Electrostatic Particle Simulation Research Articles

Kinetic theory of double layers driven by temperature anisotropy in a non-homogeneous magnetic field

A double layer (DL) is created in a plasma when the plasma is perturbed in the presence of a temperature anisotropy. We derive a new simple theory for the existence of an unstable, non-oscillatory electrostatic DL-like structure in the presence of a magnetic field gradient in a collisionless plasma with a temperature anisotropy in the direction perpendicular to the magnetic field. The DL is treated as a wave perturbation in the plasma using kinetic theory with a gyro-kinetic approximation to obtain a dispersion relation. The presence of an electron temperature anisotropy is the necessary condition to obtain an exponentially growing instability, and the corresponding growth rate is found to be the ratio of the electron kinetic energy and the electric field energy across the DL region. The theoretical predictions are then validated against a one-dimensional electrostatic particle simulation carried out in a traveling magnetic field thruster environment. An anisotropy ratio parameter was introduced, and the theoretical growth rates were found to be in good agreement with the simulation for different anisotropy ratios. An ion beam, associated with the DL dynamics, is observed within the simulation domain. A parametric study revealed that the DL-like structure loses its ambipolar shape for temperature ratios less than 10. It has been found that a stronger anisotropy is required to obtain the DL-like structure.

Development and Verification of the Three-Dimensional Electrostatic Particle Simulation Code for the Study of Blob and Hole Propagation Dynamics

Development and Verification of the Three-Dimensional Electrostatic Particle Simulation Code for the Study of Blob and Hole Propagation Dynamics

Self-consistent Langmuir waves in resonantly driven thermal plasmas

The longitudinal dynamics of a resonantly driven Langmuir wave are analyzed in the limit that the growth of the electrostatic wave is slow compared to the bounce frequency. Using simple physical arguments, the nonlinear distribution function is shown to be nearly invariant in the canonical particle action, provided both a spatially uniform term and higher-order spatial harmonics are included along with the fundamental in the longitudinal electric field. Requirements of self-consistency with the electrostatic potential yield the basic properties of the nonlinear distribution function, including a frequency shift that agrees closely with driven, electrostatic particle simulations over a range of temperatures. This extends earlier work on nonlinear Langmuir waves by Morales and O’Neil [G. J. Morales and T. M. O’Neil, Phys. Rev. Lett. 28, 417 (1972)] and Dewar [R. L. Dewar, Phys. Plasmas 15, 712 (1972)], and could form the basis of a reduced kinetic treatment of plasma dynamics for accelerator applications or Raman backscatter.

Low-frequency instabilities locally enhanced by parallel flow velocity shears in magnetized plasmas

Three-dimensional electrostatic particle simulations are performed in order to investigate the effects of ion flow parallel to magnetic-field lines and their velocity shears on low-frequency plasma instabilities in detail. In the case where the ion drift speed is so small that the low-frequency instabilities cannot take place. the ion-acoustic wave is destabilized by introducing the ion-flow velocity shear. The ion-acoustic wave is locally destabilized in the large velocity shear region. On the other hand, the ion-cyclotron instability is also destabilized when the ion drift speed exceeds a certain threshold. The flow velocity shear enhances not, only the fundamental mode but also tlie high harmonic modes. As a result. the spiky fluctuations in the time domain are locally observed in the velocity shear region. which are caused by the simultaneous existence of several coherent ion-evclotron harmonics.

Generation mechanism of electrostatic solitary structures in the Earth's auroral region

Satellite observations have revealed electrostatic solitary structures in the Earth's auroral region. These structures have positive electrostatic potentials and move along the ambient magnetic field. In this paper we performed one‐dimensional electrostatic particle simulations of electrostatic solitary waves (ESW) in plasma composed of three electron components: cold, hot, and beam electrons. First, the nearly monochromatic electrostatic acoustic waves are excited. When the amplitude of the electron acoustic (EA) waves is sufficiently large, part of hot and beam electrons are trapped by the electron acoustic waves. These waves coalesce each other during their nonlinear evolution, and at last the solitary structures with travel speed related to the beam velocity are formed at the quasi‐equilibrium stage. These structures have positive potential signatures, and they seem to be stable. Electron density cavities for cold electron component are always accompanied with these structures. In addition, the corresponding electric fields have a bipolar structure, which has also been observed in the Earth's auroral region recently. The conditions for existence of such solitary structures are investigated through our simulations, and the comparisons between our simulated results and satellite observations in the Earth's auroral regions are also discussed.

Effects of the weak magnetic field and electron diffusion on the spatial potential and negative ion transport in the negative ion source

The effects of the weak magnetic field on the negative ion (H−) extraction in a negative ion source have been studied by means of a two-dimensional electrostatic particle simulation. A particle-in-cell model is used which simulates the motion of the charged particles in their self-consistent electric field. In addition, the effect of the electron diffusion across the weak magnetic field is taken into account by a simple random-walk model with a step length Δx per time step Δt; Δx=2D⊥Δt⋅ξx, where D⊥ and ξx are the perpendicular diffusion coefficient and normal random numbers. Under this simple diffusion model, the electron diffusion has no significant effects on the H− transport. Most electrons are magnetized by the weak magnetic field and lost along the field line. As a result, more H− ions arrive instead of electrons in the region close to the plasma grid in order to ensure the plasma neutrality.

Effects of a weak transverse magnetic field on negative ion transport in negative ion sources

The effects of a weak transverse magnetic field on negative ion (H−) extraction in a negative ion source have been studied by two-dimensional electrostatic particle simulation. A particle-in-cell model is used which simulates motion of charged particles in their self-consistent electric field. The extraction of H− ions is significantly improved by the weak transverse magnetic field in simulation as well as in experiments. Since electrons are deflected by the weak magnetic field, more H− ions arrive instead of electrons in the region close to the plasma grid in order to ensure plasma neutrality. The presence of the weak magnetic field produces important modifications in positive ion flow and, as a result, in the structure of the spatial potential which collects H− ions.

Plasma-surface interaction model with secondary electron emission effects

This work represents the investigation of the region between a Maxwellian plasma source and a floating surface by a 1D–3V fully kinetic, electrostatic particle simulation. The electric field is self-consistently computed from the Poisson equation. The secondary electron emission is modelled rigorously by considering a realistic expression for the secondary emission coefficient dependent on the primary electron energy, the angle relative to the surface normal and surface materials and a realistic secondary electron distribution function is introduced at the collector surface. The minimum ion energy at the collector sheath edge is evaluated self-consistently by determining the plasma sheath, without the assumption of a monotonic potential. The model is able to simulate the space charge limited conditions as well as the positively charged wall cases. Results are compared with other secondary emission sheath theories and numerical models.

Effects of secondary electron emission from a floating surface on the plasma sheath

The paper describes the region between a Maxwellian plasma source and a floating surface by a 1D-3 V fully kinetic, electrostatic particle simulation. The electric field is self-consistently computed from the Poisson equation. The secondary electron emission is modelled by considering an expression for the secondary emission coefficient dependent on the primary electron energy and surface materials and a realistic secondary electron distribution function is introduced at the collector surface. The model is able to simulate the space-charge-limited conditions as well as the positively charged wall cases.

Two‐dimensional particle simulation of electromagnetic field signature associated with electrostatic solitary waves

We present particle simulations of electrostatic solitary waves (ESW) observed by the Geotail spacecraft and recent spacecraft in the Earth's magnetosphere. Recent particle simulations have demonstrated that ESW correspond to Bernstein‐Greene‐Kruskal electron holes formed through nonlinear evolution of electron beam instabilities. Since an electron hole is a coherent electrostatic potential structure, electron beam instabilities were conventionally studied by electrostatic particle simulations. However, the Polar spacecraft and FAST spacecraft observed electromagnetic field signatures associated with ESW. To study interaction between coherent electrostatic potentials and electromagnetic waves, we extend the previous electrostatic particle model to an electromagnetic particle model. In the present two‐dimensional simulations of an electron beam instability, electromagnetic field components are enhanced around two‐dimensional electron holes. We found that the enhancement of electromagnetic fields is due to a current formed by electrons undergoing the E × B0 drift, where the electric field is a perpendicular electrostatic field at the edge of a two‐dimensional electron hole. An electromagnetic beam mode is excited by the current due to the drifting electrons moving with the electron hole. The amplitude ratio of the electric field to the magnetic field is estimated on the basis of the present simulation result, and it is in agreement with those of the Polar and FAST observations.

Formation of electrostatic solitary waves in space plasmas: Particle simulations with open boundary conditions

We study formation process of electrostatic solitary waves (ESW) observed by recent spacecraft via one‐ and two‐dimensional electrostatic particle simulations with open boundaries. The previous simulations have demonstrated that ESW correspond to Bernstein‐Greene‐Kruskal electron holes formed by electron beam instabilities. However, since the previous simulations were performed in uniform periodic systems, wave‐particle interaction of an electron beam instability was taking place uniformly in the systems. In the present study, we inject a weak electron beam from an open boundary into the background plasma to study spatial and temporal development of a bump‐on‐tail instability from a localized source. In the open system, spatial structures of electron holes vary depending on the distance from the source of the electron beam. In an early phase of the simulation run, electron holes that are initially uniform in the direction perpendicular to the magnetic field become twisted through modulation by oblique electron beam modes. As the electron holes propagate along the magnetic field, they are aligned in the perpendicular direction through coalescence. Spatial structures of electron holes in a distant region from the source become one‐dimensional. In a long‐time evolution of the instability, ion dynamics becomes important in determining spatial structures of electron holes. A lower hybrid mode is excited locally in the region close to the source of the electron beam through coupling with electron holes at the same parallel phase velocity. The lower hybrid mode modulates electron holes excited in later phases, resulting in formation of modulated one‐dimensional potentials. Since the perpendicular electric fields of electron holes are carried by the electron holes at the drift velocity of the electron holes, they can be observed even at a distant place from the source.

Dynamic Evolution of Plasma Structures due to Local Production of Massive Negative Ions

Dynamic structures formed due to local production of massive negative ions in a plasma are investigated by means of a one-dimensional electrostatic particle simulation which is based on a Q-machine configuration. The plasma becomes unstable with a high rate of negative ion production, being accompanied by a double-layer formation generating solitary pulses with negative potential. The solitary pulses play a role in the rapid ejection of negative ions from the system.

Electrostatic particle simulations of the WDL in the auroral plasma including the effects of up-flowing ions

An upward beam of hot ions which originates in the ionosphere is commonly observed in and above the region of auroral particle acceleration. Past simulations of the weak double layer (WDL) have only included magnetospheric hot electrons and ionospheric cold ions. We simulated the formation of the WDL numerically and more realistically using a one dimensional electrostatic code. We modeled magnetospheric hot electrons, ionospheric cold ions and hot ionospheric beam ions in the system. The existence of the hot ion beam modifies the characteristics of the WDL, its magnitude of the potential drop and lifetime. We investigated the variation in the character of the WDL for different fractions of the hot ion beam component. The magnitude of the potential jump of the WDL was found to decrease but the lifetime of the WDL increase as this proportion increased. The existence of a critical value of the ratio of the hot beam ions to the cold ions, above which electrons cannot be accelerated effectively and which places an upper limit on the altitude of auroral particle acceleration region has also been shown.

Collector floating potentials in a discharge plasma

We present the results of a study on electrode floating potentialformation in a hot cathode discharge plasma. The electron component of theplasma is composed of two populations. The high-temperature component developsfrom primary electrons and the cool component from secondary electrons born byionization of cold neutral gas. A static, kinetic plasma-sheath model is usedto calculate the pre-sheath potential and the floating potential of theelectrode. For hot primary electrons a truncated Maxwellian distribution isassumed. The plasma system is also modelled numerically with a dynamic,electrostatic particle simulation. The plasma source injects temporally equalfluxes of ions and electrons with half-Maxwellian velocities. Again, the hotelectron distribution is truncated in the high-velocity tail. The plasmaparameters, such as ion temperature and mass, electron temperatures, dischargevoltages, etc, correspond to experimental values. The experimentalmeasurements of the electrode floating potential are performed in weaklymagnetized plasmas produced with hot cathode discharges in argon gas.Theoretical, simulation and experimental results are compared and they agreevery well.

Electrostatic particle simulations of solitary waves in the auroral region

We study the formation mechanism of two‐dimensional solitary waves observed in the auroral region via two‐dimensional electrostatic particle simulations. The FAST satellite observed very strong “solitary waves” in the downward current regions of the mid‐altitude auroral zone, and the Polar satellite also succeeded in detecting solitary waves in the polar region. These “solitary waves” are reported to have isolated two‐dimensional structures. The present simulation study demonstrates that such isolated two‐dimensional “solitary waves” can be generated by a simple electron two‐stream instability. We performed two simulation runs; one was a run without ion dynamics, and the other was a run with ion dynamics. By comparing these two runs, we found isolated two‐dimensional potentials are generated due to the ion dynamics. In these simulations an initial electron beam instability first forms solitary potentials isolated in the parallel direction. When the ion dynamics are neglected, these potentials become coherent in the perpendicular direction, forming one‐dimensional structures, owing to the ion dynamics, however, quasi‐perpendicular lower hybrid waves are strongly excited through coupling with parallel drifting electron potentials. Potentials are divided in the perpendicular direction by these lower hybrid waves, forming isolated two‐dimensional potentials. In a long time evolution, these isolated two‐dimensional potentials are gradually aligned in the perpendicular direction, and the perpendicular potential energy decreases. Finally, they again become one‐dimensional potentials coherent in the direction perpendicular to the ambient magnetic field.

Beam instability excited by the magnetic filter

By the one-dimensional electrostatic particle simulation, the ion beam instability is observed in the plasma divided by the magnetic filter (MF). The strength of the MF is selected to influence only electron dynamics; ions move freely across the MF. There are grounded walls at the left and right ends of the system. Particles hitting the walls are absorbed there. The high temperature and high density plasma (main plasma) faces the low temperature and low density plasma (subplasma) across the MF located at the center of the system. The averaged space potential of the main plasma is higher than that of the subplasma. Due to the potential gap at the MF, ions in the main plasma are accelerated into the subplasma. Depending on the extent of the asymmetry of the system, steady or the periodic (dynamic) state manifests. For the periodic state, high density clumps get into the subplasma and excite the strong ion beam instability. The new clump comes into the subplasma when the old clump reaches the wall.

Ion Temperature Estimated from Energy Dependence of Ion Flux to a Plasma End

Ion temperatures have been experimentally estimated from the exponential parts of volt-ampere characteristics of ion flux obtained using retarding field analyzers. This report concerns the feasibility of this measurement for a plasma with a uniform particle source, using an electrostatic particle simulation code. The results show that an ion temperature estimated from the ion flux to a plasma end is about twice as high as the ion temperature at the plasma center.

Effects of Energetic Electrons on Collector and Source Potentials in a Finite Ion Temperature Plasma

AbstractFormation of the potential in a two‐electron‐temperature plasma region facing a floating collector was studied theoretically with a kinetic plasma‐sheath model and by electrostatic particle simulation. The electrons were described by truncated full Maxwellian velocity distribution functions and the ions by an accelerated half‐Maxwellian velocity distribution function. The collector potential and the plasma source sheath or presheath potential drop were evaluated as functions of the hot to cool electron temperature ratio and the hot electron density ratio using Vlasov and Poison equations. The results showed that the presheath potential drop varied continuously with electron composition ratio for lower values of the electron temperature ratio, while for higher values in a narrow composition ratio range, triple values of the potential were found. Of the two physically acceptable values, the lower was characterized by the cool electrons and the higher by the hot electrons. It is anticipated that a current‐free double layer structure is formed in the plasma system between these two potential regions. The collector floating potential, as a function of electron composition ratio, is mainly dominated by the hot electrons, since already a small value of hot electron current is sufficient to compensate the ion saturation current. In order to complete the theoretical investigation we also study the hydrogen plasma system with the XPDP1 particule‐in‐cell simulation code composed at Berkeley. At certain plasma parameter values formation of a double layer structure was observed. The potential Values on the upper and lower side of the double layer, as well as that of the collector floating potential, corresponded very well to the calculated values. On the upper side the plasma was composed of ions, accelerated through the source sheath potential drop, and electrons consisting of cool full Maxwellian and hot truncated full Maxwellian populations. On the lower side only hot electrons and ions additionally accelerated through the double layer were found.

An Ion Drift Velocity at a Sheath Edge of a Plasma with a Finite Ion Temperature

An ion drift velocity at a sheath edge v D in a bounded plasma with a finite ion temperature is studied using a one-dimensional electrostatic particle simulation code. This code includes spatially uniform particle generation and electron heating and determines v D at the sheath edge, defined by ( n i - n e ) / n i = 0.1 with an ion density n i and an electron density n e . In comparison with the ion acoustic velocity from the fluid equations, \(v_{\rm D} = \sqrt{(T_{\rm e}{}^{\rm center} + \gamma T_{\rm i}{}^{\rm edge}) / m_{\rm i}}\) is obtained, where T e center is an electron temperature at the plasma center, T i edge is an ion temperature at the sheath edge, m i is an ion mass, and γ= (3.5 + T i edge / T e center ) / (1 + T i edge / T e center ). It is also found that a sheath potential change little but an ion acceleration potential in a presheath decreases with the increasing T i edge / T e center .

Two‐dimensional computer simulations of electrostatic solitary waves observed by Geotail spacecraft

We performed computer simulations of electrostatic solitary waves (ESW), which correspond to broadband electrostatic noise (BEN), observed by Geotail spacecraft in the magnetotail. According to Geotail/WFC data analysis, ESW are composed of sequences of impulsive solitary waves, and their potentials are revealed to have uniform structures in the direction perpendicular to the ambient magnetic field. We performed a series of two‐dimensional electrostatic particle simulations with a cold electron beam drifting against background hot electrons along the ambient magnetic field. In these simulations, spatial potentials are excited by the initial electron beam instability. They coalesce with each other and form potential troughs uniform in the direction perpendicular to the ambient magnetic field, as predicted by the Geotail observations. We varied the magnitude of the ambient magnetic field and found that this parameter critically affects the ESW formation process. These simulation results indicate that ESW are excited by the electron beam instability in the presence of the static magnetic field with a certain magnitude. ESW are also subject to the enhanced thermal fluctuations due to the limited number of superparticles in the simulations.