Electron Phase Space Research Articles

Application and testing of the L* neural network with the self‐consistent magnetic field model of RAM‐SCB

We expanded our previous work on L* neural networks that used empirical magnetic field models as the underlying models by applying and extending our technique to drift shells calculated from a physics‐based magnetic field model. While empirical magnetic field models represent an average, statistical magnetospheric state, the RAM‐SCB model, a first‐principles magnetically self‐consistent code, computes magnetic fields based on fundamental equations of plasma physics. Unlike the previous L* neural networks that include McIlwain L and mirror point magnetic field as part of the inputs, the new L* neural network only requires solar wind conditions and the Dst index, allowing for an easier preparation of input parameters. This new neural network is compared against those previously trained networks and validated by the tracing method in the International Radiation Belt Environment Modeling (IRBEM) library. The accuracy of all L* neural networks with different underlying magnetic field models is evaluated by applying the electron phase space density (PSD)‐matching technique derived from the Liouville's theorem to the Van Allen Probes observations. Results indicate that the uncertainty in the predicted L* is statistically (75%) below 0.7 with a median value mostly below 0.2 and the median absolute deviation around 0.15, regardless of the underlying magnetic field model. We found that such an uncertainty in the calculated L* value can shift the peak location of electron phase space density (PSD) profile by 0.2 RE radially but with its shape nearly preserved.

Phase-space Berry phases in chiral magnets: Dzyaloshinskii-Moriya interaction and the charge of skyrmions

The semiclassical motion of electrons in phase space, x=(R, k), is influenced by Berry phases described by a 6-component vector potential, A=(A^R, A^k). In chiral magnets Dzyaloshinskii-Moriya (DM) interactions induce slowly varying magnetic textures (helices and skyrmion lattices) for which all components of A are important inducing effectively a curvature in mixed position and momentum space. We show that for smooth textures and weak spin-orbit coupling phase space Berry curvatures determine the DM interactions and give important contributions to the charge. Using ab initio methods we calculate the strength of DM interactions in MnSi in good agreement with experiment and estimate the charge of skyrmions.

Rapid local acceleration of relativistic radiation-belt electrons by magnetospheric chorus

Recent analysis of satellite data obtained during the 9 October 2012 geomagnetic storm identified the development of peaks in electron phase space density, which are compelling evidence for local electron acceleration in the heart of the outer radiation belt, but are inconsistent with acceleration by inward radial diffusive transport. However, the precise physical mechanism responsible for the acceleration on 9 October was not identified. Previous modelling has indicated that a magnetospheric electromagnetic emission known as chorus could be a potential candidate for local electron acceleration, but a definitive resolution of the importance of chorus for radiation-belt acceleration was not possible because of limitations in the energy range and resolution of previous electron observations and the lack of a dynamic global wave model. Here we report high-resolution electron observations obtained during the 9 October storm and demonstrate, using a two-dimensional simulation performed with a recently developed time-varying data-driven model, that chorus scattering explains the temporal evolution of both the energy and angular distribution of the observed relativistic electron flux increase. Our detailed modelling demonstrates the remarkable efficiency of wave acceleration in the Earth's outer radiation belt, and the results presented have potential application to Jupiter, Saturn and other magnetized astrophysical objects.

Energetic electron precipitation characteristics observed from Antarctica during a flux dropout event

AbstractData from two autonomous VLF radio receiver systems installed in a remote region of the Antarctic in 2012 is used to take advantage of the juxtaposition of the L = 4.6 contour, and the Hawaii‐Halley, Antarctica, great circle path as it passes over thick Antarctic ice shelf. The ice sheet conductivity leads to high sensitivity to changing D region conditions, and the quasi constant L shell highlights outer radiation belt processes. The ground‐based instruments observed several energetic electron precipitation events over a moderately active 24 h period, during which the outer radiation belt electron flux declined at most energies and subsequently recovered. Combining the ground‐based data with low and geosynchronous orbiting satellite observations on 27 February 2012, different driving mechanisms were observed for three precipitation events with clear signatures in phase space density and electron anisotropy. Comparison between flux measurements made by Polar‐orbiting Operational Environmental Satellites (POES) in low Earth orbit and by the Antarctic instrumentation provides evidence of different cases of weak and strong diffusion into the bounce loss cone, helping to understand the physical mechanisms controlling the precipitation of energetic electrons into the atmosphere. Strong diffusion events occurred as the <600 keV fluxes began to recover as a result of adiabatic transport of electrons. One event appeared to have a factor of about 10 to 100 times more flux than was reported by POES, consistent with weak diffusion into the bounce loss cone. Two events had a factor of about 3 to 10 times more >30 keV flux than was reported by POES, more consistent with strong diffusion conditions.

Modeling radiation belt electron dynamics during GEM challenge intervals with the DREAM3D diffusion model

AbstractAs a response to the Geospace Environment Modeling (GEM) “Global Radiation Belt Modeling Challenge,” a 3D diffusion model is used to simulate the radiation belt electron dynamics during two intervals of the Combined Release and Radiation Effects Satellite (CRRES) mission, 15 August to 15 October 1990 and 1 February to 31 July 1991. The 3D diffusion model, developed as part of the Dynamic Radiation Environment Assimilation Model (DREAM) project, includes radial, pitch angle, and momentum diffusion and mixed pitch angle‐momentum diffusion, which are driven by dynamic wave databases from the statistical CRRES wave data, including plasmaspheric hiss, lower‐band, and upper‐band chorus. By comparing the DREAM3D model outputs to the CRRES electron phase space density (PSD) data, we find that, with a data‐driven boundary condition at Lmax = 5.5, the electron enhancements can generally be explained by radial diffusion, though additional local heating from chorus waves is required. Because the PSD reductions are included in the boundary condition at Lmax = 5.5, our model captures the fast electron dropouts over a large L range, producing better model performance compared to previous published results. Plasmaspheric hiss produces electron losses inside the plasmasphere, but the model still sometimes overestimates the PSD there. Test simulations using reduced radial diffusion coefficients or increased pitch angle diffusion coefficients inside the plasmasphere suggest that better wave models and more realistic radial diffusion coefficients, both inside and outside the plasmasphere, are needed to improve the model performance. Statistically, the results show that, with the data‐driven outer boundary condition, including radial diffusion and plasmaspheric hiss is sufficient to model the electrons during geomagnetically quiet times, but to best capture the radiation belt variations during active times, pitch angle and momentum diffusion from chorus waves are required.

Saturn chorus intensity variations

AbstractWhistler mode chorus plasma wave emissions have been observed at Saturn near the magnetic equator and the source region. During crossings of the magnetic equator along nearly constant L shells, the Cassini Radio and Plasma Wave Science Investigation often observes a local decrease in whistler mode intensity and bandwidth closest to the magnetic equator, where linear growth appears to dominate, with nonlinear structures appearing at higher latitudes and higher frequencies. We investigate linear growth rate using the Waves in a Homogeneous, Anisotropic, Multi‐component Plasma dispersion solver and locally observed electron phase space density measurements from the Electron Spectrometer sensor of the Cassini Plasma Spectrometer Investigation to determine the parameters responsible for the variation in chorus intensity and bandwidth. We find that a temperature anisotropy (T⊥/T∥ ~ 1.3) can account for linear spatiotemporal growth rate of whistler mode waves, which provides a majority of the observed frequency‐integrated power. At the highest frequencies, intense, nonlinear, frequency‐drifting structures (drift rates ~ 200 Hz/s) are observed a few degrees away from the equator and can account for a significant fraction of the total power. Chorus emission at higher frequencies is distinct from lower frequency whistler mode emission and is sometimes correlated with simultaneously observed low‐frequency electromagnetic ion cyclotron waves. These electromagnetic ion cyclotron waves appear to modulate a slow frequency drift (~15 Hz/s) which develops into nonlinear growth with much larger frequency drift associated only with the higher‐frequency chorus.

Responses of Earth's radiation belts to solar wind dynamic pressure variations in 2002 analyzed using multisatellite data and Kalman filtering

It has been difficult to establish a definitive causal link between radiation belt electron dropouts and solar wind dynamic pressure, due to adiabatic effects and observations limited to a single location in space at one time. Here we reconstruct the radial profiles of radiation belt electron phase space density (PSD) for the entire year of 2002 (solar maximum), based on a combination of the VERB radial diffusion model and data assimilation of the sparse observations from six satellites including GEO1989, GEO1990, LANL‐97A, LANL‐01A, GPSns33, and POLAR, to perform a statistical analysis of the potential relationship between electron PSD dropout and solar wind dynamic pressure variation. We capture 59 electron PSD dropout events, 81% associated with solar wind dynamic pressure sudden jumps (i.e., pulses) or modest increase, consistent with the results of Shprits et al. (2012) for the period of 1990–1991. With the continuous availability of high quality solar wind data in 2002, we further identify 41 pressure pulses and determine that 68% of them are associated with electron PSD dropouts. We also identify 49 pressure enhancements, 41% of which are associated with electron PSD dropouts. Our results support that gradual or sharp enhancements in solar wind dynamic pressure can play an important role in producing electron PSD dropouts, owing to inward intrusion of the magnetopause that enhances the loss to the magnetopause and outward radial diffusion. But we conclusively demonstrate that solar wind dynamic pressure pulses and enhancements are neither a necessary nor a sufficient condition for the formation of electron PSD dropouts, which suggests that some other mechanism(s), which remains mysterious, is required to explain electron PSD dropout occurrences without pressure pulse or modest pressure increase. For the first time, we also perform a quantitative comparison of conjunctions between electron PSD reanalysis results and satellite PSD data, which indicates a tolerable and reasonable error in assimilated PSD within a factor of 5. Differences in assimilated PSD and satellite PSD have a potential for use to evaluate the ignored processes in the physical model and to estimate the errors associated with satellite measurements.

TU‐E‐108‐11: Design and Simulation of a Short, 10 MV, S‐Band Linear Accelerator

Purpose: To design a short (27.5 cm) S‐band linear accelerator capable of producing a 10 MV x‐ray beam to enable higher photon energies for linear accelerator‐MRI hybrid systems, where the waveguide length and linac‐MR orientation is a concern. Methods: Finite element software COMSOL Multiphysics was used to design an accelerator cavity matching one published in an experiment on breakdown, to ensure that the threshold electric field published are applicable to the final waveguide geometry. This cavity was used as the basis for designing an accelerator waveguide, and the full RF field solution within the waveguide was calculated. This RF solution and an electron‐gun phase space generated using Opera3D/SCALA are input into electron tracking software PARMELA to compute the electron phase space striking the x‐ray target. The resulting electron beam is used for Monte Carlo simulations to calculate PDD curves and the beam penumbra, and compared against those produced by a Varian 10 MV. Results: The shunt impedance, Q factor, and ratio of peak‐to‐mean electric fields of the cavity were matched to those in the published study to within 0.1% error. After tuning the full waveguide, the peak surface fields are 207 MV/m, well below the breakdown threshold of 239 MV/m. The peak of the electron spectrum is centered at 10.4 MeV, with a width of 0.2 MeV, compared with 10.5 MeV and 0.3 MeV, respectively, for a Varian 10 MV linac. Monte Carlo results show dmax is 2.15 cm for a 10×10 cm2 field and the penumbra is 5.0 mm wide at 10 cm depth, compared with dmax at 2.3 cm and 5.6 mm width for a Varian 10 MV linac. Conclusion: This work demonstrates the design and modeling of a waveguide capable of producing 10 MV energy x‐rays yet short enough to be compatible with a linac‐MR system.

On the storm‐time evolution of relativistic electron phase space density in Earth's outer radiation belt

We report on internal, magnetospheric processes related to markedly different storm‐time responses of phase space density (PSD) in invariant coordinates corresponding to equatorially mirroring, relativistic electrons in Earth's outer radiation belt. Two storms are studied in detail, selected from a database of 53 events (Dstmin < −40 nT) during the THEMIS era thus far (December 2007–August 2012). These storms are well covered by a number of in situ THEMIS spacecraft and complemented by additional ground‐based and in situ observatories, and they epitomize the divergent behaviors that the outer radiation belt electrons can exhibit during active periods, even during otherwise similar Dst and auroral electrojet (AE) profiles. From our statistical results with the full database, the changes in the radial profile peak in PSD reveal notably consistent behavior with prior studies: 58% of geomagnetic storms resulted in PSD peak enhancements, 17% resulted in PSD peak depletions, and 25% resulted in no significant change in the PSD peak after the storm. For the two case studies, we examined the PSD at multiple equatorial locations (using THEMIS), trapped and precipitating fluxes from low‐Earth orbit (using POES), and chorus, hiss, EMIC, and ULF waves (using THEMIS spacecraft, ground observatories, and the GOES spacecraft). We show that (1) peaks in PSD were collocated with observed chorus waves outside of the plasmapause during the most active periods of the PSD‐enhancing storm but not during the PSD‐depleting storm, providing evidence for the importance of local acceleration by wave‐particle interactions with chorus; (2) outer belt dropouts occurred following solar wind pressure enhancements during both storms and were consistent with losses from magnetopause shadowing and subsequent outward radial transport; during the PSD‐enhancing storm, this revealed how the outer belt can replenish itself seemingly independently of the remnant of the pre‐existing belt leftover after a dropout, which in this case resulted in a double‐peaked outer belt distribution; (3) slow decay in PSD was associated with corresponding locations in L* and enhanced wave amplitudes of plasmaspheric hiss; (4) precipitation loss associated with wave‐particle interactions with hiss and EMIC waves appeared to be significantly more important during the PSD‐depleting storm than the PSD‐enhancing storm; and (5) PSD transport during the recovery phase of both storms and throughout the PSD‐enhancing storm was consistent with ULF‐wave‐driven radial diffusion away from maxima in PSD; this indicates the importance of ULF waves in redistributing outer belt PSD after local acceleration occurs. We conclude that these source, transport, and loss processes, individually well characterized by previous studies, do indeed appear to act in concert, leading to predominance of local acceleration in one case and loss in another. These processes can therefore conspire toward optimal source or loss of outer belt electrons under suitable external drivers, and the conditions resulting in wave growth for these acceleration and loss mechanisms are therefore an important area of future research.

Electron source at the outer boundary of the radiation belts: Storm time case

We examine the strength of the electron source at the outer boundary of the radiation belts using multisatellite observations from Time History of Events and Macroscale Interactions during Substorms during one moderate geomagnetic storm. The electron phase space density (PSD) as a function of the first adiabatic invariant for an equatorially mirroring population over a broad energy range is used to determine the source strength. It is found that the source strength from dipolarization at the outer boundary of the radiation belts during this storm period is well above the observed phase space densities of relativistic electrons inside the outer radiation belt, indicating that the inward radial transport can be a potential source of the relativistic electrons within the radiation belts, even in the strong pitch angle diffusion limit.

Hybrid modeling of relativistic underdense plasma photocathode injectors

The dynamics of laser ionization-based electron injection in the recently introduced plasma photocathode concept is analyzed analytically and with particle-in-cell simulations. The influence of the initial few-cycle laser pulse that liberates electrons through background gas ionization in a plasma wakefield accelerator on the final electron phase space is described through the use of Ammosov-Deloine-Krainov theory as well as nonadiabatic Yudin-Ivanov (YI) ionization theory and subsequent downstream dynamics in the combined laser and plasma wave fields. The photoelectrons are tracked by solving their relativistic equations of motion. They experience the analytically described transient laser field and the simulation-derived plasma wakefields. It is shown that the minimum normalized emittance of fs-scale electron bunches released in mulit-$\mathrm{GV}/\mathrm{m}$-scale plasma wakefields is of the order of ${10}^{\ensuremath{-}2}\text{ }\text{ }\mathrm{mm}\text{ }\mathrm{mrad}$. Such unprecedented values, combined with the dramatically increased controllability of electron bunch production, pave the way for highly compact yet ultrahigh quality plasma-based electron accelerators and light source applications.

Frequency drift of Saturn chorus emission compared to nonlinear theory

The fine structure of nonlinear drifting‐frequency chorus is observed at Saturn by the Cassini Radio and Plasma Wave Investigation. During a high‐inclination orbit in which Cassini is at near‐constant L‐shell within about 10° of the magnetic equator, moderately intense nonlinear chorus is observed. Cassini observed a region of intense chorus and large bandwidth a few degrees on either side of the magnetic equator, with lower intensities and bandwidths observed nearest the magnetic equator. Using the observed plasma wave spectra and electron phase space distribution, we have measured plasma parameters within or near the chorus generation region and evaluated the theoretical value of the frequency sweep rate, ∂f/∂t, based on the nonlinear wave growth theory of Omura et al. and the backward wave oscillator theory of Trakhtengerts. Both theories produce rates that are within a factor of 2 of the observed values, but the nonlinear wave growth theory values are closer to the observations for the cases examined. The work presented is consistent with nonlinear theory in the generation of chorus, but also reveals a distinct region of weaker or linear chorus growth nearest to the magnetic equator at Saturn.

Intensity dependence of electron gas kinetics in a laser corona

In various experimental situations relevant to the laser fusion, such as plasma near the light entrance holes of hohlraum in the indirect drive experiments or more recently in the shock ignition direct drive a relatively long underdense plasma of corona type is encountered, which is subject to an intense nanosecond laser beam. The plasma is only weakly collisional and thus in the electron phase space a complicated kinetic evolution is going on, which is taking the electron gas fairly far from the thermal equilibrium and contributes to its unstable behaviour. These phenomena impede the absorption and thermalization of the incoming laser energy, create groups of fast electrons and also may lead to a non- linear reflection of the heating laser beam. One of the key processes leading to the electron acceleration is the stimulated Raman scattering (SRS) in its non-linear phase. The SRS in the presence of electron- ion collisions requires a certain threshold intensity above which the mentioned non-dissipative phenomena can occur and develop to the stage, where they may become unpleasant for the fusion experiments. To assess this intensity limit a computational model has been developed based on the Vlasov-Maxwell kinetics describing such a plasma in 1D geometry. At a relatively high intensity of 10 16 W/cm 2 a number of non-linear phenomena are predicted by the code such as a saturation of Landau damping, which is then translated in an unfavourable time dependence of the reflected light intensity and formation of accelerated electron groups due to the electron trapping. The purpose of the present contribution is to map the intensity dependence of this non-linear development with the aim of assessing its weight in fusion relevant situations.

Nonlinear frequency shift in the course of quasistationary evolution of the plasma wave of finite amplitude

Frequency shift of the Langmuir wave in the course of a very slow increase of its amplitude is analyzed. Because of this shift, a dip arises on the plateau of trapped electron distribution at the beginning of evolution with small amplitudes. This dip is caused by electron deficiency (formation of an electron hole) in the resonance region of the electron phase space. Because of this, the dispersion of wave with small but finite amplitudes is caused by the influence of the electron hole. At sufficiently large amplitudes, the perturbation of the trapped electron distribution in the form of the electron hole practically vanishes, and the wave dispersion is described by the well-known law.

Quasi-linear modeling of gyroresonance between different MLT chorus and geostationary orbit electrons

The contributions of dayside and nightside gyroresonance of chorus waves to electron radiation belt evolution at L = 6.6 are detailedly differentiated via fully solving the two-dimensional Fokker-Plank equation. The numerical results show that the chorus waves at different regions play significantly different roles. The dayside chorus waves can cause obvious loss of energetic electrons at lower pitch angles and weak energization at larger pitch angles. The nightside chorus waves can yield significant energization at larger pitch angles, but cannot efficiently resonate with the energetic electrons at lower pitch angle. Due to the numerical difficulty in fully solving Fokker-Planck equation, the cross diffusion terms are often ignored in the previous work. Here the effect of cross diffusion at different regions is further analyzed. On the dayside, ignoring cross diffusion overestimates the electron phase space density by several orders of magnitude at lower pitch angles, and consequently the dayside chorus waves are incorrectly regarded as an effective energization mechanism. On the nightside, ignoring cross diffusion overestimates the electron phase space density (PSD) by about one order of magnitude at larger pitch angles. These numerical results suggest that cross diffusion terms can significantly affect gyroresonance of chorus waves on both the dayside and nightside, which should be included in the future radiation belt models.

Implications for the electron distribution from the stationary hydrodynamic model of a one-dimensional plasma expansion into vacuum

It is shown that the hydrodynamic model of a one-dimensional collisionless plasma expansion is contained in the kinetic description as a special case. This belongs to a specific choice for the electron distribution function. Moreover, the consequences of the use of the hydrodynamic approach regarding the temporal evolution of the electron phase space density are investigated. It turns out that only the case of a hydrodynamic description with the adiabatic constant κ=3 is physically self-consistent. Numerical simulations confirm this argumentation. The analysis for the case κ=3 is extended to the kinetics of a relativistic electron gas.

Electron source associated with dipolarization at the outer boundary of the radiation belts: Non‐storm cases

We examine the strength of the electron source associated with dipolarization at the outer boundary of the radiation belts using multisatellite observations from THEMIS. This topic is relevant to the determination on the relative roles of inward radial diffusion versus internal local acceleration for the origin of the relativistic electrons in the outer radiation belt. We focus on the electron phase space density (PSD) as a function of the first adiabatic invariant (μ) for equatorially mirroring population over a broad energy range. It is found that the source strength associated with dipolarization for non‐storm periods at the outer boundary of the radiation belts can be well above the observed fluxes of relativistic electrons inside the outer radiation belt. The PSD change due to the magnetic field strength variation dominates over PSD change from the energy flux increase with dipolarization, resulting in a strong anticorrelation between magnetic field strength and PSD values at a given μ. If observations from closely spaced satellites during the same event can be used to indicate radial transport of electrons with dipolarization, then the observed PSD at these satellites indicates frequent occurrence of non‐adiabatic process during their radial transport.

Uncovering the nonadiabatic response of geosynchronous electrons to geomagnetic disturbance

We describe an energy spectrum method for scaling electron integral flux, which is measured at a constant energy, to phase space density at a constant value of the first adiabatic invariant which removes much of the variation due to reversible adiabatic effects. Applying this method to nearly a solar cycle (1995–2006) of geosynchronous electron integral flux (E > 2.0 MeV) from the GOES satellites, we see that much of the diurnal variation in electron phase space density at constant energy can be removed by the transformation to phase space density at constant μ (4000 MeV/G). This allows us a clearer picture of underlying nonadiabatic electron population changes due to geomagnetic activity. Using scaled phase space density, we calculate the percentage of geomagnetic storms resulting in an increase, decrease, or no change in geosynchronous electrons as 38%, 7%, and 55%, respectively. We also show examples of changes in the electron population that may be different from the unscaled fluxes alone suggest. These examples include sudden electron enhancements during storms which appear during the peak of negative Dst for μ‐scaled phase space density, contrary to the slow increase seen during the recovery phase for unscaled phase space density for the same event.

Extended Tonks–Langmuir-type model with non-Boltzmann-distributed electrons and cold ion sources

AbstractA general formalism for calculating the potential distribution Φ(z) in the quasineutral region of a new class of plane Tonks–Langmuir (TL)-type bounded-plasma-system (BPS) models differing from the well-known ‘classical’ TL model (Tonks, L. and Langmuir, I. 1929 A general theory of the plasma of an arc. Phys. Rev. 34, 876) by allowing for arbitrary (but still cold) ion sources and arbitrary electron distributions is developed. With individual particles usually undergoing microscopic collision/sink/source (CSS) events, extensive use is made here of the basic kinetic-theory concept of ‘CSS-free trajectories’ (i.e., the characteristics of the kinetic equation). Two types of electron populations, occupying the ‘type-t’ and ‘type-p’ domains of electron phase space, are distinguished. By definition, the type-t and type-p domains are made up of phase points lying on type-t (‘trapped’) CSS-free trajectories (not intersecting the walls and closing on themselves) and type-p (‘passing’) ones (starting at one of the walls and ending at the other). This work being the first step, it is assumed that ε ≡ λD/l → 0+ (where λD and l are a typical Debye length and a typical ionization length respectively) so that the system exhibits a finite quasineutral ‘plasma’ region and two infinitesimally thin ‘sheath’ regions associated with the ‘sheath-edge singularities’ | dΦ/dz|z→±zs → ∞. The potential in the plasma region is required to satisfy a plasma equation (quasineutrality condition) of the form ni {Φ} =ne (Φ), where the electron density ne (Φ) is given and the ion density ni {Φ} is expressed in terms of trajectory integrals of the ion kinetic equation, with the ions produced by electron-impact ionization of cold neutrals. While previous TL-type models were characterized by electrons diffusing under the influence of frequent collisions with the neutral background particles and approximated by Maxwellian (Riemann, K.-U. 2006 Plasma-sheath transition in the kinetic Tonks–Langmuir model. Phys. Plasmas 13, 063508) or bi-Maxwellian (Godyak, V. A. et al. 1995 Tonks–Langmuir problem for a bi-Maxwellian plasma. IEEE Trans. Plasma Sci. 23, 728) electron velocity distribution functions (VDFs), which satisfy the zero-CSS-term (Vlasov) kinetic equation and imply zero electron currents, we here propose a more general class of electron VDFs allowing, in an approximate manner, for non-zero CSS terms and finite electron currents inside the plasma region. The sheath-edge and floating-wall potentials are calculated by balancing the ion and electron current densities at sheath-edge singularities. In a first detailed application, the type-t and type-p electron VDFs are assumed to be ‘inner’ and ‘outer’ cut-off Maxwellians respectively, with different amplitudes and ‘formal’ temperatures, implying the perfectly CSS-free limit. For the special case of equal type-t and type-p electron VDF amplitudes and formal temperatures, the classical Boltzmann distribution for electrons is formally retrieved. Special cases with other amplitude and formal-temperature ratios show significant deviations from the classical case.

Effect of ion-to-electron mass ratio on the evolution of ion beam driven instability in particle-in-cell simulations

In particle-in-cell (PIC) simulation studies of ion-ion two-stream instability, a reduced ion-to-electron mass ratio is often employed to save computation time. It is tacitly assumed that electrons do not play a significant role in the evolution of the instability as the ion-ion interactions are regarded to occur on time scales much slower than the response time of electrons. However, as the effect of such a reduced mass ratio has never been closely examined, we have studied the evolution of the ion beam driven instability using a one-dimensional electrostatic PIC code by rescaling the simulation parameters according to the ion-electron mass ratio. We made a reference simulation run with a mass ratio of 100 first and compared the results to the simulation results using the real mass ratio with parameters rescaled from those of the reduced mass ratio. External electric fields were applied in these simulations, which accelerated the electrons and excited an ion acoustic type instability, forming electron phase space holes. Merging of the electron holes affected the ion dynamics significantly when the reduced mass ratio was used, while the interplay between the electron and ion dynamics became different depending on the rescaling methods in the case of the real mass ratio. Another simulation test with much enhanced external electric field results in similar mass ratio dependence. The present simulation results clearly show that the reduced mass ratio should be used cautiously in PIC simulations as the electron dynamics can modify the ion instabilities significantly by affecting the ion motions.