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NASA NTRS2022

Design of Hypervelocity Flow Generator (HFG) and Its Diagnostics

Ground facilities for hypersonic research are a key element for successful development of aerodynamically proven hypervelocity vehicles. Design concepts and diagnostics of a hypervelocity flow generator (HFG) were made as a test platform for hypersonic/hypervelocity spacecraft models at the NASA Langley Research Center. The HFG is a hypersonic flow field generator using optically heated gas which is blown into an 80 cu m vacuum chamber. The vacuum chamber is kept at a stable vacuum pressure with a combination of three large vacuum pumps, while the HFG is in the test mode. The HFG provides a relatively small test section with approximately a 20 cm window. This facility was designed to generate 2.45 km/sec of flow speed, and potentially generate a continuous flow with the nozzle and vacuum system. The window in test section provides a direct view of the shock wave around a model in order to measure temperature, pressure, and density profile within the shock layer. One of the key test goals under this project is to understand why the emission spectra from the standing shockwave plasma predicted by Lora-Loran codes are significantly different from the measured emission spectra from the Flight Investigation Reentry Environment (FIRE II) Flight. The correct estimate of the thermal loading on the leading edge of hypersonic vehicles greatly affects the aerodynamic design, the material selection for the vehicle, and the cooling requirement and can be obtained by the precise modeling of emission spectra from shockwave plasma. However, the estimation of thermal loading is not an easy task due to complex non-equilibrium radiative process within high temperature shock layers that still falls into a category of cold plasma. Direct flight experiments are the most desirable, but not a cost-effective approach. Analysis by computational fluid dynamics (CFD) offers many test flexibilities. However, the CFD codes must be fully tested and validated with experimental data before the codes are effectively used for practical design. Large discrepancies between experiments and codes appear in hypersonic/hypervelocity flow regimes at high altitudes of 60 km ~ 90 km. This HFG facility offers some important parameters for CFD code validation, such as collision cross-sections, relaxation times, reaction rate coefficients and transportation coefficients. The HFG test facility is based on the ejection flow of high temperature gas heated over to 3500 K through a nozzle. The tungsten gas chamber of the HFG is heated up to a desired temperature by a 60 kW optical power beam source. This system consists of an optical power source, a thermal chamber, an expansion nozzle, a test section, and an 80 cu m vacuum tank. 60 kW optical input power is obtained from the 150 kW Vortek arc lamp system (by Vortek Industries, Vancouver, Canada). This optical beam is focused to heat the gas chamber within which a flow media is heated. The maximum achievable temperature of the flow medium reached approximately 3500 K or even higher but is limited by the melting point of the chamber material used. The exhaust velocity through the nozzle was determined by the stagnation temperature and the molecular weight of the working medium at the test section. To provide design parameters, a NASA Chemical Equilibrium with Application (CEA) computer program is used for the simulation of aerothermal data. This CEA program can calculate chemical equilibrium and properties of complex mixtures using shock tube parameters. For nitrogen gas at 2666 K stagnation temperature, the maximum achievable velocity at the test section is approximately 2.45 km/sec which is within the range of the thermal velocity of 8000 K shock layer. Based on the calculation through the CEA program, the design parameters of a HFG were determined and implemented for the test section that includes an expansion nozzle. The installed test section of the experimental facility can sustain a condition of a re-entry vehicle from the Space at an altitude of 60-90 km. After installation of the HFG, the system was fully tested and its operational parameters were measured. An 80 cu m vacuum chamber of HFG was set at 1 torr level to keep a stable downstream condition. The pumping time to reach the minimum vacuum pressure (~ 1 torr) at the test chamber from atmospheric pressure was approximately an hour using Kinney (MBV-14000/MB -1600/KT-300) and Stokes (Model 1772 and 412) pumps. Such a setup condition allowed a continued stable operation of the HFG experiment with flowrates through 1-, 3-, or 5-mm diameters of nozzle throat. The flow characteristics of the HFG for various operating conditions were performed using a focused Schlieren method. At 0.8 torr chamber pressure, a barrel shock was observed at the test section. With a sphere obstacle of 12 mm diameter in the flow, a bow shock (~ 2-mm thickness) was observed by a focused Schlieren visualization method.

Hypervelocity flow↗

NASA NTRS2002

A Desorbed Gas Molecular Ionization Mechanism for Arcing Onset in Solar Arrays Immersed in a Low-Density Plasma

Previous experimental studies have hypothesized that the onset of Solar Array Arc (SAA) initiation in low-density space plasmas is caused by a desorbed gas molecular ionization mechanism. Indeed past investigations performed at the NASA Glenn Plasma Interaction Facility tend to not only support the desorbed gas molecular ionization mechanism, but have gone as far as identifying the crucial molecular species that must be present for molecular ion dominated process to occur. When electrical breakdown occurs at a triple junction site on a solar array panel, a quasi-neutral plasma cloud is ejected. Assuming the main component of the expelled plasma cloud by weight is due to water vapor, the fastest process available is due to HO molecules and OH(+) ions, or more succinctly, dissociative molecular-ion dominated recombination processes: H2O(+) + e(-) yields H* + OH*. Recently published spectroscopic observations of solar array arc spectra in ground tests have revealed the well-known molecular OH band (302 to 309nm), as well as the molecular SiH band (387nm peak), and the molecular CH band (432nm peak). Note that the OH band is observed in emission arcs where water vapor is present. Strong atomic lines were also observed for H(sub beta) at 486nm and H(sub alpha) at 656.3nm in prior ground testing. Independent supporting evidence of desorbed gas molecular ionization mechanisms also come from measurements of arc current pulse widths at different capacitances. We will revisit an earlier first order approximation demonstrating the dependence of arc current pulse widths on the square root of the capacitance. The simple arc current pulse width model will be then be used to estimate the temperature of the arc plasma (currently believed to be somewhere in the range of 3 to 5 eV). The current paper then seeks to extend the outlined work by including numerous vacuum chamber measurements obtained with a quadrupole mass spectrometer. A small solar array was mounted inside the vacuum chamber. A plasma source, also mounted inside the vacuum chamber, is used to simulate a low-density plasma environment. The solar array is then biased to a high negative potential and allowed to arc while a mass spectrometer is used to record the partial pressure of H2O and to track other significant changes in mass (1 to 150) AMU.

Galofaro, J.↗

NASA NTRS1959

Tensile Properties of Molybdenum and Tungsten from 2500 to 3700 F

Specimens of commercially pure sintered tungsten, arc-cast unalloyed molybdenum, and two arc-cast molybdenum-base alloys (one with 0.5 percent titanium, the other with 0.46 percent titanium and 0.07 percent zirconium) were fabricated from 1/2-inch-diameter rolled or swaged bars. All specimens were evaluated in short-time tensile tests in the as-received condition, and all except the molybdenum-titanium-zirconium alloy were tested after a 30-minute recrystallization anneal at 3800 F in a vacuum of approximately 0.1 micron. Results showed that the tungsten was considerably stronger than either the arc-cast unalloyed molybdenum or the molybdenum-base alloys over the 2500 to 3700 F temperature range. Recrystallization of swaged tungsten at 3800 F considerably reduced its tensile strength at 2500 F. However, above 3100 F, the as-swaged tungsten specimens recrystallized during testing, and had about the same strength as when recrystallized at 3800 F before evaluation. The ductility of molybdenum-base materials was very high at all test temperatures; the ductility of tungsten decreased sharply above about 3120 F.

Hall, Robert W.↗

NASA NTRS1976

Ice in space: An experimental and theoretical investigation

The thermodynamics of water ice formation was experimentally investigated under a wide variety of conditions, including those of outer space. This information, and in particular, the lifetime of ice particles as a function of solar distance is an absolute requirement for proper interpretation of photometric profiles of comets. The sublimation of ice particles in a nonequilibrium situation was studied. An oscillating fiber microbalance was used to measure the sublimation rate of water droplets (which were suspended on a long quartz fiber which was oscillating in a vacuum chamber). The influence of particle size, surface temperature, and the index refraction from simulated solar radiation were studied in relation to ice formation. Also examined was the influence of impurities (clathrates) on ice formation. Windows in the vacuum chamber allowed the ice particles to be exposed to a 1 kilowatt xenon arc lamp which was used to simulate solar radiation. Ice is proposed as a possible energy source for comets, as amorphous water ice and ammonia in low temperature and pressure environments demonstrated a clear energy release upon warming. Motion pictures of ice formation were taken and photographs are shown.

Patashnick, H.↗

DOE OSTI2022

Thermal analysis of RHIC arc dipole magnet cold mass with EIC beam screen

The existing RHIC storage rings – including their superconducting magnet arcs – will be used for the hadron storage ring of the Electron-Ion Collider (EIC). The vacuum chamber of these magnets was not designed for the EIC hadron beams, with shorter bunches and of higher average current than the RHIC beams. With the current stainless steel beam pipe, the resistive-wall (RW) heating will exceed the dynamic heat load budget. Limiting the RW heating is important to prevent the superconducting magnets from quenching and to maintain a low screen temperature necessary to impede the rise of RW heating (higher resistance at higher temperature) as well as to achieve desired ultra-high vacuum. In addition, simulations predict the formation of electron cloud which would further contribute to the dynamic heat load and could compromise the quality and stability of the beam. To reduce the resistive-wall heating and suppress electron cloud, a beam screen will be installed in the vacuum chamber of the RHIC SC magnets. The screen will have a high RRR copper layer at its inner face – useful to reduce the resistive-wall impedance thanks to its high conductivity especially at cryogenic temperatures – and will be coated with a thin layer of amorphous carbon, a material with low secondary electron yield to suppress the formation of electron clouds. The baseline solution envisages a screen that will be cooled by thermal contact to the 4.55 K beam pipe. Detailed thermal analysis have been conducted in ANSYS 2020 for an arc dipole cold mass equipped with a beam screen in order to study the feasibility of a passively-cooled screen and guide its design. Temperature-dependent thermal conductivity properties of all materials in the operating (cryogenic) temperature range are considered. Suitable assumptions and simplifications are made to model the magnet coil and calculate its homogenized thermal conductivity. Sensitivity studies with respect to layer thicknesses and area of contact are carried out and results are presented.

43 PARTICLE ACCELERATORS↗

NASA NTRS1988

Radiometric calibrations of portable sources in the vacuum ultraviolet

The primary UV radiometric calibration standards of the Atomic and Plasma Radiation Division of the NBS are the hydrogen arc and the blackbody line arc. The secondary standards are the argon mini- and maxiarcs, and the deuterium arc lamp. Calibration methods involving both spectral radiance and irradiance, as well as the evaluation of their uncertainties, are discussed. Attention is given to the establishment of an irradiance scale, and the absolute spectral irradiance, measured as a function of wavelength, at a 50-cm distance from the field aperture for five different continuum sources.

Klose, Jules Z.↗

DOE OSTI2024

Integral analysis of the effect of material dimension and composition on tokamak neutronics *

Abstract The neutronics performance of a tokamak has been identified as an important factor in designing a fusion power plant. The design of the tokamak should not only meet operational parameters such as sufficient tritium breeding, but also safety parameters such as low structural material activation. This paper investigates the impacts of the neutronics metrics for the ARC-class tokamak, a compact tokamak with an immersion blanket, by perturbing the first five layers of structural material—first wall, inner vacuum vessel, coolant salt channel, neutron multiplier, and outer vacuum vessel. The goal of this work is to provide insight into shaping and scaling the flux on each layer to obtain optimized operational and safety metrics through quantification of the responses from each perturbation. Results show that increased first wall thickness can increase the tritium breeding ratio (TBR) in specific configurations with high 6 Li enrichments and that vacuum vessels decrease TBR for low- 6 Li enrichment configurations. It was also found that the neutron multiplier can either increase or decrease TBR depending on the configuration. The response of metrics to the change in layer thickness and enrichment also varies depending on the vacuum vessel material. The integral impacts of 6 Li enrichment, layer thicknesses, and vacuum vessel material choice are investigated and presented in this paper.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

High Average Power RF Window with Improved Multipactor Coating

Multipactor emission can be a serious issue for vacuum electron devices operating at megawatt power levels. It can lead to catastrophic failure from surface arcs or excessive heating of ceramic windows. Titanium nitride is effective at suppressing multipactor emission; however, sputter coating is not strongly bonded to surfaces and issue related to lifetime have arisen. It’s difficult to ensure a uniform coating over large surfaces. This research investigated atomic layer deposition (ALD) as an improved alternative to sputtered coatings. Test windows were fabricated and coated with TiN using ALD, then tested for RF loss and secondary emission. All ALD samples showed RF loss less than 0.01dB with secondary emission yield equal to or better than reported measurements with sputter coated windows. The program also designed a preliminary ALD system capable of coating windows up to 24 inches in diameter.

43 PARTICLE ACCELERATORS↗

NASA NTRS1983

Performance of an ablator for Space Shuttle inorbit repair in an arc-plasma airstream

An ablator patch material performed well in an arc plasma environment simulating nominal Earth entry conditions for the Space Shuttle. Ablation tests using vacuum molded cones provided data to optimize the formulation of a two part polymer system for application under space conditions. The blunt cones were made using a Teflon mold and a state of the art caulking gun. Char stability of formulations with various amounts of catalyst and diluent were investigated. The char was found to be unstable in formulations with low amounts of catalyst and high amounts of diluent. The best polymer system determined by these tests was evaluated using a half tile patch in a multiple High Temperature Reusable surface Insulation tile model. It was demonstrated that this ablator could be applied in a space environment using a state of the art caulking gun, would maintain the outer mold line of the thermal protection system during entry, and would keep the bond line temperature at the aluminum tile interface below the design limit.

Stewart, D. A.↗

NASA NTRS2009

Comparisons of Air Radiation Model with Shock Tube Measurements

This paper presents an assessment of the predictive capability of shock layer radiation model appropriate for NASA s Orion Crew Exploration Vehicle lunar return entry. A detailed set of spectrally resolved radiation intensity comparisons are made with recently conducted tests in the Electric Arc Shock Tube (EAST) facility at NASA Ames Research Center. The spectral range spanned from vacuum ultraviolet wavelength of 115 nm to infrared wavelength of 1400 nm. The analysis is done for 9.5-10.5 km/s shock passing through room temperature synthetic air at 0.2, 0.3 and 0.7 Torr. The comparisons between model and measurements show discrepancies in the level of background continuum radiation and intensities of atomic lines. Impurities in the EAST facility in the form of carbon bearing species are also modeled to estimate the level of contaminants and their impact on the comparisons. The discrepancies, although large is some cases, exhibit order and consistency. A set of tests and analyses improvements are proposed as forward work plan in order to confirm or reject various proposed reasons for the observed discrepancies.

Bose, Deepak↗

NASA NTRS2003

Solar Array in Simulated LEO Plasma Environment

Six different types of solar arrays have been tested in large vacuum chambers. The low earth orbit plasma environment was simulated in plasma vacuum chambers, where the parameters could be controlled precisely. Diagnostic equipment included spherical Langmuir probes, mass spectrometer, low-noise CCD camera with optical spectrometer, video camera, very sensitive current probe to measure arc current, and a voltage probe to register variations in a conductor potential. All data (except video) were obtained in digital form that allowed us to study the correlation between external parameters (plasma density, additional capacitance, bias voltage, etc) and arc characteristics (arc rate, arc current pulse width and amplitude, gas species partial pressures, and intensities of spectral lines). Arc inception voltages, arc rates, and current selections are measured for samples with different coverglass materials and thickness, interconnect designs, and cell sizes. It is shown that the array with wrapthrough interconnects have the highest arc threshold and the lowest current collection. Coverglass design with overhang results in decrease of current collection and increase of arc threshold. Doubling coverglass thickness cases the increase in arc inception voltage. Both arc inception voltage and current collection increase significantly with increasing a sample temperature to 80 C. Sustained discharges are initiated between adjacent cells with potential differences of 40 V for the sample with 300 micron coverglass thickness and 60 V for the sample with 150 micron coverglass thickness. Installation of cryogenic pump in large vacuum chamber provided the possibility of considerable outgassing of array surfaces which resulted in significant decrease of arc rate. Arc sites were determined by employing a video-camera, and it is shown that the most probable sites for arc inception are triple-junctions, even though some arcs were initiated in gaps between cells. It is also shown that the arc rate increases with increasing of ion collection current. The analysis of optical spectra (240-800 nm) reveals intensive narrow atomic lines (Ag, H) and wide molecular bands (OH, CH, SiH, SiN) that confirms a complicated mechanism of arc plasma generation. The results obtained seem to be important for the understanding of the arc inception mechanism, which is absolutely essential for progress toward the design of high-voltage solar array for space application.

Vayner, Boris↗

NASA NTRS2004

Solar Array in Simulated LEO Plasma Environment

Six different types of solar arrays have been tested in large vacuum chambers. The low Earth orbit plasma environment was simulated in plasma vacuum chambers, where the parameters could be controlled precisely. Diagnostic equipment included spherical Langmuir probes, mass spectrometer, low-noise CCD camera with optical spectrometer, video camera, very sensitive current probe to measure arc current, and a voltage probe to register variations in a conductor potential. All data (except video) were obtained in digital form that allowed us to study the correlation between external parameters (plasma density, additional capacitance, bias voltage, etc) and arc characteristics (arc rate, arc current pulse width and amplitude, gas species partial pressures, and intensities of spectral lines). Arc inception voltages, arc rates, and current collections are measured for samples with different coverglass materials and thickness, interconnect designs, and cell sizes. It is shown that the array with wrapthrough interconnects have the highest arc threshold and the lowest current collection. Coverglass design with overhang results in decrease of current collection and increase of arc threshold. Doubling coverglass thickness causes the increase in arc inception voltage. Both arc inception voltage and current collection increase significantly with increasing a sample temperature to 80 C. Sustained discharges are initiated between adjacent cells with potential differences of 40 V for the sample with 300 m coverglass thickness and 60 V for the sample with 150 m coverglass thickness. Installation of cryogenic pump in large vacuum chamber provided the possibility of considerable outgassing of array surfaces which resulted in significant decrease of arc rate. Arc sites were determined by employing a video-camera, and it is shown that the most probable sites for arc inception are triple-junctions, even though some arcs were initiated in gaps between cells. It is also shown that the arc rate increases with increasing of ion collection current. The analysis of optical spectra (240-800 nm) reveals intensive narrow atomic lines (Ag, H) and wide molecular bands (OH, CH, SiH, SiN) that confirms a complicated mechanism of arc plasma generation. The results obtained seem to be important for the understanding of the arc inception mechanism, which is absolutely essential for progress toward the design of high-voltage solar array for space application.

Vayner, Boris↗

NASA NTRS2024

Defining the Operational Envelope for Air Flows in the Miniature Arc-Jet Research Chamber (mARC II)

The second-generation 30 kW miniature Arc-jet Research Chamber (mARC II) at NASA Ames Research Center produces high enthalpy flows relevant for entry systems ground testing. The mARC II facility has recently undergone upgrades, including the installation of a new vacuum system to address the issues preventing it from maintaining underexpanded flow under test conditions. In this work, we present data obtained from an Integrated Systems Testing campaign and provide an initial assessment of arc-jet performance following the upgrades. Air is used as the working gas for the standard mARC II arc-heater configuration with two constrictor disks. Seven runs were investigated for five test conditions to assess the lowest achievable stagnation point heat fluxes for air flow rates of 0.15 or 0.25 g s −1 . The heat flux was measured using a water-cooled Gardon gauge (Ø4.76 mm, 3/16" hemispherical) at 70 mm from the nozzle exit plane. The new vacuum system produced test box pressures in the medium (fine) vacuum range (~0.03 torr, 4 Pa) prior to gas addition and successfully maintained underexpanded flow after gas addition. The upgrade yielded a ~4X reduction in heat flux relative to the previous system for the same set test conditions. We report the lowest heat fluxes measured in mARC II to date, ranging from 26 to 81 W cm −2 , for sonic flow enthalpies of 4–14 MJ kg −1 . Bulk enthalpies estimated using an energy balance method (EB 2 ) are reported for the first time using mARC II.Initial data suggests EB 2 generally estimates lower enthalpies than sonic flow methods for mARC II. Lastly, laminar axisymmetric Navier–Stokes simulations were performed using the NASA DPLR code. Numerical heat flux results show good agreement with experiments at low arc powers (3–15% difference at the minimum set arc current), but discrepancy increases with arc power (49% difference at the maximum set arc current).

Pitot tube↗

NASA NTRS2024

Defining the Operational Envelope for Air Flows in the Miniature Arc-Jet Research Chamber (mARC II)

arc-jet↗

NASA NTRS1971

Simulated space environment tests on cadmium sulfide solar cells

Cadmium sulfide (Cu2s - CdS) solar cells were tested under simulated space environmental conditions. Some cells were thermally cycled with illumination from a Xenon-arc solar simulator. A cycle was one hour of illumination followed immediately with one-half hour of darkness. In the light, the cells reached an equilibrium temperature of 60 C (333 K) and in the dark the cell temperature dropped to -120 C (153 K). Other cells were constantly illuminated with a Xenon-arc solar simulator. The equilibrium temperature of these cells was 55 C (328 K). The black vacuum chamber walls were cooled with liquid nitrogen to simulate a space heat sink. Chamber pressure was maintained at 0.000001 torr or less. Almost all of the solar cells tested degraded in power when exposed to a simulated space environment of either thermal cycling or constant illumination. The cells tested the longest were exposed to 10.050 thermal cycles.

Clarke, D. R.↗

NASA NTRS1977

Outer planets probe testing

An atmospheric entry Probe is being developed by NASA Ames Research Center (ARC) to conduct in situ scientific investigations of the outer planets' atmospheres. A full scale engineering model of an MDAC-E Probe configuration, was fabricated by NASA ARC. Proof-of-concept test validation of the structural and thermal design is being obtained at NASA ARC. The model was successfully tested for shock and dynamic loading and is currently in thermal vacuum testing.

Smittkamp, J. A.↗

NASA NTRS2003

Simulation of Mini-Magnetospheric Plasma Propulsion (M2P2) Interacting with an External Plasma Wind

Substantial progress has been made over the last year in the development of the laboratory Mini-Magnetospheric Plasma Propulsion (M2P2) prototype. The laboratory testing has shown that that the plasma can be produced at high neutral gas efficiency, at high temperatures (a few tens of eV) with excellent confinement up to the point where chamber wall interactions dominate the physics. This paper investigates the performance of the prototype as it is opposed by an external plasma acting as a surrogate for the solar wind. The experiments were performed in 5ft diameter by 6ft long vacuum chamber at the University of Washington. The solar wind source comprised of a 33 kWe arc jet attached to a 200 kWe inductively generated plasma source. The dual plasma sources allow the interaction to be studied for different power levels, shot duration and production method. It is shown that plasma from the solar wind source (SWS) is able to penetrate the field of the M2P2 magnetic when no plasma is present. With operation of the M2P2 plasma source at only 1.5 kWe, the penetration of the SWS even at the highest power of operation at 200 kWe is stopped. This deflection is shown to be greatly enhanced over that produced by the magnet alone. In addition it is shown that with the presence of the SWS, M2P2 is able to produce enhanced magnetized plasma production out to at least 10 magnet radii where the field strength is only marginally greater than the terrestrial field. The results are consistent with the initial predictions that kWe M2P2 systems would be able to deflect several hundred kWe plasma winds to produce enhanced propulsion for a spacecraft.

Winglee, R. M.↗

NASA NTRS2003

Experimental Study of Arcing on High-Voltage Solar Arrays

The main obstacle to the implementation of a high-voltage solar array in space is arcing on the conductor-dielectric junctions exposed to the surrounding plasma. One obvious solution to this problem would be the installation of fully encapsulated solar arrays which were not having exposed conductors at all. However, there are many technological difficulties that must be overcome before the employment of fully encapsulated arrays will turn into reality. An alternative solution to raise arc threshold by modifications of conventionally designed solar arrays looks more appealing, at least in the nearest future. A comprehensive study of arc inception mechanism suggests that such modifications can be done in the following directions: 1) To insulate conductor-dielectric junction from a plasma environment (wrapthrough interconnects); 2) To change a coverglass geometry (overhang); 3) To increase a coverglass thickness; 4) To outgas areas of conductor-dielectric junctions. The operation of high-voltage array in LEO produces also the parasitic current power drain on the electrical system. Moreover, the current collected from space plasma by solar arrays determines the spacecraft floating potential that is very important for the design of spacecraft and its scientific apparatus. In order to verify the validity of suggested modifications and to measure current collection five different solar array samples have been tested in a large vacuum chamber. Each sample (36 silicon based cells) consists of three strings containing 12 cells connected in series. Thus, arc rate and current collection can be measured on every string independently, or on a whole sample when strings are connected in parallel. The heater installed in the chamber provides the possibility to test samples under temperature as high as 80 C that stimulates the LEO operational temperature. The experimental setup is described below.

Vayner, Boris↗