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At least 19 records

A dynamic protein interactome drives energy conservation and electron flux in Thermococcus kodakarensis

ABSTRACT Life is supported by energy gains fueled by catabolism of a wide range of substrates, each reliant on the selective partitioning of electrons through redox ( red uction and ox idation) reactions. Electron flux through tunable and regulated protein interactions provides dynamic routes for energy conservation, but how electron flux is regulated in vivo , particularly for archaeal metabolisms that support rapid growth at the thermodynamic limits of life, is poorly understood. Identification of bona fide in vivo protein assemblies and how such assemblies dictate the totality of electron flux is critical to our understanding of the regulation imposed on metabolism, energy production, and energy conservation. Here, 25 key proteins in central metabolic redox pathways in the model, genetically accessible, hyperthermophilic archaeon Thermococcus kodakarensis , were purified to reveal an extensive, dynamic, and tightly interconnected network of protein interactions that responds to environmental cues (such as the availability of various reductive sinks) to direct electron flux to maximize energetic gains. Interactions connecting disparate functions suggest many catabolic and anabolic activities occur in spatial proximity in vivo , and while protein complexes have been historically defined under optimal conditions, many of these complexes appear to maintain alternative partnerships in changing conditions. The totality of the results obtained redefines our understanding of in vivo assemblies driving ancient metabolic strategies supporting the growth of modern Archaea. IMPORTANCE Given the potential for rational genetic manipulations of biofuel- and biotech-promising archaea to yield transformative results for major markets, it is a priority to define how the metabolisms of such species are controlled, at least in part, by in vivo protein assemblies, and from such, define routes of energy flux that can be most efficiently altered toward biofuel or biotechnological gains. Proteinaceous electron carriers (PECs, such as ferredoxins) offer the potential for specific protein–protein interactions to coordinate selective reductive flow. Employing the model, genetically accessible, hyperthermophilic archaeon, Thermococcus kodakarensis , we establish the metabolic protein interactome of 25 key redox proteins, revealing that each redox active protein has a dynamic partnership profile, suggesting catabolic and anabolic activities may occur in concert and in temporal and spatial proximity in vivo . These results reveal critical importance in evaluating the newly identified partnerships and their role and utility in providing regulated redox flux in T. kodakarensis .

Williams, Sere A. (ORCID:0000000235509590)

Radio Frequency Transients Correlated with Electron Flux Measured On-Board the STP-Sat6

We analyzed transient electromagnetic signatures, referred to as spacecraft environment discharges (SEDs) or on-board discharges (OBDs), and the in-situ particle environment simultaneously measured by the Radio Frequency Sensor (RFS) and the Space and Atmospheric Burst Reporting System Z-plasma spectrometer (SABRS-ZPS), respectively. These sensors are on-board the U.S. Department of Defense Space Test Program Satellite 6 (STP-Sat6) in geostationary orbit. Radio frequency signatures of SEDs on STP-Sat6 have relatively high peak amplitudes; they often caused amplitude-saturation in the so-called high band (120–140 MHz frequency range) of the RFS likely due to the proximity of their source to the RFS’s dipole antennas. We examined the occurrence rate of SEDs reported by the RFS and its temporal relationship to electron flux in the 7.9–12.2 keV range. Peaks in SED count rates were time-correlated with peaks in electron flux. The electron-flux peaks appeared to lead the SED count rate peaks by 24–45 min for the 7.9–12.2 keV energies. This indicates that incidence of electrons at this relatively low-energy range likely resulted in ramping up of the charging of the spacecraft leading to periods of high occurrence rates of discharges in and around the spacecraft.

54 ENVIRONMENTAL SCIENCES

Gyrokinetic profile prediction and validation of a negative triangularity plasma in ASDEX Upgrade

In this work, gyrokinetic simulations are performed with the CGYRO code (Candy et al 2016 J. Comput. Phys. 324 73–93) for a negative triangularity H-mode plasma in ASDEX Upgrade, and compared with experimental measurements. The PORTALS framework (Rodriguez-Fernandez et al 2024 Nucl. Fusion 64 076034) is used to accelerate the prediction of kinetic profiles for this plasma, using surrogate modeling and Bayesian optimization. Ion heat flux, electron heat flux, and electron particle flux are simultaneously matched across the simulated radial regime of the plasma (normalized radius $r/a = 0.35-0.90$), and the resulting ion temperature, electron temperature, and electron density profiles match well with the experimental profile data within this radial range. A synthetic Correlation Electron Cyclotron Emission diagnostic is applied to find well-matched electron temperature fluctuation properties between simulation and experiment. The flux-matched profiles provide a basis for investigation of the turbulence nature across the plasma radius, revealing the dominance of Trapped Electron Mode turbulence at $r/a = 0.35$, the dominance of Ion Temperature Gradient turbulence at $r/a = 0.55$, 0.75, and 0.83, and an instability boundary at $r/a = 0.90$.

gyrokinetic simulation

Limits on the Low-energy Electron Antineutrino Flux from the Brightest Gamma-Ray Burst of All Time

The electron antineutrino flux limits are presented for the brightest gamma-ray burst (GRB) of all time, GRB221009A, over a range of 1.8–200 MeV using the Kamioka Liquid Scintillator Antineutrino Detector. Using multiple time windows ranging from minutes to days surrounding the event to search for electron antineutrinos coincident with the GRB, we set an upper limit on the flux under the assumption of several power-law neutrino source spectra, with power-law indices ranging from 1.5 to 3 in steps of 0.5. No excess was observed in any time windows ranging from seconds to days around the event trigger time T 0 . For a power-law index of 2 and a time window of T 0 ± 500 s, a flux upper limit of 2.34 × 10 9 cm −2 was calculated. The limits are compared to the results presented by IceCube.

79 ASTRONOMY AND ASTROPHYSICS

Effect of Impurities on the Redox Properties of Goethite

Iron oxide minerals regulate the flux of electrons in the environment and are important hosts for trace and minor, yet critical, elements. Here, we present the first evidence of a direct link between the local coordination environments of Ni and Zn and the redox properties of their host phase goethite (α-FeOOH), the most abundant Fe(III) (oxyhydr)oxide at Earth’s surface. Here, we used aqueous redox measurements to show that the redox potential E H 0 , and hence the mineral’s stability, follows the order: pure goethite ≥ Zn-goethite > Ni-goethite. Parallel X-ray absorption and scattering measurements demonstrate, using quantum-informed analysis, that the local coordination environment of the smaller impurity, Ni, causes more bulk strain energy than Zn, which nearly accounts for the difference in E H 0 between Ni- and Zn-goethite. Our theory-informed, experimental study reveals how two common impurities affect the stability of goethite with implications for the biogeochemical reactivity of Fe(III) (oxyhydr)oxide in mediating elemental and electron fluxes in the environment.

42 ENGINEERING

Rerouting reductant flux via protein tethering enhances biohydrogen production in Thermococcus kodakarensis

Microbes that generate copious amounts of hydrogen (H 2 ) via dark fermentation are a promising means to evolve and improve renewable biofuels. Many anaerobic hyperthermophilic archaea, such as the fast-growing, genetically tractable, heterotroph Thermococcus kodakarensis, produce generous quantities of H2 and provide an idealized platform to further optimize naturally high levels of biohydrogen reduction. Precise genetic manipulations and modifications to growth conditions have already resulted in substantial increases to H2 output but additional improvements are desired. An unexamined and potentially valuable route towards increased H 2 production is to tether select electron donor and acceptor proteins together to reroute and maximize the flow of electrons towards H 2 production. Such strategies have shown promise in Bacteria and Eukarya but have not yet been investigated in thermophilic Archaea. Here, we generate and evaluate twelve novel T. kodakarensis strains wherein a proteinaceous electron carrier (a ferredoxin, Fd) is physically tethered to the membrane-bound-hydrogenase (MBH), the sole H 2 producing enzyme, to direct electron flux towards biohydrogen generation. Growth assessments and H 2 output measurements demonstrate that strains encoding protein-fusions evolve up to ~ 40% more H2 per cell than the host strain. Eliminating H 2 consumption and alternative routes of electron sinks in concert with protein tethering further increased H2 output per cell for a maximum increase of ~ 66% over the host strain. Our results demonstrate that rerouting electron flux via protein tethering coupled with the elimination of reductant sinks is a promising means towards improved biohydrogen production in T. kodakarensis. KEY POINTS: Protein tethering between redox proteins can reroute electron flux in vivo. Enforced protein proximity results in ~ 40% increases in H2 production per cell. Protein-tethering provides a generalizable framework to redirect redox metabolism.

59 BASIC BIOLOGICAL SCIENCES

First JSNS 2 measurement of the electron neutrino flux using the 12 C⁡(𝜈 𝑒 ,𝑒 − )⁢ 12 N g.s. reaction

JSNS2 (J-PARC Sterile Neutrino Search at J-PARC Spallation Neutron Source) is an experiment searching for sterile neutrinos through the observation of ν¯μ→ν¯e appearance oscillations, using neutrinos produced by muon decay-at-rest. A key aspect of the experiment involves accurately understanding the neutrino flux and the quantities of pions and muons, which are progenitors of (anti)neutrinos, given that their production rates have yet to be measured. We present the first electron-neutrino flux measurement using C12(νe,e−)12Ng.s. reaction in JSNS2, yielding a flux of (6.7±1.6(stat)±1.7(syst))×10−9 cm−2 proton−1 at the JSNS2 detector location, located at 24 meters distance from the mercury target. This flux measurement is consistent with predictions from simulations based on hadron models.

Particle decays

Anisotropic Heating and Parallel Heat Flux in Electron-only Magnetic Reconnection with Intense Guide Fields

Electron-only reconnection (E-REC) is a process recently observed in the Earth’s magnetosheath, where magnetic reconnection occurs at electron kinetic scales, and ions do not couple to the reconnection process. Electron-only reconnection is likely to have a significant impact on the energy conversion and dissipation of turbulence cascades at kinetic scales in some settings. This paper investigates E-REC under different intensities of strong guide fields (the ratio between the guide field and the in-plane asymptotic field strength is 5, 10 and 20, respectively) via two-dimensional fully kinetic particle-in-cell simulations, focusing on electron heating. The simulations are initialized with a force-free current sheet equilibrium under various intensities of strong guide fields. Similarly to previous experimental studies, electron temperature anisotropy along separatrices is observed, which is found to be mainly caused by the variations of parallel temperature. Both regions of anisotropy and parallel temperature increase/decrease along separatrices become thinner with increasing guide fields. Besides, we find a transition from a quadrupolar to a hexapolar (six-polar) to an octopolar (eight-polar) structure in temperature anisotropy and parallel temperature as the guide field intensifies. Non-Maxwellian electron velocity distribution functions (EVDFs) at different locations in the three simulations are observed. Our results show that parallel electron velocity varies notably with different guide field intensities and finite parallel electron heat flux density is observed. The three simulations exhibit features of the Chew–Goldberger–Low theory, with the level of consistency increasing as the guide field strength increases. This explains the electron parallel temperature variations and the shape of the EVDFs observed along the separatrices. This work may provide insights into the understanding of electron heating and parallel heat flux density in E-REC observed in the turbulent magnetosheath.

79 ASTRONOMY AND ASTROPHYSICS

PreMevE‐MEO: Predicting Ultra‐Relativistic Electrons Using Observations From GPS Satellites

Abstract Ultra‐relativistic electrons with energies greater than or equal to two megaelectron‐volt (MeV) pose a major radiation threat to spaceborne electronics, and thus specifying those highly energetic electrons has a significant meaning to space weather communities. Here we report the latest progress in developing our predictive model for MeV electrons in the outer radiation belt. The new version, primarily driven by electron measurements made along medium‐Earth‐orbits (MEO), is called PREdictive MEV Electron (PreMevE)‐MEO model that nowcasts ultra‐relativistic electron flux distributions across the whole outer belt. Model inputs include >2 MeV electron fluxes observed in MEOs by a fleet of GPS satellites as well as electrons measured by one Los Alamos satellite in the geosynchronous orbit. We developed an innovative Sparse Multi‐Inputs Latent Ensemble NETwork (SmileNet) which combines convolutional neural networks with transformers, and we used long‐term in situ electron data from NASA's Van Allen Probes mission to train, validate, optimize, and test the model. It is shown that PreMevE‐MEO can provide hourly nowcasts with high model performance efficiency and high correlation with observations. This prototype PreMevE‐MEO model demonstrates the feasibility of making high‐fidelity predictions driven by observations from longstanding space infrastructure in MEO, thus has great potential of growing into an invaluable space weather operational warning tool.

79 ASTRONOMY AND ASTROPHYSICS

Strong gradient effects on neoclassical electron transport and the bootstrap current in large aspect ratio tokamaks

Standard approaches to neoclassical theory do not extend into regions of strong gradients in tokamaks such as the pedestal and internal transport barriers. Here, we calculate the modifications to neoclassical electron physics inside strong gradient regions of large aspect ratio tokamaks in the banana regime. We show that these modifications are due to the different ion flow and the strong poloidal variation of the potential. We also provide a physical interpretation of the mechanisms that drive poloidal asymmetries and hence a poloidal electric field. We apply our model to two specific example cases of pedestal profiles, calculating the neoclassical electron flux and the bootstrap current. We find that, depending on the ion flow, weak gradient neoclassical theory overestimates or underestimates the neoclassical electron transport and the bootstrap current in regions with strong gradients. We show that the determination of the mean parallel flow is more complex than in weak gradient neoclassical theory. For vanishing turbulence, we can determine the radial electric field for a given flow profile in the pedestal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Mitigation of Boiling-Induced Thermal Degradation Using Microporous Nickel Inverse Opals Structures

Engineered microporous structures have received much attention in high-heat-flux electronics cooling due to their high thermal conductivity and permeability, and large surface area for heat transfer, but are susceptible to boiling-induced thermal degradation. Here, this study investigates the efficacy of nickel inverse opals (NiIOs) in mitigating structural degradation caused by corrosion-assisted erosion during pool boiling with water as the working fluid. First, we compared the reliability of NiIOs to copper inverse opals (CuIOs) for a 3-day pool boiling test at constant heat flux. The NiIOs demonstrated superior resistance to thermal degradation due to their inherent corrosion resistance and mechanical strength. Subsequently, we conducted a more controlled experiment to show the effect of heat flux on the degradation of the NiIOs while excluding the effect of temperature variations. Pool boiling tests of 20-μm-thickness NiIOs covering an area of ∼11 × 11 mm 2 with a 2.5 × 2.5 mm 2 heater at the center were conducted at heat flux levels of 20%, 40%, and 60% of the critical heat flux (CHF) for 3 days. The NiIOs subjected to heat flux levels of 20% and 40% CHF showed minimal degradation, while the sample subjected to 60% CHF showed erosion on the top surface due to higher bubble formation and departure rate. These results show the potential of NiIOs as a promising solution for long-term thermal management in high-power electronic devices, although design considerations for maximum allowable heat flux are necessary for reliable operation.

36 MATERIALS SCIENCE

Measurements of the electron energy distribution function in partially magnetized low temperature plasmas

While Langmuir probes (LPs) are relatively simple and inexpensive plasma diagnostics for the electron density, temperature, and the electron energy distribution function (EEDF), the interpretation of the measured current–voltage (I–V) characteristic is complicated considerably by the presence of a magnetic field. In regimes where the electron gyroradius is comparable to the probe radius, the electron flux to the probe surface is retarded by reduced mobility across field lines and can no longer be described by a thermal model. Predicting the current collected by the probe in these regimes requires accurate estimates of the plasma diffusion coefficients, which are usually difficult to obtain. In this work, we measure electron energy distribution functions in E×B plasmas with magnetized electrons and non-magnetized ions in argon and krypton gases, using both a LP and laser Thomson scattering (LTS) at various magnetic fields. Using the LTS measurements to provide a robust benchmark for comparison, we compare existing theories describing the flux to the probe under magnetized conditions. We find that even when the electron gyroradius associated with the effective electron temperature is small compared to the probe radius, the EEDF computed using classical probe theory is still robust at energies higher than the energy at which the gyroradius becomes larger than the probe size. For plasmas that are not strongly non-Maxwellian, we formulate a method to extract robust density and temperature measurements using physics-informed fitting techniques to analyze EEDFs computed using classical theory.

Devin, E. G. [Princeton Plasma Physics Laboratory

Outer Radiation Belt Dynamics During the October 2012 Storm Revisited: Rapid Inward Radial Transport From a Dynamic Outer Boundary

Earth's outer radiation belt electron flux is highly variable and can be enhanced by over an order of magnitude over timescales less than one day, as observed during the October 2012 storm. Previous studies of this storm (e.g., Reeves et al., 2013, https://doi.org/10.1126/science.1237743) have invoked local acceleration to explain this. However, here, we argue that the observations can instead be explained by fast inward radial transport. One method often invoked to distinguish between these two acceleration processes is the existence of local peaks in electron phase space density (PSD) as a function of L* at fixed first, M, and second, K, adiabatic invariants. However, this method relies on the assumption that the evolution of the PSD as a function of L* occurs over timescales slower than the satellite orbital period. Here, high spatiotemporal resolution data from the Global Positioning System (GPS) spacecraft constellation is used to show that enhancements in the PSD occur during the October 2012 storm over short timescales not resolvable by the Van Allen Probes. In addition, Geostationary Operational Environmental Satellite spacecraft data also indicate that these enhancements are consistent with relativistic electron injections. A radial diffusion model is shown to reproduce the PSD dynamics observed by the Van Allen Probes, once rapid variations at the simulation outer boundary are included, consistent with GPS data. This verifies that apparently “locally growing” peaks in PSD along high apogee satellite orbits can be produced by fast inward radial transport without requiring the action of any local acceleration processes.

99 GENERAL AND MISCELLANEOUS

Derivations of the Total Radiation Belt Electron Content

Abstract We present multiple derivations of the Total Radiation Belt Electron Content (TRBEC), an indicator of the global number of electrons that instantaneously occupy the radiation belts. Derived from electron flux measurements, the TRBEC reduces the spatial information into a scalar quantity that concisely describes global aspects of the system. This index provides a simple, global, and long‐term assessment of the radiation belts that enables systematic analysis. In this work, we examine the TRBEC using the adiabatic invariants of which has been used in previous articles as this coordinate system removes reversible adiabatic effects. We then introduce a new expression to compute the TRBEC using the non‐adiabatic coordinates of , relevant in the contexts of energetic electron precipitation, chorus, and hiss scattering where adiabatic invariant quantities are no longer conserved. From both expressions of the TRBEC we demonstrate that an erroneous factor of that appeared in previous works using the adiabatic derivation led to an overestimate of the reported electron populations. In addition, we quantify electron loss in the outer radiation belt via a case study using the Van Allen Probes data over a 20‐day period from March 2013 specifying particle populations both in terms of the aforementioned adiabatic and non‐adiabatic variables. The total number of electrons in the outer radiation belt reached upwards of electrons at the peak of the storm, a rest mass of roughly 10 g.

Astronomy & Astrophysics

Molecular-Resolution Electron Imaging of Defects and Dynamics at the Ice-Water Interface

Water crystallization into hexagonal ice (type I h ) is one of the most critical processes relevant to the Earth’s environment and human activities. However, despite recent breakthroughs in imaging non-equilibrium condensed ice structures, the ice-water interface has never been imaged at a molecular resolution. This is primarily due to the low stability of the hydrogen bonds in ice under high-resolution microscopy conditions and a lack of methods to prepare compatible samples. Here, this presentation describes the first molecular-resolution imaging of ice crystallized from liquid water and the ice-water interface using high-resolution transmission electron microscopy (HRTEM). By encapsulating deionized (DI) water between two amorphous carbon (a-C) TEM grids and subsequently freezing it with liquid N 2 on a cryo sample stage, we generated two types of ice: non-equilibrium, condensed ice from the atmosphere and encapsulated ice from the DI water (Fig. 1A). Condensed ice usually shows irregular, spherulitic shapes (Fig. 1B). Selected area electron diffraction (SAED) shows that they are a mixture of cubic and hexagonal crystals (Fig. 1C). On the contrary, encapsulated ice forms thin films that contain large-area single-crystalline regions of hexagonal ice oriented along the [0001] zone axis (Fig. 1D). Differential electron energy-loss spectroscopy (EELS) confirmed the high purity of the encapsulated ice free from organic contaminations that are common in other encapsulation methods for HRTEM such as graphene liquid cells. These single-crystalline areas are robust under the electron beam up to ~100 e/Å 2 s. Aberration-corrected HRTEM imaging in these areas achieved a line resolution of ~1.3 Å (Fig. 1E and F). This platform allows us to study near-equilibrium ice structures and dynamics at an unprecedented spatial resolution (Fig. 2). For example, we discovered subdomain-rich regions near the defective crystal edges despite the structure appearing single-crystalline according to diffraction criteria. These subdomains connect via low-angle grain boundaries with flat energy landscapes as a function of tilt angles (according to simulations), showing the high tolerance of ice to defect structures. When we tuned the sample temperature and electron flux rate, we observed radiolysis-controlled bubble generation and dissolution in ice single crystals near a steady state of bubble dynamics. Furthermore, rich beam-induced melting and recrystallization dynamics were observed at the ice-water interface with lattice resolution. These data represent the first observation of the ice-water phase transformation at the sub-nanometer level. In summary, the methods developed in this work enabled molecular-resolution observations of ice and the ice-water interface and shed light on the microstructures and phase transformation pathways. Finer control on the temperature, electron irradiation profile, and imaging detector could eventually lead to real-time observation of ice nucleation in water and address long-standing questions in the nucleation pathways.

74 ATOMIC AND MOLECULAR PHYSICS

Azimuthal and axial structures in 3D particle-in-cell simulation of Penning discharge

We report the results of a 3D particle-in-cell simulation of cylindrical Penning discharge with the axial magnetic field in the so-called reflex configuration, where the cathode and anti-cathode are biased to the same negative potential. The discharge is supported by thermal electron emission from the cathode. Electron and ion collisions, including ionization, are fully accounted for. The emphasis is on a specific regime in which the plasma potential at the center of the discharge is positive with respect to the chamber walls, serving as an anode. Spatial and temporal scales of the observed azimuthal and axial fluctuations and structures are characterized. It is suggested that azimuthal structures are caused by the dissipative gradient-drift instability. We find that the axial fluctuations related to the plasma-beam instabilities are weakly correlated with the azimuthal perturbations of the density, so that the azimuthal modes rotate as a whole and do not show any axial shear. The behavior of the electric potential is more involved, demonstrating intermittent standing wave and propagating structures in the axial direction that modulate the electron transport, producing the standing wave pattern (along the z-direction) in the radial electron flux.

3D PIC simulation of discharge

Effects of a magnetic field on hot electron generation from laser-plasma instabilities

We performed two-dimensional simulations of turbulent laser-plasma instabilities in the presence and absence of external magnetic fields using the Laser Plasma Simulation Environment (LPSE) code. The results demonstrate that, in the presence of a magnetic field, the transition from ballistic to gyrating electron motion enhances the energy transfer from electron plasma waves to the electron population. Although stronger magnetic fields produce a larger population of hot electrons, these electrons tend to remain confined near the quarter-critical density, where the instabilities also localize, thereby reducing the potential for hot electron transport deeper into the target. Additionally, we present a scaling analysis that quantifies hot electron generation as a function of plasma electron temperature, density scale length, and applied magnetic field strength. These findings may have important applications for controlling hot electron flux and mitigating preheat in inertial confinement fusion targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Mode transitions and spoke structures in E × B Penning discharge

Two-dimensional particle-in-cell simulations in the (radial-azimuthal) plane perpendicular to the axial direction of a cylindrical $E$ x $B$ Penning discharge are presented. The low-pressure discharge is self-consistently supported by plasma ionization from the electron beam injected axially, along the direction of the external magnetic field. It is shown that with the increasing strength of the external magnetic field, the discharge undergoes a sequence of transitions between several azimuthal modes. Azimuthal m > 1 spiral arm structures are excited at low magnetic field values as plasma confinement improves and the radial density profile becomes peaked. With a larger field, spiral arms with m > 1 are replaced by the m = 1 spoke mode, most clearly seen in plasma density. A transition from spiral arms to the spoke regime occurs when the plasma potential in the center changes from weakly positive (or zero) to negative. Further increase in the magnetic field results in a well-developed m = 1 spoke mode with additional small-scale higher-frequency m > 1 structures inside and around the spoke. It is shown that while ionization and collisions affect some characteristics of the observed fluctuations, the basic features of the spoke and m > 1 spiral structure remained similar without ionization. The role of energy conservation in small-scale high-frequency modes and spoke dynamics is discussed. It is demonstrated that in regimes with the m = 1 spoke mode, additional m = 4 harmonics of the ion and electron fluxes to the wall appear due to the square boundary. The frequency of the m = 1 mode is weakly affected by the geometry of the boundary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY