Bohm Diffusion Research Articles

Ion Diffusive Transport Across the Separatrix Between the Low‐Latitude Mantle and the Plasma Sheet by Kinetic Alfvén Waves: MMS Observation

AbstractTo understand the entry of the cool low‐latitude mantle ions into the tail plasma sheet near the flanks under persistent interplanetary magnetic field By, we evaluate the role of the cross‐field diffusive transport by kinetic Alfvén waves (KAWs) by investigating two events observed by multiscale (MMS) spacecraft. Around the separatrix between the open and closed field‐line regions, a two‐component mixing of hot plasma sheet ions of a few keV with cool mantle ions of a few hundred eV was observed, indicating transport across the separatrix. The waves observed between 0.01 and 10 Hz around the separatrix had characteristics consistent with those of KAWs. The consistency allowed us to estimate the wave vectors as a function of frequency by fitting KAW dispersion to the observations. Using the observed wave powers, plasma moments, and the estimated wave vectors, we computed the cross‐field diffusion rates associated with KAWs. The diffusion rates were found to be comparable to or larger than the Bohm diffusion rates during the intervals when the two‐component mixing was observed, indicating that the KAW diffusive transport can play a role in the entry of low‐latitude mantle ions into the plasma sheet.

Analysing the effects of heating and gas puffing in Proto-MPEX helicon and auxiliary heated plasmas *

The Material Plasma Exposure Experiment (MPEX) is being constructed at Oak Ridge National Laboratory to investigate critical fusion reactor issues, such as plasma–material interactions (PMIs) under reactor-relevant conditions and time scales. The linear device Proto-MPEX was used as a test bed to address anticipated research and development issues associated with heating scenarios and establish the physics basis for MPEX. The SOLPS-ITER code suite has been applied to understand plasma and neutral transport in Proto-MPEX and to increase confidence in predictive simulations for MPEX. Coupling between COMSOL and SOLPS is performed to implement a 2D electron heating profile of the helicon source. The simulations show reasonable agreement with the experimental data for plasma with helicon and auxiliary electron cyclotron heating (ECH). Both Bohm and constant diffusion (D: 0.5 m2 s−1 and : 1 m2 s−1) simulations show similar levels of agreement with respect to the sparse experimental data available, assuming a few per cent impurity concentration. ECH significantly increases the target electron temperature, however, the target electron density is reduced compared to helicon-only heated plasmas due to an increase in flow velocity and radial losses. The simulations show that further increasing the ECH power results in an increase in the target electron density due to increased recycling flux and ionization. The results indicate that ECH significantly enhances the target heat flux, with ECH power of 50 kW increasing the target heat flux from 0.4 to 17 MW m−2. It is found that a small amount of gas puffing (GP) near the target plate can further increase the target heat fluxes at the higher ECH power cases, but the target heat flux is reduced at higher GP conditions due to a significant reduction in electron temperature via radiation. ECH and GP scenarios can generate a higher target flux, facilitating improved PMI studies with more reactor-relevant plasma conditions.

Study on the influence of magnetic field on the performance of a 5 kW hall thruster

Hall thruster is a kind of plasma optics device, which is used mainly in space propulsion. To study the influence of magnetic field on the performance of a 5 kW hall thruster, a two-dimensional PIC-MCC model was built. The Bohm diffusion was modeled by using a Brownian motion instead of the Bohm collision method and the near-wall conduction was modeled by a secondary electron emission model. When the mass flow rate is 5 mg/s, the thruster performance like thrust, efficiency and discharge current was simulated under a discharge voltage from 300 to 1,000 voltage. At first, the performance under constant magnetic field was simulated. The results showed that the magnetic field could not restrain the electrons as the discharge voltage increased. Later, the performance under varied magnetic field was simulated. The results showed that increasing the magnetic field strength with the increasing discharge voltage could restrain the electrons more efficiently, which proved that increasing the magnetic field strength is necessary for high specific impulse operation of hall thruster. At last, the performance measurement experiment of the thruster was carried out, and the experimental results verified the accuracy of the simulation results.

ON THE PHYSICAL PARAMETERS OF THE STELLARATOR – SOURCE OF NEUTRONS WITH NEOCLASSICAL LOSSES, TAKING INTO ACCOUNT RECYCLING AND BOHM LOSSES

The results of calculations of the physical parameters of the stellarator used as a neutron source for initiating nuclear reactions in a blanket of a hybrid reactor are presented. The calculations were carried out assuming the implementation of neoclassical transport processes, taking into account recycling and Bohm losses. The crushing effect of Bohm diffusion on the results of neutron yields is shown.

Ion Thruster Discharge Modeling with Adjustment of Coefficient of Anomalous Electron Conductivity

The results of plasma simulations in a discharge chamber of a Direct Current gridded ion thruster are dependent on the choice of anomalous electron conductivity model. Usually, additional electron diffusion is used to reproduce the experimental conductivity level. Up-to-date, the existing numerical models use different values of the additional diffusion coefficient, and this choice is often nonrigorous or insufficiently justified. In this research, the influence of the additional diffusion coefficient on the results of an axisymmetrical Full-Particle in Cell simulation of plasma in the discharge chamber of a Direct Current gridded ion thruster was investigated. The modeled thruster had a rated power of 3 kW, a thrust of 85 mN, and a specific impulse of 4500 s. The magnitude of the additional diffusion was varied from zero to the value of Bohm diffusion . gave the best agreement of the simulation results with the experimental data for the chosen thruster. A qualitative analysis of the plasma parameter distributions inside the discharge chamber at various anomalous electron conductivity coefficients is also provided. The profile of the ion current density through the ion-optical system obtained in the simulation is in sufficient agreement with experimental data.

Performance Simulation of a 5 kW hall Thruster

Hall thruster is a kind of plasma optics device, which is used mainly in 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.

Detecting the intrinsic X-ray emission from the O-type donor star and the residual accretion in a supergiant fast X-ray transient in its faintest state

We report on the results of an XMM–Newton observation of the supergiant fast X-ray transient (SFXT) IGR J08408-4503 performed in June 2020. The source is composed of a compact object (likely a neutron star) orbiting around an O8.5Ib-II(f)p star, LM Vel. The X-ray light curve shows a very low level of emission, punctuated by a single, faint flare. We analysed spectra measured during the flare and during quiescence. The quiescent state shows a continuum spectrum that is well deconvolved to three spectral models: two components are from a collisionally ionized plasma (with temperatures of kT1 = 0.24 keV and kT2 = 0.76 keV), together with a power-law model (photon index, Γ, of ∼2.55), dominating above ∼2 keV. The X-ray flux emitted at this lowest level is 3.2 × 10−13 erg cm−2 s−1 (0.5–10 keV, corrected for the interstellar absorption), implying an X-ray luminosity of 1.85 × 1032 erg s−1 (at 2.2 kpc). The two-temperature collisionally ionized plasma is intrinsic to the stellar wind of the donor star, while the power-law can be interpreted as emission due to residual, low-level accretion onto the compact object. The X-ray luminosity contributed by the power-law component only, in the lowest state, is (4.8 ± 1.4)×1031 erg s−1, which is the lowest quiescent luminosity detected from the compact object in an SFXT. Thanks to this very faint X-ray state caught by XMM–Newton, X-ray emission from the wind of the donor star LM Vel could be well-established and studied in detail for the first time, along with a very low level of accretion onto the compact object. The residual accretion rate onto the compact object in IGR J08408-4503 can be interpreted as the Bohm diffusion of (possibly magnetized) plasma entering the neutron star magnetosphere at low Bondi capture rates from the supergiant donor wind at the quasi-spherical, radiation-driven settling accretion stage.

Optimizing the ion diffusion in bipolar-pulse HiPIMS discharge (BP-HiPIMS) via an auxiliary anode

The investigation of plasma dynamics and optimization of target particle diffusion are particularly important and urgent in the recently emerging bipolar-pulse high-power impulse magnetron sputtering (BP-HiPIMS) discharge. In this paper, a novel approach, in which an external auxiliary anode was installed in front of the sputtering target, was proposed to optimize electric field distribution and guide particle diffusion, named as AABP-HiPIMS. A positive pulse voltage was applied to the auxiliary anode in synchronization with the target positive pulse voltage, which was achieved by connecting the target and auxiliary anode through a diode in series. Advantageously, no additional power supply needs to be provided in AABP-HiPIMS. The discharge characteristics of this new plasma source were investigated in detail. A theoretical model was successfully built to reveal the transformation process of the target current from the net ion current to the net electron current by systematically analyzing the collapsing process of the target sheath and charged-particle movement in E × B fields. The optimization of ion diffusion was investigated by diagnosing plasma parameters using a Langmuir probe and emissive probe together. The measurements illustrate that, as expected, the electron density in AABP-HiPIMS during the positive pulse phase has been effectively increased ∼2.5 times on average compared to that in the conventional BP-HiPIMS. Correspondingly, the plasma potential distribution illustrates that the potential gradient pointing to the auxiliary anode centre is more beneficial for control of ion diffusion and to enhance ion flux towards the downstream. Additionally, for better selection of the magnetron process parameters, the characteristic time of plasma decay during the positive pulse was estimated using the Bohm diffusion theory. The rough calculation of flight time for electrons from z = 35 to 95 mm was ∼70 μs in BP-HiPIMS and ∼50 μs in AABP-HiPIMS, respectively. The effects of negative pulse duration and positive pulse amplitude on plasma parameters were investigated. Measurements of plasma potentials suggest that adopting a relatively short duration negative pulse and a slightly higher amplitude positive pulse, as well as employing the externally applied auxiliary anode, are the optimum choices for improving both the flux and energy of deposited particles when preparing films on the floating substrate.

Analytical modeling of the anomalous electron collision frequency in partially magnetized E × B plasmas

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.

Magnetized particle transport in multi-MA accelerators

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), N. Bennett et al., Phys. Rev. Accel. Beams 22, 120401 (2019)]. 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.

Electron dynamics in radio frequency magnetron sputtering argon discharges with a dielectric target

We demonstrate a self-consistent and complete description of electron dynamics in a typical electropositive radio frequency magnetron sputtering (RFMS) argon discharge with a dielectric target. The electron dynamics, including the electron power absorption dynamics in one radio frequency (RF) period, is studied via a fully kinetic 2d3v particle-in-cell/Monte Carlo collision (PIC/MCC) electrostatic simulation. The interplay between the fundamental plasma parameters is analyzed through their spatiotemporal dynamics. Due to the influence of magnetic trap on the electron transport, a spatially dependent charging that perturbs the electric potential is observed on the dielectric target surface, resulting in a spatially dependent ion energy distribution along the target surface. The E × B drift-to-discharge current ratio is in approximate agreement with Bohm diffusion. The electron power absorption can be primarily decoupled into the positive Ohmic power absorption in the bulk plasma region and the negative pressure-induced power absorption near the target surface. Ohmic power absorption is the dominant electron power absorption mechanism, mostly contributed by the azimuthal electron current. The power absorption due to electron inertial effects is negligible on time-average. Both the maximum power absorption and dissipation of electrons appear in the bulk plasma region during the second half of the RF period, implying a strong electron trapping in magnetron discharges. The contribution of secondary electrons is negligible under typical RFMS discharge conditions.

Empirical model of magnetic field line spreading in isotropic turbulence with varying mean field

In many astrophysical phenomena, understanding the diffusion of the magnetic eld line random walk (FLRW) is central to understand cosmic ray transport. In 3D uctuations, the behavior of the FLRW can be characterized by the Kubo number R = (b/B 0)(l ⫽⃥ /l ∧ ) [1], where the parameters b and B 0 are the rms magnetic uctuation and the large-scale mean eld, respectively. The parameters l ∥ and l ∧ are coherence scales parallel and perpendicular to B 0, respectively. For isotropic turbulence, in which l ∥ = l ∧ , Sonsrettee et al. [2] found that Corrsin-based theories can be applied to study the FLRW’s behavior for a whole range of R by varying b/B 0. Sonsrettee et al. [2] used Corrsin-based theory with three models of eld line spreading to examine the R-scaling of the asymptotic diffusion coefficients for the FLRW. The models are the diffusive decorrelation (DD) model [3{5], the random ballistic decorrelation (RBD) model [6], and the ordinary differential equation (ODE) model [7]. To improve the theory of the FLRW in isotropic turbulence with B 0 = 0, Sonsrettee [8] proposed the empirical (EMP) model of magnetic eld line spreading to determine the asymptotic diffusion coefficients. Benchmarked against the previous models, the EMP model is the best model to predict computer simulation results (with ≤ 0:9% error). In this work, we extend the previous works [2, 8] by formulating the EMP model to explore the R scaling FLRW behavior in isotropic magnetic turbulence by varying B 0. In the limit of very low R, we obtain the the closed-form solution of the FLRW for the EMP model. In order to develop the closed-form solution at any R, we employ the Padé approximants to the EMP model. The EMP model predicts that, with increasing R, the FLRW behavior transits from quasilinear diffusion to Bohm diffusion. This work shows that the theoretical results of the EMP model match the computer simulation results for the FLRW in Kolmogorov turbulence better than the other models significantly.

Effects of the dynamic cathode sheath on electron transport at the initial period of HiPIMS pulse studied by Langmuir probe measurements and 2D PIC-MCC simulation

In high power impulse magnetron sputtering (HiPIMS) discharge, the cathode sheath is a particularly vital section which determines the spatial distribution of electric field and the energy and transport of charged particles. In this work, a single Langmuir probe is employed to explore the effects of dynamic cathode sheath on electron transport at the initial period of HiPIMS pulse. Measurements show that the electron temperature is as high as ~20 eV and the plasma density is much lower than ~1015–1016 m−3 at the beginning of HiPIMS pulse t < 3 μs; correspondingly, a feature of small low-energy amplitude and extended high-energy tail is found in the electron energy distribution function (EEDF). And the high-energy electrons can escape the magnetic trap and gradually diffuse to further axial positions, even to z = 140 mm with only several microseconds delay. The diffusion coefficient of electrons D⊥ is larger than the typical Bohm diffusion at z > 32 mm in our discharge case. The two-dimension Particle-in-cell Monte Carlo collision (2D PIC-MCC) simulation results are well in agreement with the experimental results. The net positive charge density ∆n near the target is lower than ~+9.2×1014 m−3 at t = 0.5 μs, and the charge separation is up to ~0.4. In this case, the cathode sheath has a large thickness and the axial electric field EZ outside the sheath is as strong as dozens of 10 kVm−1. The simulation results confirm, for the case of the expanding sheath, (i) the electrons can be accelerated and escape the magnetic trap with weak constraint; (ii) the electron group can maintain their kinetic energy when they diffuse from the ionization region (IR) to bulk plasma (BP). When the net charge density increases to ~+3×1016 m−3 at t = 2.5 μs, the sheath thickness is condensed to ~1 mm with ~600 V voltage drop.

How to Understand the Planck´s Oscillators? Wien Peaks, Planck Distribution Function and Its Decomposition, the Bohm Sheath Criterion, Plasma Coupling Constant, the Barrier of Determinacy, Hubble Cooling Constant. (24.04.2020)

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 &amp;ldquo;Wien Peaks&amp;rdquo; and the Planck Distribution Function and proposed the &amp;ldquo;core-shell&amp;rdquo; model of the photon. There are known many &amp;ldquo;Wien Peaks&amp;rdquo; defined for different contexts. We have introduced a thermodynamic approach to define the Wien Photopic Peak at the wavelength &amp;lambda; = 555 nm and the Wien Scotopic Peak at the wavelength &amp;lambda; = 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&amp;acute;s Oscillators might open a new way for the description of &amp;ldquo;Heat&amp;rdquo; and &amp;ldquo;Light&amp;rdquo; processes.

Stretching of the Super-Elastic Double-Helix Geon. Wheeler´s Thermal Geons as Quanta of Heat and Momentum. Bohm´s Diffusion and the Heating of the Solar Corona and Heating of the Earth - Geon Engineering. Milgrom-Verlinde Constant. Mareš - Šesták constant

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.

Electron extraction enhancement via the magnetic field in a miniature microwave discharge neutralizer

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.

Cosmic ray acceleration in hydromagnetic flux tubes

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.

A Review of Alfvénic Turbulence in High‐Speed Solar Wind Streams: Hints From Cometary Plasma Turbulence

AbstractSolar wind turbulence within high‐speed streams is reviewed from the point of view of embedded single nonlinear Alfvén wave cycles, discontinuities, magnetic decreases (MDs), and shocks. For comparison and guidance, cometary plasma turbulence is also briefly reviewed. It is demonstrated that cometary nonlinear magnetosonic waves phase‐steepen, with a right‐hand circular polarized foreshortened front and an elongated, compressive trailing edge. The former part is a form of “wave breaking” and the latter that of “period doubling.” Interplanetary nonlinear Alfvén waves, which are arc polarized, have a ~180° foreshortened front and with an elongated trailing edge. Alfvén waves have polarizations different from those of cometary magnetosonic waves, indicating that helicity is a durable feature of plasma turbulence. Interplanetary Alfvén waves are noted to be spherical waves, suggesting the possibility of additional local generation. They kinetically dissipate, forming MDs, indicating that the solar wind is partially “compressive” and static. The ~2 MeV protons can nonresonantly interact with MDs leading to rapid cross‐field (~5.5% Bohm) diffusion. The possibility of local (~1 AU) generation of Alfvén waves may make it difficult to forecast High‐Intensity, Long‐Duration AE Activity and relativistic magnetospheric electrons with great accuracy. The future Solar Orbiter and Solar Probe Plus missions should be able to not only test these ideas but to also extend our knowledge of plasma turbulence evolution.

The ecology of flows and drift wave turbulence in CSDX: A model

This paper describes the ecology of drift wave turbulence and mean flows in the coupled drift-ion acoustic wave plasma of a CSDX linear device. A 1D reduced model that studies the spatiotemporal evolution of plasma mean density n¯, and mean flows v¯y and v¯z, in addition to fluctuation intensity ε, is presented. Here, ε=〈ñ2+(∇⊥ϕ̃)2+ṽz2〉 is the conserved energy field. The model uses a mixing length lmix inversely proportional to both axial and azimuthal flow shear. This form of lmix closes the loop on total energy. The model self-consistently describes variations in plasma profiles, including mean flows and turbulent stresses. It investigates the energy exchange between the fluctuation intensity and mean profiles via particle flux 〈ñṽx〉 and Reynolds stresses 〈ṽxṽy〉 and 〈ṽxṽz〉. Acoustic coupling breaks parallel symmetry and generates a parallel residual stress Πxzres. The model uses a set of equations to explain the acceleration of v¯y and v¯z via Πxyres∝∇n¯ and Πxyres∝∇n¯. Flow dynamics in the parallel direction are related to those in the perpendicular direction through an empirical coupling constant σVT. This constant measures the degree of symmetry breaking in the 〈kmkz〉 correlator and determines the efficiency of ∇n¯ in driving v¯z. The model also establishes a relation between ∇v¯y and ∇v¯z, via the ratio of the stresses Πxyres and Πxzres. When parallel to perpendicular flow coupling is weak, axial Reynolds power PxzRe=−〈ṽxṽz〉∇v¯z is less than the azimuthal Reynolds power PxyRe=−〈ṽxṽy〉∇v¯y. The model is then reduced to a 2-field predator/prey model where v¯z is parasitic to the system and fluctuations evolve self-consistently. Finally, turbulent diffusion in CSDX follows the scaling: DCSDX=DBρ⋆0.6, where DB is the Bohm diffusion coefficient and ρ⋆ is the ion gyroradius normalized to the density gradient |∇n¯/n¯| −1.

Interaction of ultracold non-ideal ion–electron plasma with a uniform magnetic field

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