered electron-wall collisions as main mechanism in the electron transport then a higher magnetic field is required and in consequence configuration C was designed. These three configurations are intended to provide a better understanding of the influence of the magnetic field in the thruster discharge.

The two approaches to describe the diffusion process of test particles in a two-dimensional random velocity field are compared to each other: the method of decorrelation trajectories and the moment approximation. The frozen turbulence case is considered, because it is the most complicated test for statistical theories. The results of considered analytical approaches are verified by direct numerical simulation., На основi детального аналiзу порiвняно два пiдходи до опису дифузiї частинок у двовимiрному випадковому полi швидкостi, а саме метод декорельованих траєкторiй та наближення моментами. Розглянуто заморожену турбулентнiсть, оскiльки вона є найбiльш складним тестом для перевiрки статистичних теорiй. Результати аналiтичних наближень порiвняно з даними числового моделювання.

Kinetic theory has been employed to investigate the magnetized plasma-sheath structure and its characteristics in the presence of more than one species of negatively charged particles: hot electrons, cold electrons, and negative ions. The cold electrons and negative ions are considered to obey a Maxwellian distribution, whereas the hot electrons follow a truncated Maxwellian distribution. The Bohm sheath condition has been extended for the case of more than one species of negatively charged particles, in which the concentration of hot electrons has a crucial role in achieving the Bohm velocity. The thermal motion of hot electrons is much higher compared to cold electrons and negative ions, such that the variation of hot electron concentrations and the temperature ratio of hot to cold electrons play a key role in the determination of the plasma-sheath parameters: particle densities, electrostatic potential, the flow of positive ions towards the wall, and sheath thickness. We have estimated the deviation of the resultant drift velocity of positive ions on the plane perpendicular to the wall from the parallel component at the presheath–sheath interface. It is found that the deviation between the two velocity components increases with an increase in the obliqueness of the magnetic field. Furthermore, the results obtained from the kinetic trajectory simulation model are compared with the results obtained using a fluid model; the results are qualitatively similar, although the potential varies by less than 4% in terms of the magnitude at the wall.

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 one-dimensional hydrodynamic model is developed for a magnetized plasma sheath, consisting of Maxwell electrons, q-non-extensive electrons, and thermal ions. A significant change is observed in the quantities characterizing isolated dust particles in the presence of superextensive electrons (q

Taking into account the dust grain size distribution, the Bohm criterion is revisited by means of a one-dimensional, stationary, and non-magnetized theoretical model. An argon plasma is considered where the electrons are characterized by the Boltzmann distribution; however, the other species are described by the fluid equations. The dust grain charge number is described by the orbit motion limited model and their size is modeled by a Gaussian law. The generalized Bohm criterion has been calculated by using the Sagdeev's pseudo-potential approach. The numerical results show that the Bohm velocity values are greater than those of the classical model where the dust grains are absent, and they exhibit a peak. Moreover, by taking into account the dust size distribution, the obtained Bohm velocity values are practically comparable to those found in the mono-size model for a mean radius of the dust grains. Furthermore, it is found that the presence of mono-energetic electrons increases the Bohm velocity values. The dust grain surface potential at equilibrium is also calculated and discussed.

In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. Based on the great works of Wilhelm Wien and Max Planck we have presented a new look on the “Wien Peaks” and the Planck Distribution Function and proposed the “core-shell” model of the photon. There are known many “Wien Peaks” defined for different contexts. We have introduced a thermodynamic approach to define the Wien Photopic Peak at the wavelength λ = 555 nm and the Wien Scotopic Peak at the wavelength λ = 501 nm to document why Nature excellently optimized the human vision at those wavelengths. There could be discovered many more the so-called Wien Thermodynamic Peaks for other physical and chemical processes. We have attempted to describe the so-called Planck oscillators as coupled oscillations of geons and dyons. We have decomposed the Planck distribution function in two parts. Inspired by the Bohm Diffusion and the Bohm Sheath Criterion we have defined the plasma coupling constant that couple oscillations of geons and photons. The difference of the Planck least action of photons and the least action of geons might define the Barrier of Determinacy that create a limit for the resolution in the Microworld. We have newly formulated the Hubble cooling constant and inserted it into the Newton-Zwicky Cooling Law of photons for the description of the cooling of old photons. This proposed view on Planck´s Oscillators might open a new way for the description of “Heat” and “Light” processes.

A double flush-mounted probe method is proposed to analyze the characteristics of intermediate-pressure plasmas (10–100 Pa) by a sheath criterion. The analytical model mainly focuses on the effect of the ion drift velocity in the sheath edge and then provides a correction factor for the measured ion-collection current. The reduction of the ion current is attributed to ion–neutral collisions leading to the modified Bohm velocity. To validate this method, the ion density is calculated and compared with that measured by two types of cylindrical probes, and the results agree well with the data measured by other probes. On the basis of this work, the double flush-mounted probe can be adopted to diagnose plasma parameters accurately, without a reference electrode, in collisional and certain complex plasma environments, such as the reentry plasma sheath.

In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. Based on the great works of Julian Schwinger and John Archibald Wheeler we will study properties of geons formed by fusion of two soft x-ray particles (dyons) in the Schwarzschild gravitation core in our Sun at temperature 16 * 106 K. There are now several Teams that are able to achieve this fusion temperature in their special instruments (Tokamak, HL-2M Tokamak, Wendelstein 7-X, NIF, etc.) and to study properties of those formed geons. Thermal geons are with us all the time but they are very deeply hidden in our experiments. We have newly introduced Mareš - Šesták constant as the ratio of geon momentum to heat quantum of geon. The key information to enter into the World of geons was the empirical formula of David Bohm - the very well-known Bohm diffusion. From this formula we have extracted the amplitude, wavelength, frequency, quantum of the geon action, displacement law for geons, etc. It was found that geons are highly sensitive to the magnetic field strength. At a low magnetic field strength, the “inflation of geons” can occur. This effect could explain the Superheating of the Solar corona and the observed Heating of the Earth during two last centuries influenced by the changes in the Earth´s magnetic field. Geon engineering might modify the geon volume through the magnetic field strength. On the other hand, we were stimulated by the works of Mordehai Milgrom and Eric Verlinde and derived the Milgrom-Verlinde constant describing the gravitational field strength leading to the Newtonian gravitational constant on thermodynamic principles. The quantum of the geon momentum might open a new way how to understand gravitational phenomena. Can it be that Nature cleverly inserted geons into our experimental apparatuses and into our very-well known Old Formulae? We want to pass this concept into the hands of Readers of this Journal better educated in the Mathematics, Physics, and Thermodynamics.

International audience; Edge-to-center plasma density ratios – so-called h factors – are important parameters for global models of plasma discharges as they are used to calculate the plasma losses at the reactor walls. There are well-established theories for h factors in the one-dimensional case. The purpose of this paper is to establish h factors in two-dimensional (2D) systems, with guidance from a 2D particle-in-cell (PIC) simulation. We derive analytical solutions of a 2D fluid theory that includes the effect of ion inertia, but assumes a constant (independent of space) ion collision frequency (using an average ion velocity) across the discharge. Predicted h factors from this 2D fluid theory have the same order of magnitude and the same trends as the PIC simulations when the average ion velocity used in the collision frequency is set equal to the ion thermal velocity. The best agreement is obtained when the average ion velocity varies with pressure (but remains independent of space), going from half the Bohm velocity at low pressure, to the thermal velocity at high pressure. The analysis also shows that a simple correction of the widely-used 1D heuristic formula may be proposed to accurately incorporate 2D effects.

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

International audience; To address the so-called Bohm boundary conditions, generally imposed at the walls that intercept in a tokamak the magnetic field lines, we consider a simple one-dimensional hyperbolic system that constitutes a minimal transport model for ionic density and momentum. We show that as soon as the solution is smooth, a spectrally accurate approximation can be obtained. To this end, we describe a stabilized spectral element method (SEM) and propose a direct imposition of the Bohm boundary condition in an explicit time marching.

The broad-band X-ray observations of the youngest known galactic supernova remnant, G1.9+0.3, provide unique information about the particle acceleration at the early stages of evolution of supernova remnants. Based on the publicly available X-ray data obtained with the Chandra and NuSTAR satellites over two decades in energy, we derived the energy distribution of relativistic electrons under the assumption that detected X-rays are of entirely synchrotron origin. The acceleration of electrons was found to be an order of magnitude slower than the maximum rate provided by the shock acceleration in the nominal Bohm diffusion regime. We discuss the implications of this result in the context of contribution of SNRs to the Galactic Cosmic Rays at PeV energies., 6 pages, 5 figures sibmitted to A&A

The spectral shape of the synchrotron X-ray emission from SN 1006 reveals the fundamental role played by radiative losses in shaping the high-energy tail of the electron spectrum. We analyze data from the XMM-Newton SN 1006 Large Program and confirm that in both nonthermal limbs the loss-limited model correctly describes the observed spectra. We study the physical origin of the observed variations of the synchrotron cutoff energy across the shell. We investigate the role played by the shock velocity and by the electron gyrofactor. We found that the cutoff energy of the synchrotron X-ray emission reaches its maximum value in regions where the shock has experienced its highest average speed. This result is consistent with the loss-limited framework. We also find that the electron acceleration in both nonthermal limbs of SN 1006 proceeds close to the Bohm diffusion limit, the gyrofactor being in the range η ∼ 1.5-4. We finally investigate possible explanations for the low values of cutoff energy measured in thermal limbs.

This study analyzes the dependence of electron extraction efficiency, which is defined as the ratio of the extracted electron current to the generated electron current, on the orifice shapes and magnetic fields of a miniature microwave discharge xenon neutralizer via three-dimensional particle-in-cell simulations with Monte Carlo collisions (PIC–MCCs). The PIC–MCC simulation results show that the orifice shapes do not significantly affect the discharge characteristics or the electron extraction efficiency. However, the efficiency achieves a 1.5-times higher value in a new magnetic field configuration, referred to as MF-2, where the magnetic field lines pass through nearly the entire area of the orifices. This improvement is attributed to the reduction in the electron backflow and the electron loss toward both the downstream inside surface and the outside wall of the discharge chamber. In addition, there are relatively small plasma fluctuations in the discharge chamber for MF-2 due to its low Bohm diffusion coefficient, where no rotating spokes, which are often seen in other E ×B devices, are observed. As a result, the electron loss toward the downstream surface inside the discharge chamber is reduced, and this decrease in the electron loss also contributes to the increase in the extraction efficiency., This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Y. Sato et al., Jnl. of App. Phy. 126, 243302 (2019) and may be found at https://doi.org/10.1063/1.5127805.

An analytic solution is presented in this paper for the electric potential near a wall in a confined plasma. This is well fitted for both the sheath and pre-sheath regions. In the sheath region, the potential is well adapted to the differential equation proposed by Bohm. In the pre-sheath region, the potential is also well suited, decaying to zero electric field in the plasma, which is a physical condition. The potential is also valid for any value of the parameter K measuring the dimensionless Bohm velocity.

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.

Nonlinear magnetoacoustic waves in dense electron-positron-ion plasmas are investigated by using three fluid quantum magnetohydrodynamic model. The quantum mechanical effects of electrons and positrons are taken into account due to their Fermionic nature (to obey Fermi statistics) and quantum diffraction effects (Bohm diffusion term) in the model. The reductive perturbation method is employed to derive the Korteweg-de Vries (KdV) equation for low amplitude magnetoacoustic soliton in dense electron-positron-ion plasmas. It is found that positron concentration has significant impact on the phase velocity of magnetoacoustic wave and on the formation of single pulse nonlinear structure. The numerical results are also illustrated by taking into account the plasma parameters of the outside layers of white dwarfs and neutron stars/pulsars.

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

When a material spreads in turbulent flow, areas with high concentration are formed by the local turbulence. These high concentration islands can lead to heavy damage. In this study, the high concentration areas are extracted as pulses by a conditional sampling technique, and statistical analysis were performed in order to investigate the difference between the pulses and concentration plume. Assuming homogeneous flow, a series of images by Planar Laser Induced Fluorescence and Particle Image Velocimetry techniques are acquired at several downstream positions. For PLIF images, a conditional sampling technique is used to extract the high concentration areas. For simultaneous PIV and PLIF images, wavelet analysis is performed to probe into the relationship between high concentration pulses and velocity fluctuation. Turbulent diffusion coefficient of the high concentration areas is found to increase with the downstream distance whereas that of the concentration plume is constant, which implies that the diffusion process of the pulses differs from that of the plume. Besides by wavelet analysis result, it is indicated that concentration fluctuation in the pulses is negatively correlated with streamwise velocity fluctuation. It is concluded that high concentration pulses and plume have different generative mechanisms.

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 magnetized liner inertial fusion (MagLIF) approach to inertial confinement fusion [1] involves subsonic/isobaric compression and heating of a deuterium-tritium plasma with frozen-in magnetic flux by a heavy cylindrical liner. In order to understand the transport of magnetic flux, a recent paper [2] developed self-similar solutions in one dimension for the loss of heat and magnetic flux from a semi-infinite planar medium of high plasma beta and constant pressure to a liner wall due to diffusion and advection. The resistive diffusion included the Nernst effect based on the classical Branginskii plasma transport terms. These solutions were compared against a one dimensional Lagrangian code that also included the Ettingshausen effect in the thermal diffusion. The present work generalizes the results of [2] in two ways. First, we demonstrate new exact self-similar solutions obtained for a planar geometry and suitable for code verification, such as magnetic reconnection. Second, we use our Lagrangian code to address a similar problem of heat and flux loss in a transverse magnetic field but for a deuterium plasma bounded by a cylindrical liner of finite radius. In a finite volume the plasma may stay isobaric, but the pressure cannot remain constant in time because of heat losses to the liner. Consequently, exact self-similar solutions are not possible, and the above mentioned numerical code, verified in [2], is extended to cylindrical geometry. We will investigate the case with large electron Hall parameter and large plasma beta to determine if the effective diffusion coefficients for heat and magnetic flux losses decrease inversely with the first power of the Hall parameter, as in the planar case and in Bohm diffusion, or more strongly.

We present an ordinary case in the momentum diffusion equation for the electron spectrum evolution and investigate the energy spectra and time dependent properties of flare in Mrk 421 in the frame of a time-dependent one-zone synchrotron self-Compton model. In this model, electrons are accelerated to extra-relativistic energy through the strong magnetic turbulence and evolve with time, and non-thermal photons are produced by both synchrotron and inverse Comtpon scattering off synchrotron photons. Moreover, non-thermal photons during a pre-flare are produced by the relativistic electrons in the steady state and those during a flare are produced by the electrons whose injection rate is changed during some time interval. We apply the model to the energy spectra and time-dependent properties of flares in Mrk 421 by reproducing the pre-burst spectrum of the source and varying the injection rate in the Bohm diffusion (q=1) and the hard sphere approximation (q=2) case, respectively. Our results show that Bohm diffusion case leads to hard photon spectra, and hard sphere case approximation seems to reproduce the energy spectra and the time dependent properties of flare still better., Comment: 10 pages, 7 figures, published in MNRAS (2014MNRAS.442.3166Z)

The most common type of electric propulsion in space exploration is the Hall Effect Thruster (HET), mainly due to its high specific impulse and high thrust to power ratio. However, uncertainties about the thruster's lifetime prediction have prevented widespread integration of HETs. Among these limitations, wall erosion of acceleration channel is of greatest concern. The experimental methods of erosion are time consuming and costly, and they are often limited to one single configuration. Hence, developing a computational model not only decreases the costs but also shortens the design time of a HET. This thesis investigates the feasibility of a uid erosion modelling with a multi-physics software (COMSOL) to further decrease the time and the development cost. First of all, this thesis provides an overview of available plasma modelling techniques and the physics behind the erosion phenomenon. Moreover, the effective parameters and available modules in the multiphysics software as well as their theoretical background were studied and discussed in detail. The Electron Anomalous phenomenon and pressure instability are determined as the main limiting factors for such a model. A non-magnetized model is included to find an optimal value for pressure and to reduce the probability of pressure instability occurrence in magnetized model. To fulfill this task, several simulations for various pressure values (0.005 Torr, 0.05 Torr, and 0.5 Torr) were conducted. Next, the simulation of magnetized/full model has been carried out with addition of magnetic coils in non-magnetized model. To avoid the Electron Anomalous phenomenon, the Bohm diffusion approach was implemented. In addition, a full Particle-In-Cell (PIC) simulation of a typical HET (SPT-100) with the similar input parameters as in fluid model was conducted, and the results were compared and validated using experimental data. The PIC model was intended to be utilized to investigate the accuracy of erosion model in multiphysics software. The results of this thesis indicate that current application of erosion model in COMSOL is not possible whilst high accuracy of the erosion model based on PIC approach can be achieved. Finally, the application of semi-empirical method through direct input of magnetic field data can allow short time simulation of a HET in COMSOL to gain insight about the preliminary behaviour of plasma, however, the simulation of an erosion model requires either a built-in PIC algorithm in COMSOL or a PIC based code.

Bohm’s mechanics was built for explaining individual results in measurements, and mainly for getting rid of the enigmatic reduction postulate. Its main idea is that particles have at any time definite positions and velocities. An additional axiom is that particles follow continuous trajectories that admit the first derivative in time, the velocity. In the quantum theory, if the position of a quantum object is well-defined at some time, a Δt time later the object may be found anywhere in space, so, the velocity defined as Δx/Δt is completely undefined. This incompatibility is regarded in standard quantum theory as nature’s property. The disagreement between quantum and Bohm’s mechanics is particularly strong in wave-like phenomena, e.g. interference. For a particle traveling through an interference fringe, Bohm’s velocity formula shows a dependence of the time-of-flight on the fringe length. Such a dependence is not supported by the quantum theory. Thus, for deciding which prediction is correct one has to measure times-of-flight. But this is a problem. If one detects a particle at two positions and records the detection times, the time difference is meaningless, because the first position measurement disturbs the particle’s Bohm velocity (if exists). This text suggests a way around: instead of measuring positions and times, the particles are raised to an excited, unstable level, by passing them through a laser beam. The unstable level will decay in time, s.t. the density of probability of the excited atoms will indicate the time elapsed since excitation. For comparing the Bohmian and quantum predictions, this text proposes in continuation to send the beam of excited particle upon a mirror. Bohm’s velocity leads to anomalies in the reflected wave.

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.

We employ a recently developed test-particle simulation code to explore the Bohm diffusion and the scattering anisotropy of charged particles interacting with magnetic turbulence. By computing parallel and perpendicular mean free paths, it is shown that a dominant mean magnetic field and a large particle mean free path along the mean magnetic field break the scattering symmetry. In such cases, a strong scattering anisotropy is found, which is in good agreement with recent analytical calculations. It is also shown that the assumption of the Bohm diffusion in isotropic turbulence is only valid for some special cases.

A semi-analytical static sheath (SASS) model can provide a spatial potential profile on a biased surface with microstructures, which can be used for predicting ion trajectories on the surface. However, two- or three-dimensional SASS models require a search procedure for a sheath edge equipotential profile, at which ions have the Bohm velocity, as the starting positions for calculating ion trajectories. This procedure can be troublesome when surface microstructures have complex structures. This difficulty is due to the fact that the SASS model cannot handle a presheath region. In this work, we propose a modified SASS model that can handle a presheath region. By using the modified SASS model, ion trajectories can be calculated from edges with arbitrary geometry without searching for the equipotential profile corresponding to sheath edges.

A 1-D fluid code simulation of the region above the racetrack in a magnetron discharge has been developed to yield predictions for the temporal evolution of the axial plasma parameters during pulsed DC operation. To take into account anomalous cross-field diffusion transport rates, an effective magnetic field profile has been calculated based on the real experimental values, to yield ratios in the effective electron gyro and collision frequencies comparable with Bohm diffusion. Pulse frequencies from 100 to 500 kHz are considered, with gas pressures ranging from 0.25 to 0.65 Pa. The model results for the plasma potential, electron and ion densities, during the pulse cycle agree well with experimental measurements made in the Liverpool magnetron using time-resolved Langmuir and emissive probes. In the bulk plasma, the predictions for electron temperature are close to the measured values; however, in the sheath region they are artificially high due to the model assumption that only Maxwellian distributed electrons exist in all regions of the discharge. This inadequacy in the model and the methods to improve has been discussed. Results for DC magnetrons are also shown.

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.