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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Mergers, cooling flows, and evaporation

Mergers (the capture of cold gas, especially) can have a profound influence on the hot coronal gas of early-type galaxies and clusters, potentially inducing symptoms hitherto attributed to a cooling flow, if thermal conduction is operative in the coronal plasma. Heat can be conducted from the hot phase into the cold phase, simultaneously ionizing the cold gas to make optical filaments, while locally cooling the coronal gas to mimic a cooling-flow. If there is heat conduction, though, there is no standard cooling-flow since radiative losses are balanced by conduction and not mass deposition. Amongst the strongest observational support for the existence of cooling-flows is the presence of intermediate temperature gas with x-ray emission-line strengths in agreement with cooling-flow models. Here, x-ray line strengths are calculated for this alternative model, in which mergers are responsible for the observed optical and x-ray properties. Since gas around 10(exp 4) K is thermally stable, the cold cloud need not necessarily evaporate and hydrostatic solutions exist. Good agreement with the x-ray data is obtained. The relative strengths of intermediate temperature x-ray emission lines are in significantly better agreement with a simple conduction model than with published cooling-flow models. The good agreement of the conduction model with optical, infrared and x-ray data indicates that significantly more theoretical effort into this type of solution would be profitable.

Sparks, W. B.↗
NASA NTRS2003

Understanding Organics in Meteorites and the Pre-Biotic Environment

(1) Refinement of the analytic capabilities of our experiment via characterization of molecule-specific response and the effects upon analysis of the type of sample under investigation; (2) Measurement of polycyclic aromatic hydrocarbons (PAHs) with high sensitivity and spatial resolution within extraterrestrial samples; (3) Investigation of the interstellar reactions of PAHs via the analysis of species formed in systems modeling dust grains and ices; (4) Investigations into the potential role of PAHs in prebiotic and early biotic chemistry via photoreactions of PAHs under simulated prebiotic Earth conditions. To meet these objectives, we use microprobe laser-desorption, laser-ionization mass spectrometry (MuL(exp 2)MS), which is a sensitive, selective, and spatially resolved technique for detection of aromatic compounds. Appendix A presents a description of the MuL(exp 2)MS technique. The initial grant proposal was for a three-year funding period, while the award was given for a one-year interim period. Because of this change in time period, emphasis was shifted from the first research goal, which was more development-oriented, in order to focus more on the other analysis-oriented goals. The progress made on each of the four research areas is given below.

Zare, Richard N.↗
NASA NTRS2007

Development of Multifunctional Radiation Shielding Materials for Long Duration Human Exploration Beyond the Low Earth Orbit

One of the major challenges for long duration human exploration beyond the low Earth orbit and sustained human presence on planetary surfaces would be development of materials that would help minimize the radiation exposure to crew and equipment from the interplanetary radiation environment, This radiation environment consists primarily of a continuous flux of galactic cosmic rays (GCR) and transient but intense fluxes of solar energetic particles (SEP). The potential for biological damage by the relatively low percentage of high-energy heavy-ions in the GCR spectrum far outweigh that due to lighter particles because of their ionizing-power and the quality of the resulting biological damage. Although the SEP spectrum does not contain heavy ions and their energy range is much lower than that for GCRs, they however pose serious risks to astronaut health particularly in the event of a bad solar storm The primary purpose of this paper is to discuss our recent efforts in development and evaluation of materials for minimizing the hazards from the interplanetary radiation environment. Traditionally, addition of shielding materials to spacecrafts has invariably resulted in paying a penalty in terms of additional weight. It would therefore be of great benefit if materials could be developed not only with superior shielding effectiveness but also sufficient structural integrity. Such a multifunctional material could then be considered as an integral part of spacecraft structures. Any proposed radiation shielding material for use in outer space should be composed of nuclei that maximize the likelihood of projectile fragmentation while producing the minimum number of target fragments. A modeling based approach will be presented to show that composite materials using hydrogen-rich epoxy matrices reinforced with polyethylene fibers and/or fabrics could effectively meet this requirement. This paper will discuss the fabrication of such a material for a crewed vehicle. Ln addition, the capability of synthesizing radiation shielding materials for habitat structures primarily from Lunar or Martian in-situ resources will also be presented. Such an approach would significantly _reduce the cost associated with transportation of such materials and structures from earth. Results from radiation exposure measurements will be presented demonstrating the shielding effectiveness of the developed materials. Mechanical testing data will be discussed to illustrate that the specific mechanical properties of the developed composites are comparable to structural aluminum based alloys currently used for the space shuttle and space station.

Sen, S.↗
NASA NTRS2018

Metallic Wall Hall Thrusters

A Hall thruster apparatus having walls constructed from a conductive material, such as graphite, and having magnetic shielding of the walls from the ionized plasma has been demonstrated to operate with nearly the same efficiency as a conventional nonmagnetically shielded design using insulators as wall components. The new design is believed to provide the potential of higher power and uniform operation over the operating life of a thruster device.

Goebel, Dan Michael↗
NASA NTRS2017

Candidate Nutritional Countermeasure to Mitigate Adverse Effects of Spaceflight

Problem statement: During spaceflight, astronauts are subjected to microgravity as well as radiation, both of which have adverse effects on bones, soft tissues and organs, possibly by shared mechanisms. For this reason there is a need to identify broad-spectrum countermeasures to protect multiple tissues from both insults.6.The spaceflight environment poses multiple challenges to homeostasis, including microgravity and ionizing radiation. Together, these factors contribute to cellular stress, and effects include increased generation of reactive oxygen species (ROS), oxidative and DNA damage, cell cycle arrest and cell senescence. We have shown that a purified diet supplemented with dried plum (DP, 25) conferred full protection of cancellous structure from the rapid bone loss caused by exposure to ionizing radiation (Schreurs et al. 2016). Based on these promising results for a new countermeasure to prevent space radiation induced-tissue damage, we will conduct additional studies to advance the potential countermeasure to a higher CRL level. We will test the DP diet for its ability to prevent bone loss caused by simulated microgravity as well as exposure to radiation. This will be achieved by exposing mice to each factor (simulated microgravity and radiation) alone and in combination. We hypothesize that spaceflight conditions lead to oxidative damage and bone loss, and that DP, a dietary additive rich in antioxidant and polyphenolic compounds, is an effective countermeasure for multiple tissues, including bone. To test this hypothesis we will accomplish the following aims: Aim 1 Determine if the antioxidant rich diet DP prevents simulated microgravity-induced bone loss. Aim 2 Determine if DP prevents simulated spaceflight-induced bone loss (microgravity and radiation combined). Aim 3 Determine if DP is effective as a countermeasure for adverse effects of simulated microgravity and radiation on non-skeletal tissues (brain, eye).

Schreurs, Ann-Sofie↗
NASA NTRS2021

Genomic Changes Driven by Radiation-Induced DNA Damage and Microgravity in Human Cells

The space environment consists of a complex mixture of different types of ionizing radiation and altered gravity that represents a threat to humans during space missions. In particular, individual radiation sensitivity is strictly related to the risk of space radiation carcinogenesis. Therefore, in view of future missions to the Moon and Mars, there is an urgent need to estimate as accurately as possible the individual risk from space exposure to improve the safety of space exploration. In this review, we survey the combined effects from the two main physical components of the space environment, ionizing radiation and microgravity, to alter the genetics and epigenetics of human cells, considering both real and simulated space conditions. Data collected from studies on human cells are discussed for their potential use to estimate individual radiation carcinogenesis risk from space exposure.

space radiation↗
NASA NTRS1995

Radiogenic cell transformation and carcinogenesis

Radiation carcinogenesis is one of the major biological effects considered important in the risk assessment for space travel. Various biological model systems, including both cultured cells and animals, have been found useful for studying the carcinogenic effects of space radiations, which consist of energetic electrons, protons and heavy ions. The development of techniques for studying neoplastic cell transformation in culture has made it possible to examine the cellular and molecular mechanisms of radiation carcinogenesis. Cultured cell systems are thus complementary to animal models. Many investigators have determined the oncogenic effects of ionizing and nonionizing radiation in cultured mammalian cells. One of the cell systems used most often for radiation transformation studies is mouse embryonic cells (C3H10T1/2), which are easy to culture and give good quantitative dose-response curves. Relative biological effectiveness (RBE) for heavy ions with various energies and linear energy transfer (LET) have been obtained with this cell system. Similar RBE and LET relationship was observed by investigators for other cell systems. In addition to RBE measurements, fundamental questions on repair of sub- and potential oncogenic lesions, direct and indirect effect, primary target and lesion, the importance of cell-cell interaction and the role of oncogenes and tumor suppressor genes in radiogenic carcinogenesis have been studied, and interesting results have been found. Recently several human epithelial cell systems have been developed, and ionizing radiation have been shown to transform these cells. Oncogenic transformation of these cells, however, requires a long expression time and/or multiple radiation exposures. Limited experimental data indicate high-LET heavy ions can be more effective than low-LET radiation in inducing cell transformation. Cytogenetic and molecular analyses can be performed with cloned transformants to provide insights into basic genetic mechanism(s) of radiogenic transformation of human epithelial cells.

NASA Discipline Radiation Health↗
NASA NTRS2001

The Transition from Hydrogen Bonding to Ionization in (HCI)n(NH3)n and (HCI)n(H2O)n Clusters: Consequences for Anharmonic Vibrational Spectroscopy

Anharmonic vibrational frequencies and intensities are calculated for 1:1 and 2:2 (HCl)(sub n)(NH3)(sub n) and (HCl)(sub n)(H2O)(sub n) complexes, employing the correlation-corrected vibrational self-consistent field method with ab initio potential surfaces at the MP2/TZP computational level. In this method, the anharmonic coupling between all vibrational modes is included, which is found to be important for the systems studied. For the 4:4 (HCl)(sub n)(H2O)(sub n) complex, the vibrational spectra are calculated at the harmonic level, and anharmonic effects are estimated. Just as the (HCl)(sub n)(NH3)(sub n) structure switches from hydrogen-bonded to ionic for n=2, the (HCl)(sub n)(H2O)(sub n) switches to ionic structure for n=4. For (HCl)2(H2O)2, the lowest energy structure corresponds to the hydrogen-bonded form. However, configurations of the ionic form are separated from this minimum by a barrier of less than an O-H stretching quantum. This suggests the possibility of experiments on ionization dynamics using infrared excitation of the hydrogen-bonded form. The strong cooperative effects on the hydrogen bonding, and concomitant transition to ionic bonding, makes an accurate estimate of the large anharmonicity crucial for understanding the infrared spectra of these systems. The anharmonicity is typically of the order of several hundred wave numbers for the proton stretching motions involved in hydrogen or ionic bonding, and can also be quite large for the intramolecular modes. In addition, the large cooperative effects in the 2:2 and higher order (HCl(sub n)(H2O)(sub n) complexes may have interesting implications for solvation of hydrogen halides at ice surfaces.

Chaban, Galina M.↗
DOE OSTI2022

Electronic states and transitions of PrO and PrO + probed by threshold ionization spectroscopy and spin–orbit multiconfiguration perturbation theory

The precise ionization energy of praseodymium oxide (PrO) seeded in supersonic molecular beams is measured with mass-analyzed threshold ionization (MATI) spectroscopy. Here, a total of 33 spin–orbit (SO) states of PrO and 23 SO states of PrO + are predicted by second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Electronic transitions from four low-energy SO levels of the neutral molecule to the ground state of the singly charged cation are identified by combining the MATI spectroscopic measurements with the MCQDPT2 calculations. The precise ionization energy is used to reassess the ionization energies and the reaction enthalpies of the Pr + O → PrO + + e – chemi-ionization reaction reported in the literature. An empirical formula that uses atomic electronic parameters is proposed to predict the ionization energies of lanthanide monoxides, and the empirical calculations match well with available precise experimental measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Effects of delta ray electrons on measurement uncertainties of harp system

A harp system, which is a multi-wire beam profile monitoring (MWPM) system, is planned upstream of the spallation target to make in situ calibration of beam current density configuration on the target along with beam imaging from luminescent coating on the beam entrance window at the Second Target Station (STS) of the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL). This beam interception-based beam diagnostics system on the target will be used to ensure that the maximum beam loads on the target are within the design range during neutron production. Current design of the harp consists of three layers of measurement wires each of which is sandwiched between voltage biasing wire planes. The signal obtained from each measurement wire layer is disturbed by secondary electrons (SE) and delta rays produced by beam-matter interactions in neighboring wires and ionization of residual gases in accelerator vacuum. While the backgrounds from SE can be suppressed by voltage biasing, the delta-ray electrons with kinetic energies above keV ranges overcome the electric potential bias. In this paper, we study the effects of delta-rays on the measurement uncertainties of MWPM using the particle transport simulation code FLUKA. Furthermore, the cases where the harp system is installed in the proximity of a large delta ray sources such as proton beam window or in the core vessel filled with sub-atmospheric gas have been studied.

Lee, Yong Joong↗
DOE OSTI2022

A Critical Review of Radiolysis Issues in Water-Cooled Fission and Fusion Reactors: Part I, Assessment of Radiolysis Models

A critical review is presented on modeling of the radiolysis of the coolant water in nuclear power reactors with emphasis on ITER. The review is presented in two parts: In Part I, we assess previous work in terms of compliance with important chemical principles and conclude that no model proposed to date is completely satisfactory, in this regard. Thus, some reactions that have been proposed in various radiolysis models are not elementary in nature and can be decomposed into two or more elementary reactions, some of which are already included in the models. These reactions must be removed in formulating a viable model. Furthermore, elementary reactions between species of like charge are also commonly included, but they can be discounted upon the basis of Coulombic repulsion under the prevailing conditions (T < 350 °C) and must also be removed. Likewise, it is concluded that the current state of knowledge with respect to radiolytic yields (i.e., G-values) is also unsatisfactory. More work is required to ensure that the yields used in radiolysis models are truly “primary” yields corresponding to a time scale of nanoseconds or less. This is necessary to ensure that the impact of the reactions that occur outside of the spurs (ionizing particle tracks in the medium) are not counted twice. In Part II, the authors review the use of the radiolysis models coupled with electrochemical models to predict the water chemistry, corrosion potential, crack growth rate in Type 304 SS, and accumulated damage in the coolant circuits of boiling water reactors, pressurized water reactors, and the test fusion reactor, ITER. Based on experience with fission reactors, the emphasis should be placed on the control of the electrochemical corrosion potential because it is the parameter that best describes the state of corrosion in coolant circuits.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1981

Rocket experiments

Payloads designed to study the ionization and the ionizing sources (energetic particles) during periods of auroral activity are described. These include a probe experiment to measure the variation in electron concentration, to measure electron temperature, and to measure the vehicle potential; a propagation experiment to obtain the electron concentration and the electron collision frequency; and an energetic particle experiment to measure particle energy spectra.

Source record↗
NASA NTRS1995

Power MOSFETs Formed In Silicon Carbide

High-performance power metal/oxide/semiconductor field-effect transistors (MOSFETs) fabricated in silicon carbide. Devices offer potential advantages over silicon-based MOSFETs, including lower "on" - state resistances at same rated voltages, ability to operate at higher temperatures, and higher thermal conductivity. Also more resistant to damage by ionizing radiation, an advantage for switching appications in nuclear facilities.

Palmour, John W.↗
NASA NTRS2000

What Quasars Really Look Like: Unification of the Emission and Absorption Line Regions

We propose a simple unifying structure for the inner regions of quasars and AGN. This empirically derived model links together the broad absorption line (BALS), the narrow UV/X-ray ionized absorbers, the BELR, and the 5 Compton scattering/fluorescing regions into a single structure. The model also suggests an alternative origin for the large-scale bi-conical outflows. Some other potential implications of this structure are discussed.

Elvis, Martin↗
DOE OSTI2020

Ambient Mass Spectrometry Rapid Analysis Methods for Trace Inorganics

The ability to rapidly detect and characterize the chemistry of trace quantities of inorganic species has multiple potential applications, including nuclear safeguards, nuclear forensics, and environmental monitoring. Some mass spectrometric methods currently exist, but they are costly and time-intensive, often destroying chemical information in the process of ionization. Ambient mass spectrometry is a relatively new analytical method in which samples are introduced to the mass spectrometer from atmospheric pressure, rather than from high vacuum. Ambient MS can operate with gentler ionization methods such as electrospray ionization (ESI) and paper-spray ionization (PSI), reducing fragmentation and preserving the chemical information of the analyte. This may be useful for determining the intended purpose of material in a sample. Strontium, part of nuclear fallout, is analyzed here to test these new analytical methods for viability. Electrospray ionization mass spectrometry functions by spraying the sample as a solution through a needle charged to a few kV. A nebulizing gas flows out along with the sample to create the spray before droplets enter a drying chamber with heated drying gas to remove the solvent molecules. From there bare analyte ions enter the mass spectrometer. This method has the advantage of relatively fast sample preparation and stable ionization. More stable ionization produces higher-quality data. Paper-spray ionization mass spectrometry operates by applying sample to a paper triangle. The paper triangle is then electrified in a metal clamp to a few kV before spray solvent is applied. The spray solvent transports analyte in the sample to the tip, where it is ionized and enters the mass spectrometer. One advantage of this method is reduced sample preparation - an analyst can even swipe a surface and cut a triangle directly from the swipe. The data analysis serves to rapidly process tens of samples all at once. The mass spectrometer outputs a file containing a few hundred spectra for each sample. The pipeline processes each one to identify peaks of interest. A full palette of data analysis metrics are generated, including plots of the raw data and plots of calculated values such as isotopic ratios. The pipeline filters the raw data to remove noise and background peaks, as well as peaks representing detector saturation. A heat map is generated to show the overall spectrum in mass-time- intensity space. Post-processing, we obtained the desired calibration curves, demonstrating that both ESI-MS and PSI-MS are viable methods for quantifying trace amounts of inorganics while retaining their chemical speciation information. ESI-MS demonstrated a linear response region of 100 ppb to 20 ppm, with a limit-of-detection of around 100 ppb. At top left is an example spectrum with the {sup 88}SrNO{sub 3} peak identified to show the retention of chemical speciation. PSI-MS showed a linear response region of around 1 ppb to 1 ppm, with a limit-of-detection of near 1 ppb. PSI-MS produced more erratic results than ESI-MS, likely due to the variability in ionization resulting from manual positioning of the paper triangle near the MS inlet. Future efforts will focus on improving the repeatability of PSI-MS as well as analyzing other species of interest such as cerium and uranium. Improvements will also be made to create more reliable data extraction and intelligent data filtering.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS2011

Annular MHD Physics for Turbojet Energy Bypass

The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated assuming weakly ionized flows obtained from pulsed nanosecond discharges. The equations for a 1-D, axisymmetric MHD generator/accelerator are derived and numerically integrated to determine the generator/accelerator performance characteristics. The concept offers a shockless means of interacting with high speed inlet flows and potentially offers variable inlet geometry performance without the complexity of moving parts simply by varying the generator loading parameter. The cycle analysis conducted iteratively with a spike inlet and turbojet flying at M = 7 at 30 km altitude is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at an aggressive 2200 deg K. The annular MHD Hall generator/accelerator is L = 3 m in length with a B(sub r) = 5 Tesla magnetic field and a conductivity of sigma = 5 mho/m for the generator and sigma= 1.0 mho/m for the accelerator. The calculated isentropic efficiency for the generator is eta(sub sg) = 84 percent at an enthalpy extraction ratio, eta(sub Ng) = 0.63. The calculated isentropic efficiency for the accelerator is eta(sub sa) = 81 percent at an enthalpy addition ratio, eta(sub Na) = 0.62. An assessment of the ionization fraction necessary to achieve a conductivity of sigma = 1.0 mho/m is n(sub e)/n = 1.90 X 10(exp -6), and for sigma = 5.0 mho/m is n(sub e)/n = 9.52 X 10(exp -6).

Schneider, Steven J.↗
NASA NTRS2011

Environmental Signatures for Habitability: What to Measure and How to Rank the Habitability Potential of Mars

The environmental signatures for habitability are not necessarily biosignatures, even though on Earth, they are definitive proof of habitability. It is the constant overprint of the chemical signatures of life that makes it difficult to recognize the chemical and physical properties of a potentially habitable environment as distinct from an inhabited one. Mars Science Laboratory (MSL) will soon embark on a mission to Mars to assess its past or present habitability, so it is useful to examine how we measure habitability on Earth and prepare for how that approach may differ for Mars. This exercise includes: (a) articulation of fundamental assumptions about habitability, (b) an inventory of factors that affect habitability, (c) development of metrics, measurement approach and implementation, and (d) a new classification scheme for planetary habitability that goes beyond the binary "yes" or "no." There may be dozens of factors that affect habitability and they can be weighted as a function of specific environment. However a robotic, in situ investigation even on Earth has constraints that prevent the measurement of every environmental factor, so metrics must be reduced to the most relevant subset, given available time, cost, technical feasibility and scientific importance. Many of the factors could be measured with a combination of orbital data and the MSL payload. We propose that, at a minimum, a designation of high habitability potential requires the following conditions be met: (a) thermally stable with respect to extremes and frequency of fluctuation, (b) has more than one energy source, (c) sufficient chemical diversity to make compounds with covalent and hydrogen bonding, (d) can moderate ionizing radiation enough to allow a stable or evolving pool of organic molecules, (e) must have water or other high quality polar solvent, (f) must be able to renew chemical resources (e.g., plate tectonics, volcanism or something else we haven't envisioned). A measurement approach we have taken to measure habitability on Earth is : 1. Study remote sensing data, maps, etc. 2. Decide how big an area to measure. 3. Determine the spatial sampling rate. 4. Determine the temporal sampling rate. 5. Determine the order of measurements 6. Decide where to begin measurements 7. Select locations at field site and proceed While science drives each of the steps, there are additional constraints, e.g., technical, time, cost, safety (risk). This approach is also executable on Mars. Measurement of past habitability is more challenging both for Earth and Mars where access to the past means subsurface access and confrontation with unknowns about preservation of the martian past. Some environments preserve evidence of past habitability better than others, and this is where selection of the landing site to maximize the preservation potential of habitability indicators will be key. Mars presents an opportunity to discover transitional states between habitable or not, and we offer a ranking scale for planetary habitability with Mars as the second test subject: CLASS ONE Uninhabitable and likely has never been so CLASS TWO Has a high potential but no confirmed observation of life (as defined above) CLASS THREE Inhabited (we find life) 3-A Globally inhabited 3-B Primitive life; early in its evolution, but not yet globally established 3-C Exists only in refugia -- planet heading toward class four CLASS FOUR Post-habitable (there once was life, but now it's gone) MSL provides an opportunity to carefully investigate the habitability of at least one site on Mars and it will reveal much about the possible states of planetary habitability

Conrad, Pamela G.↗
DOE OSTI2025

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↗