Electron Larmor Radius Research Articles

Electron-scale turbulence characteristics with varying electron temperature gradient in LHD

Electron-scale turbulence, whose wavelength is the electron Larmor radius, is thought to have the potential to cause stiffness in an electron temperature gradient and degrade the confinement of future burning plasma in which the electron heating by alpha particles is dominant. The dependence of electron-scale turbulence and electron heat flux on the electron temperature inverse gradient length Rax/LTe , were investigated. The electron temperature gradient was successfully varied in the range of −3<Rax/LTe<12 by controlling the injection power of on/off-axis electron cyclotron heating. The results show a significant increase in the electron-scale turbulence with increasing Rax/LTe , especially in conditions where Electron Temperature Gradient (ETG) instability is linearly unstable, suggesting the presence of ETG turbulence at high Rax/LTe . The electron heat flux also increases steeply with increasing Rax/LTe . In addition, the electron-scale turbulence is observed even at Rax/LTe∼0 , which is stable in linear GKV calculations. Finding the cause of this phenomenon is an interesting task for the future.

The role of electron current in high-β plasma equilibria

This paper is aimed at investigating the role of electrons in creation of currents in plasma equilibria with high plasma pressure (β≈1). Despite the long history of studies of these equilibria, there is still no consensus on what kind of particle species is responsible for the creation of the diamagnetic current and what characteristic size the current layer should have. For example, simulations of isothermal plasma injection into a multi-cusp magnetic trap [J. Park et al., Front. Astron. Space Sci. 6, 74 (2019)] demonstrate the formation of a transition layer with a thickness comparable to the electron Larmor radius, where the equilibrium current is carried by electrons. At the same time, studies of a diamagnetic bubble created by a hot-ion plasma in a mirror trap [I. Kotelnikov, Plasma Phys. Control Fusion 62, 075002 (2020)] assume ion dominance and completely ignore electron currents. In this paper, we show that the equilibrium initially governed by the ion diamagnetic current is unstable against perturbations at the ion-cyclotron frequency harmonics, and this instability forces the plasma to come to a new equilibrium state in which the current is mainly created by the E×B-drift of electrons. The same type of equilibrium is also found to form in a more realistic problem setup when plasma is continuously injected into the uniform vacuum magnetic field.

Investigation of the collisionless plasmoid instability based on gyrofluid and gyrokinetic integrated approach

In this work, the development of two-dimensional current sheets with respect to tearing modes, in collisionless plasmas with a strong guide field, is analysed. During their nonlinear evolution, these thin current sheets can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. We carry out a detailed study of the effect of a finite $\beta _e$ , which also implies finite electron Larmor radius effects, on the collisionless plasmoid instability. This study is conducted through a comparison of gyrofluid and gyrokinetic simulations. The comparison shows in general a good capability of the gyrofluid models in predicting the plasmoid instability observed with gyrokinetic simulations. We show that the effects of $\beta _e$ promotes the plasmoid growth. The effect of the closure applied during the derivation of the gyrofluid model is also studied through the comparison among the variations of the different contributions to the total energy.

Influence of plasma parameters on the effectiveness of multi-cusp magnetic field confinement in negative ion sources

Cusp-shaped magnetic fields are widely used to confine plasmas in various applications. This field configuration allows to localise plasma losses: the width of such loss cone, usually called leak width, was found to be proportional to the geometric mean of the ion and electron Larmor radii, so that it becomes smaller for increasing magnetic field intensity. At the same time, plasma diffusion towards the walls is reduced in the regions where the field lines are parallel to the surfaces, leading to the formation of a Plasma Exclusion Zone (PEZ) whose characteristic dimension was found to be proportional to the distance between the magnets. Besides field intensity and geometry, the confinement effectiveness might also be affected by plasma properties such as electron temperature, plasma potential across the sheath and collisionality. Specifically, this contribution describes a numerical analysis performed by means of a 2D-3V Particle-In-Cell code of the dependencies of both the PEZ size and the leak width on magnetic field intensity and plasma potential, focusing on typical conditions found in plasma sources for negative ion beams. The leak width was found to be larger than its theoretical prediction regardless of the specific plasma parameters. The PEZ was found to be affected not only by the distance between the magnets. In particular, the plasma potential was found to strongly affect the plasma behaviour within the cusp region.

Spatial structures of rf ring-shaped magnetized sputtering plasmas with two facing cylindrical ZnO/Al2O3 targets

Spatial structures of the ion flux to the substrate are measured in an rf ring-shaped magnetized sputtering plasma with two facing cylindrical ZnO/Al2O3 targets at various argon gas pressures of 0.13, 0.67, and 0.93 Pa. Spatial distributions of the Hall parameter and Larmor radius of electrons and ions are also discussed by using simulated values of the magnetic flux density. The magnitude of the ion flux for 0.13 and 0.67 Pa is of the order of 1020 m−2 s−1, while for 0.93 Pa it is of the order of 1021 m−2 s−1 at a fixed rf power of 20 W. The radial profile of the ion flux has a peak at the position of the ring-shaped groove near an rf electrode and then becomes uniform further away from the electrode at all gas pressures. It is found that the axial profile of the deviation from a uniform profile estimated from the radial profile of the ion flux has two decay characteristics (1st decay length of 13.9–17.5 mm and 2nd decay length of 52.6–66.7 mm) and their decay lengths decrease with increasing the gas pressure.

Formation of a Plasma Layer During the Passage of the Moon through the Magnetic Ropes of the Solar Wind

In the absence of a dense atmosphere and a general magnetic field around the Moon, solar wind particles reach the lunar surface and are almost completely absorbed. When the Moon passes through the plasma medium of the solar wind magnetic ropes, the electric currents of the rope can strongly change the electric potential of the lunar surface on the day and night surfaces, and in the case when the current density vectors of the rope and the direction to the Sun are close to colinear, there is the possibility of sufficiently strong ring currents, the magnetic field of which tends to displace the magnetic field of the rope and lead to the formation of a plasma layer with a height of the order of the electron Larmor radius.

Development of a cruciform radio-frequency closed magnetron sputtering source including four sectorial magnetron sputtering discharges for uniform target utilization

A rotational cruciform radio frequency magnetron source has been developed by including four sectorial magnetron sputtering discharges for uniform target utilization. The Larmor radius and Hall parameter of electrons are discussed by considering the E × B drift motion of electrons using simulated magnetic field profiles, where the electric field, E, is vertical to the target and the magnetic field, B, is parallel to the target, respectively. Temporal evolutions of ion saturation current Iis, as a measure for the ion flux to the target, are measured by a Langmuir probe at a fixed axial distance of 5 mm from the target and at various radial positions. It is found that the time variation of Iis at each radial position is obtained as predicted from the cruciform magnetron sputtering discharge. The time-averaged ion saturation current profile to the target is in good agreement with the target erosion profile. A maximum target utilization of 78.0% is achieved.

The fully-kinetic investigations on the ion acceleration mechanisms in an electron-driven magnetic nozzle

A fully kinetic particle-in-cell study is conducted to investigate the ion acceleration mechanisms in an electron-driven magnetic nozzle. All five powers contributing to the axial kinetic energy of ions are derived and evaluated under different magnetic field strength and inlet density profiles. Among them, the electrothermal and electromagnetic acceleration contributes over 98% of the total accelerating power. The dominating acceleration mechanism is found to be the electrothermal acceleration, covering two thirds of the axial accelerating power in the electron-driven magnetic nozzle. The electromagnetic mechanism is found to originate from four sources, among which the major accelerating and decelerating one are the diamagnetic acceleration driven by radial gradient of electron pressure and the E × B mechanism due to the inward ion detachment. The power induced by the viscous-stress of electrons contributes 14%–23% of the decelerating power, indicating the non-negligible influence of finite electron Larmor radius effect on the ion acceleration. Results indicates that the net effect of electromagnetic mechanism can even be decelerating when the magnetic field is too high with a uniform inlet. Finally, the conversion efficiency from the inlet thermal energy to the ion axial kinetic energy is derived and evaluated, which can reach as high as 65.0% under 0.25 T with a Gaussian-profile inlet. Raising the magnetic field to 0.75 T or a uniform inlet will decrease the conversion efficiency.

Simulation of transport in the FT-2 tokamak up to the electron scale with GENE

Prior experimental work on the FT-2 tokamak has observed electron density fluctuations at electron Larmor radius scales using the enhanced scattering (ES) diagnostic (Gusakov et al 2006 Plasma Phys. Control. Fusion 48 A371–6, Gurchenko and Gusakov 2010 Plasma Phys. Control. Fusion 52 124035). Gyrokinetic GENE simulations of conditions at the upper hybrid resonance layer probed by the ES diagnostic show the presence of the anticipated turbulence from the electron temperature gradient (ETG) driven instability in linear and nonlinear simulations. Ion-scale turbulence is responsible for majority of the transport via trapped electron modes, while impurities act to merge the spectrum of the ion and the electron scale instabilities into a continuum. The linear spectrum at electron scales is characterized by maximal growth rate at a significant ballooning angle θ 0, and at ion scales the turbulence is broad in the ballooning angle distribution. The neoclassical shearing rate obtained from GENE breaks symmetry in nonlinear simulations of ETG turbulence, which manifests itself as an asymmetric turbulence spectrum. The electron density fluctuation spectrum obtained with GENE corresponds well to the ES measurement at electron scales, as do the fluxes obtained from the ion-scale simulations.

Laser photo-detachment combined with Langmuir probe in magnetized electronegative plasma: how the probe size affects the plasma dynamic?

Laser photo-detachment combined with a Langmuir probe (LP) is used to diagnose negative ion properties in electronegative plasmas. The technique relies on the combined use of a laser pulse and an LP. The laser pulse converts negative ions into electron–atom pairs, while the LP tracks the temporal evolution of electron current (laser photo-detachment signal) that is analyzed to retrieve the negative ion density. Although an external magnetic field is frequently used to enhance the negative ion production and extraction, the data analysis often neglects the effects of the magnetic field on the probe current. This work investigates the response of an electronegative plasma to a laser pulse in the presence of an external magnetic field through a two-dimensional particle-in-cell/Monte Carlo collision model. The results show that a low electron density region surrounding the probe, called a flux-tube, can form for a probe size comparable with or larger than the electron Larmor radius. The formation of the flux-tube strongly affects the components of the laser photo-detachment signal, leading to an important oscillation of probe current during the plateau phase, i.e. the amplitude of the AC component of the probe current is in the same magnitude order of the DC component of this current, and an important overshoot in comparison to the current rise. Numerical results are qualitatively compared to measurements obtained from the RAID negative ion source.

Enhancement of Ablative Rayleigh-Taylor Instability Growth by Thermal Conduction Suppression in a Magnetic Field.

Ablative Rayleigh-Taylor instability growth was investigated to elucidate the fundamental physics of thermal conduction suppression in a magnetic field. Experiments found that unstable modulation growth is faster in an external magnetic field. This result was reproduced by a magnetohydrodynamic simulation based on a Braginskii model of electron thermal transport. An external magnetic field reduces the electron thermal conduction across the magnetic field lines because the Larmor radius of the thermal electrons in the field is much shorter than the temperature scale length. Thermal conduction suppression leads to spatially nonuniform pressure and reduced thermal ablative stabilization, which in turn increases the growth of ablative Rayleigh-Taylor instability.

Spectrum of kinetic plasma turbulence at 0.3-0.9 astronomical units from the Sun.

We investigate spectral properties of turbulence in the solar wind that is a weakly collisional astrophysical plasma, accessible to in situ observations. Using the Helios search coil magnetometer measurements in the fast solar wind, in the inner heliosphere, we focus on properties of the turbulent magnetic fluctuations at scales smaller than the ion characteristic scales, the so-called kinetic plasma turbulence. At such small scales, we show that magnetic power spectra between 0.3 and 0.9 AU from the Sun have a generic shape ∼f^{-8/3}exp(-f/f_{d}), where the dissipation frequency f_{d} is correlated with the Doppler shifted frequency f_{ρe} of the electron Larmor radius. This behavior is statistically significant: all the observed kinetic spectra are well described by this model, with f_{d}=f_{ρe}/1.8. Our results indicate that the electron gyroradius plays the role of the dissipation scale and marks the end of the electromagnetic cascade in the solar wind.

Excitation of zonal flow by intermediate-scale toroidal electron temperature gradient turbulence

On the basis of gyrokinetic theory, we derive nonlinear equations for the zonal flow (ZF) generation in intermediate-scale electron temperature gradient (ETG) turbulence (with wavelength much shorter than the ion Larmor radius but much longer than the electron Larmor radius) in nonuniform tokamak plasmas. Both the spontaneous and forced generation of ZFs are kept on the same footing. The resultant Schrödinger equation for the ETG amplitude is characterized by a Navier–Stokes type nonlinearity, which is typically stronger than the Hasegawa–Mima type nonlinearity resulting from the fluid approximation. The physics underlying the three stages of ZF generation process is clarified, and the role of parallel mode structure decoupling is discussed. It is found that ZFs can be more easily excited in the intermediate-scale ETG turbulence than in the short wavelength regime.

Local analysis of electrostatic modes in a two-fluid E×B plasma

A local study of linear electrostatic modes, applicable to the dynamics perpendicular to the magnetic field in a plasma with crossed electric and magnetic fields, is presented. The analysis is based on a two-fluid model that takes into account the finite-electron-gyroradius effects through a rigorous gyroviscosity tensor and includes a dissipative friction force in the electron momentum equation. A comprehensive dispersion relation, valid for arbitrary electron temperature, is derived, which describes properly all the relevant waves for wavelengths longer than the electron Larmor radius. For a homogeneous and dissipationless plasma, such a fluid dispersion relation agrees with the long-wavelength limit of the kinetic electron–cyclotron-drift instability dispersion relation that extends the results to arbitrary short wavelengths. The general fluid dispersion relation covers different parametric regimes that depend on the relative ion-to-electron drift velocity and on the presence of equilibrium inhomogeneities and/or dissipation. Depending on such conditions, its roots yield as follows: two-stream instabilities, driven solely by the relative drift between species; drift-gradient instabilities, driven by the combination of the relative drift and equilibrium gradients; and drift-dissipative instabilities, driven by the combination of the relative drift and friction. Instability thresholds are determined and some distinctive unstable modes are described analytically.

A novel quiescent quasi-steady state of a toroidal electron plasma

The existence of a novel quiescent quasi-steady state of the toroidal electron cloud is reported. This is achieved by first constructing a maximum entropy mean-field solution for pure electron plasma at zero-inertia limit (ρ¯L/L→0, where ρ¯L is average electron Larmor radius and L is typical mean spatial gradient length scale), which is then used as “seed” solution to a high fidelity 3D3V PIC solver, at finite density of pure electron plasma in small aspect ratio toroidal configuration. The electron cloud is shown to attain a quiescent quasi-steady state satisfying full equations of motion and hence accurate to all orders in ρ¯L/L, with far superior confinement properties as compared to typical initial condition used in today's laboratories. Salient features include the absence of center of charge motion, naturally shaped centrally peaked density, and potential concentric surfaces. The variation of temperatures T¯∥(R,t) and T¯⊥(R,t) (averaged over the toroidal direction) with major radius R is reported for the first time for a toroidal electron plasma. For the small aspect ratio of O(1) considered here, the temperature profiles are such that T¯∥(R,t) and T¯⊥(R,t) fall with R as 1/R2 and 1/R3, respectively. Our solution to this long-standing problem of finding a quiescent quasi-steady of a toroidal charge cloud may have direct relevance to not only pure electron plasma but also to pure ion plasma.

Kinetic approach to THz radiation generation at femtosecond laser pulse ponderomotive effect on plasma in magnetic field.

For a semibounded plasma in a constant magnetic field and interacting with short laser pulse, a kinetic equation is derived, which makes it possible to describe the low-frequency movements of electrons. In the linear approximation in laser radiation intensity the solution of kinetic equation is obtained taking into account mirror reflection of electrons by the plasma surface. Using this solution, we derived low-frequency currents generated by low-frequency field and ponderomotive force that changes during the pulse affect. Under the assumption that characteristic spatial scales of changes in the low-frequency field and ponderomotive force exceed the Larmor radius of electrons, we studied low-frequency currents near the plasma surface. If the electron cyclotron frequency exceeds the inverse pulse duration, then low-frequency currents differ from their values in a homogeneous plasma only at a distance from the surface not exceeding several Larmor radii. Taking this fact into account, a solution to the equation for low-frequency field in the plasma was obtained. The terahertz (THz) magnetic field generated by nonlinear currents is found. It is shown that the maximum value of the generated field is attained at cyclotron frequency comparable with the product of the plasma frequency square and laser pulse duration.

Numerical simulation of the plasma acceleration process in a magnetically enhanced micro-cathode vacuum arc thruster

A particle-in-cell simulation is conducted to investigate the plasma acceleration process in a micro-cathode vacuum arc thruster. A coaxial electrode structure thruster with an applied magnetic field configuration is used to investigate the effects of the distribution of the magnetic field on the acceleration process and the mechanism of electrons and ions. The modeling results show that due to the small Larmor radius of electrons, they are magnetized and bound by the magnetic field lines to form a narrow electron channel. Heavy ions with a large Larmor radius take a long time to keep up with the electron movement. The presence of a magnetic field strengthens the charge separation phenomenon. The electric field caused by the charge separation is mainly responsible for the ion acceleration downstream of the computation. The impact of variations in the distribution of the magnetic field on the acceleration of the plasma is also investigated in this study, and it is found that the position of the magnetic coil relative to the thruster exit has an important impact on the acceleration of ions. In order to increase the axial velocity of heavy ions, the design should be considered to reduce the confinement of the magnetic field on the electrons in the downstream divergent part of the applied magnetic field.

Characteristics of a rotational windmill-shaped radio frequency magnetron sputtering plasma for effective target utilization

A rotational windmill-shaped radio frequency magnetron plasma source has been developed for improving the target utilization rate. Two kinds of magnet arrangements are designed by taking into account the E × B drift motion of electrons using simulated magnetic field profiles, where the electric field, E, is vertical to the target and the magnetic field, B, is parallel to the target, respectively. It is found that the Hall parameters of the electrons in the magnetron area have a higher value ranging from 12 to 110 for both magnet arrangements. This is high enough to magnetize electrons, while the electron Larmor radius is as low as 0.3–2.8 mm. The target utilization rate has attained approximately 65 % and 70 % for an initial and for an improved magnet arrangements, respectively. The improved magnet arrangement has a uniform profile of the target erosion compared with the initial magnet arrangement.

Numerical study of energy loss rate of fast proton in cold dense electron gas in strong magnetic field

Energy loss of a proton propagating through a low-temperature gas of magnetized electrons is studied by molecular dynamics method for the case when proton velocity is much more than electrons thermal velocity. Strong uniform magnetic field is considered when electron Larmor radius is much smaller than distance of closest approach (Coulomb radius). High electron density, and hence small values of the Coulomb logarithm, is considered. The dependence of energy loss on angle between the proton velocity and the magnetic field direction is studied. Results of calculations are compared to Derbenev and Skrinskii theoretical approach to average friction force.

A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and the arbitrarily large deviations from thermal equilibrium that are present in the plasma periphery of tokamak devices. The formulation of the gyrokinetic model is based on a second-order accurate description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behaviour of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function. The collisional effects are included by a nonlinear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a Hermite–Laguerre velocity-space polynomial basis. Then, the gyrokinetic equation is projected onto the same basis yielding the spatial and temporal evolution of the Hermite–Laguerre expansion coefficients. A closed set of fluid equations for the lowest-order coefficients is presented. The Hermite–Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell equations derived from a variational principle where the velocity integrals are explicitly evaluated.