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At least 163 records · Page 9

Linearized ray-trace analysis

A new, coordinate-free version of the exact ray-trace equations for optical systems consisting of conic reflecting, refracting and reference surfaces is presented. These equations are differentiated to obtain closed-form optical sensitivity dyadics. For computation, the sensitivities are evaluated in a single global coordinate frame and combined in linearized ray-trace matrix difference equations that propagate the rays and the sensitivities from element to element. One purpose of this analysis is to create optical models that can be directly integrated with models of the instrument structure and control systems for dynamic simulation.

Redding, David C.↗

Evaluation of HAN-TEAN Stabilizers using Microcalorimetry

HAN-TEAN (hydroxylammonium nitrate - triethanolammonium nitrate - in water) is being considered for various propellant applications. This propellant has advantages in terms of insensitivity to impact and fire, low vapor pressure and environmentally benign reaction products. One office concerns with HAN-TEAN is its stability and shelf-life, especially when contaminated with trace metals. Stabilizer systems, consisting of anti-oxidants and/or chealating agents were investigated for their ability to control the decomposition of HAN-TEAN. Isothermal microcalorimetry, an ultrasensitive heat measurement technique, was used to monitor the decomposition of HANTEAN at near ambient temperatures. Isothermal microcalorimetry measures the heat flow from a reaction vessel into a surrounding heat sink. Microcalorimetry is approximately 1,000 times more sensitive than accelerating rate calorimetry (ARC) or differential scanning calorimetry (DSC) for measuring heat flow. Samples of HAN-TEAN containing the stabilizers were spiked with 50 ppm iron and the heat evolution monitored for a period of at least 30 days. Ten stabilizer combinations were tested and the rates of HAN-TEAN decomposition were lowered by 74 to 95 percent in the presence of iron.

Hornung, Steven D.↗

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

Chattopadhyay, Aditi↗

Test of the Equivalence Principle in an Einstein Elevator

The scientific goal of the experiment is to test the equality of gravitational and inertial mass (i.e., to test the Principle of Equivalence) by measuring the independence of the rate of fall of bodies from the composition of the falling body. The measurement is accomplished by measuring the relative displacement (or equivalently acceleration) of two falling bodies of different materials which are the proof masses of a differential accelerometer. The goal of the experiment is to measure the Eotvos ratio delta-g/g (differential acceleration/common acceleration) with an accuracy goal of a few parts in 10(exp 15). The estimated accuracy is about two orders of magnitude better than the present state of the art. The experiment is a null experiment in which a result different from zero will indicate a violation of the Equivalence Principle. The main goal of the study to be carried out under this grant is the flight definition of the experiment and bread boarding of critical components of the experiment that will enable us to be ready for the following phases of the project. The project involves an international cooperation in which the responsibility of the US side is the flight definition of the experimental facility while the responsibility of the non-US partners is the flight definition and laboratory prototyping of the differential acceleration detector. In summary, the experiment to be designed is for taking differential acceleration measurements with a high-sensitivity detector (the sensor) during free fall conditions lasting up to 30 s in a disturbance-free acceleration environment. The experiment strategy consists in letting the sensor free fall inside a few meters long (in the vertical direction) evacuated capsule that is falling simultaneously in the rarefied atmosphere after release from a helium balloon flying at a stratospheric altitude.

Shapiro, Irwin I.↗

Test of the Equivalence Principle in an Einstein Elevator

The scientific goal of the experiment is to test the equality of gravitational and inertial mass (i.e., to test the Principle of Equivalence) by measuring the independence of the rate of fall of bodies from the composition of the falling body. The measurement is accomplished by measuring the relative displacement (or equivalently acceleration) of two falling bodies of different materials which are the proof masses of a differential accelerometer. The goal of the experiment is to measure the Eoetvoes ratio sigma g/g (differential acceleration/common acceleration) with an accuracy goal of several parts in 10(exp 15). The estimated accuracy is about two orders of magnitude better than the present state of the art. The main goal of the study to be carried out under this grant is part of the flight definition of the experiment and laboratory testing of key components. The project involves an international cooperation in which the responsibility of the US side is the flight definition of the experimental facility while the responsibility of the non-US partners is the flight definition and laboratory prototyping of the differential acceleration detector.In summary, the experiment to be designed is for taking differential acceleration measurements with a high-sensitivity detector (the sensor) during free fall conditions lasting up to 30 s in a disturbance-free acceleration environment. The experiment strategy consists in letting the sensor free fall inside a few meters long (in the vertical direction) evacuated capsule that is falling simultaneously in the rarefied atmosphere after release from a helium balloon flying at a stratospheric altitude.

Shapiro, Irwin I.↗

Delta excitations and shell-model information in heavy-ion, charge-exchange reactions

We calculate total cross sections for coherent pion production using localized plane-wave approximations for the shell-structure of valence nucleons that are excited to delta particles in the intermediate state in the (12C, 12B) and (12C, 12N) charge-exchange, heavy-ion reactions. We find comparable agreement to projectile downshift data for 12C(12C, 12B)12N. Then we improve the formalism by replacing the localized plane wave bound states with harmonic oscillator states which are imbedded in a multipole expansion approach and calculate pion differential cross sections to test for the sensitivity of the spectra to the single-particle mass parameter.

NASA Program Space Medicine↗

Solar Dynamics Observatory Guidance, Navigation, and Control System Overview

The Solar Dynamics Observatory (SDO) was designed and built at the Goddard Space Flight Center, launched from Cape Canaveral on February 11, 2010, and reached its final geosynchronous science orbit on March 16, 2010. The purpose of SDO is to observe the Sun and continuously relay data to a dedicated ground station. SDO remains Sun-pointing throughout most of its mission for the instruments to take measurements of the Sun. The SDO attitude control system (ACS) is a single-fault tolerant design. Its fully redundant attitude sensor complement includes sixteen coarse Sun sensors (CSSs), a digital Sun sensor (DSS), three two-axis inertial reference units (IRUs), and two star trackers (STs). The ACS also makes use of the four guide telescopes included as a part of one of the science instruments. Attitude actuation is performed using four reaction wheels assemblies (RWAs) and eight thrusters, with a single main engine used to provide velocity-change thrust for orbit raising. The attitude control software has five nominal control modes, three wheel-based modes and two thruster-based modes. A wheel-based Safehold running in the attitude control electronics box improves the robustness of the system as a whole. All six modes are designed on the same basic proportional-integral-derivative attitude error structure, with more robust modes setting their integral gains to zero. This paper details the final overall design of the SDO guidance, navigation, and control (GN&C) system and how it was used in practice during SDO launch, commissioning, and nominal operations. This overview will include the ACS control modes, attitude determination and sensor calibration, the high gain antenna (HGA) calibration, and jitter mitigation operation. The Solar Dynamics Observatory mission is part of the NASA Living With a Star program, which seeks to understand the changing Sun and its effects on the Solar System, life, and society. To this end, the SDO spacecraft carries three Sun-observing instruments: Helioseismic and Magnetic Imager (HMI), led by Stanford University; Atmospheric Imaging Assembly (AIA), led by Lockheed Martin Space and Astrophysics Laboratory; and Extreme Ultraviolet Variability Experiment (EVE), led by the University of Colorado. The basic mission is to observe the Sun for a very high percentage of the 5-year mission (10-year goal) with long stretches of uninterrupted observations and with constant, high-data-rate transmission to a dedicated ground station to be located in White Sands, New Mexico. These goals guided the design of the spacecraft bus that will carry and service the three-instrument payload. Overarching design goals for the bus are geosynchronous orbit, near-constant Sun observations with the ability to fly through eclipses, and constant HGA contact with the dedicated ground station. A three-axis stabilized ACS is needed both to point at the Sun accurately and to keep the roll about the Sun vector correctly positioned with respect to the solar north pole. This roll control is especially important for the magnetic field imaging of HM I. The mission requirements have several general impacts on the ACS design. Both the AIA and HMI instruments are very sensitive to the blurring caused by jitter. Each has an image stabilization system (ISS) with some ability to filter out high frequency motion, but below the bandwidth of the ISS the control system must compensate for disturbances within the ACS bandwidth or avoid exciting jitter at higher frequencies. Within the ACS bandwidth, the control requirement imposed by AIA is to place the center of the solar disk no more than 2 arc sec, 3 , from a body-defined target based on one of the GTs that accompany the instrument. This body-defined target, called the science reference boresight (SRB), was determined from the postlaunch orientation of the GTs by averaging the bounding telescope boresights for pitch to get a pitch SRB coordinate, and by averaging the bounding boresights for yaw toet the yaw SRB coordinate. The location of this SRB in the 0.5-deg field-of-view for each GT then becomes the central target for each telescope; one GT is selected for use as the ACS controlling guide telescope (CGT) at any given time. Fine Sun-pointing is effected based on this SRB for all three instruments when the Sun is within the linear range of the CGT. In addition to limiting jitter, HMI science requires averaging several observations, making the instrument sensitive to low frequency motion that induces differential motion between each observation. This requires the spacecraft attitude to be stable about the roll axis to approximately 10 arcsec over a ten-minute period. Instrument calibrations require that the spacecraft point the SRB up to 2.5 degrees in pitch and yaw away from the center of the Sun, placing the Sun outside the field-of-view of the guide telescopes. In such instances, when the GTs cannot provide the definitive target for the ACS, on-board attitude determination combined with ephemeris prediction of the Sun direction must provide the definitive target. EVE is capable of observing the Sun with less dependence on attitude control. However, the ground data processing needs for calibrations result in the most strict attitude knowledge requirements for the mission: [35,70,70] arcsec, 3 , of knowledge with respect to the center of the solar disk. In addition to driving the ACS sensor selection, the knowledge requirements, which have their effect primarily during Inertial mode calibrations, drive the accuracy requirements for the solar ephemeris. The need to achieve and maintain geosynchronous orbit (GEO) drove the need for high-efficiency propulsive systems and appropriate attitude control. The main engine provided high specific impulse for the maneuvers to attain GEO, while the smaller ACS thrusters managed the disturbance torques of the larger engine and provided the capability for much smaller adjustment burns on orbit. SDO s large solar profile means that solar radiation pressure is a large torque disturbance, and the momentum buildup from this disturbance and the GEO altitude drives the ACS to use thrusters to manage vehicle momentum. The demanding data capture budget for the mission, however, requires SDO to avoid frequent thruster maneuvers, while concerns about on-orbit jitter restrict the maximum desired wheel speeds desired from the RWAs. The plan for on-orbit wheel speed and momentum management will be discussed as well as what is now being done in operation after the jitter environment was characterized. The SDO ACS hardware complement is single-fault tolerant. Two main processors carry virtually identical copies of the command and data handling and ACS software, and two identical attitude control electronics (ACE) boxes carry Coldfire processors with contingency ACS software and other hardware interface cards; the ACE structure allows reaction wheels to be commanded by the Sun-pointing Safehold independent of the Mil Std 1553 data bus. The sixteen Adcole CSSs are grouped into primary and backup sets of eight sensors, each set providing the ability to calculate a sun vector. Each set of eight eyes provides full 4 -steradian coverage. The Adcole DSS comprises an optics head and a separate electronics box providing a 1553 data interface. The electronics box is mounted inside the Faraday cage created by the spacecraft bus module. The DSS head with its 32- deg square FOV is mounted on the instrument module with its boresight along the spacecraft X axis, nearly aligned with the Sun during observations. Adcole has designed the DSS calibration parameters so that the accuracy is 0.24 arcminutes within 10 deg of the boresight, and diminishes to 3 arcminutes as the Sun moves towards the edges of its FOV . This DSS calibration scheme provides higher accuracy attitude determination over the range of the instrument calibration maneuvers.

Morgenstern, Wendy M.↗

A Raman Study of Carbonates and Organic Contents in Five CM Chondrites

Carbonates comprise the second most abundant class of carbon-bearing phases in carbonaceous chondrites after organic matter (approximately 2 wt.%), followed by other C-bearing phases such as diamond, silicon carbide, and graphite. Therefore, understanding the abundances of carbonates and the associated organic matter provide critical insight into the genesis of major carbonaceous components in chondritic materials. Carbonates in CM chondrites mostly occur as calcite (of varying composition) and dolomite. Properly performed, Raman spectroscopy provides a non-destructive technique for characterizing meteorite mineralogy and organic chemistry. It is sensitive to many carbonaceous phases, allows the differentiation of organic from inorganic materials, and the interpretation of their spatial distribution. Here, with the use of Raman spectroscopy, we determine the structure of the insoluble organic matter (IOM) in the matrix and carbonate phases in five CM chondrites: Jbilet Winselwan, Murchison, Nogoya, Santa Cruz, and Wisconsin Range (WIS) 91600, and interpret the relative timing of carbonate precipitation and the extent of the associated alteration events.

Chan, Q. H. S.↗

Differential Dynamic Microscopy: A Novel Approach for Dynamics and Micro-rheology of Active Soft Matter

Differential dynamic microscopy (DDM) is a highly sensitive and cost-effective technique for studying the dynamics and micro-rheology of active soft matter in real time and at high resolution. In this work, we extend the capabilities of DDM, notably its size, to suit to space research and overcome challenges such as the environmental limited resources (e.g. Artemis, ISS, Cube sat, etc.).

Amine Missaoui↗

Linear Back-Drive Differentials

Linear back-drive differentials have been proposed as alternatives to conventional gear differentials for applications in which there is only limited rotational motion (e.g., oscillation). The finite nature of the rotation makes it possible to optimize a linear back-drive differential in ways that would not be possible for gear differentials or other differentials that are required to be capable of unlimited rotation. As a result, relative to gear differentials, linear back-drive differentials could be more compact and less massive, could contain fewer complex parts, and could be less sensitive to variations in the viscosities of lubricants. Linear back-drive differentials would operate according to established principles of power ball screws and linear-motion drives, but would utilize these principles in an innovative way. One major characteristic of such mechanisms that would be exploited in linear back-drive differentials is the possibility of designing them to drive or back-drive with similar efficiency and energy input: in other words, such a mechanism can be designed so that a rotating screw can drive a nut linearly or the linear motion of the nut can cause the screw to rotate. A linear back-drive differential (see figure) would include two collinear shafts connected to two parts that are intended to engage in limited opposing rotations. The linear back-drive differential would also include a nut that would be free to translate along its axis but not to rotate. The inner surface of the nut would be right-hand threaded at one end and left-hand threaded at the opposite end to engage corresponding right- and left-handed threads on the shafts. A rotation and torque introduced into the system via one shaft would drive the nut in linear motion. The nut, in turn, would back-drive the other shaft, creating a reaction torque. Balls would reduce friction, making it possible for the shaft/nut coupling on each side to operate with 90 percent efficiency.

Waydo, Peter↗

Second-order design sensitivities for linear elastic problems

The subject of this paper is the efficient and accurate determination of second-order design sensitivities in elastic bodies. The approach being carried out here is the direct differentiation of the governing derivative boundary element method (DBEM) formulation of the problem. Second-order sensitivities of boundary stresses are obtained in an elegant manner. A numerical implementation of the method is carried out with isoparametric quadratic boundary elements and numerical results are presented for several sample problems. Considerable savings in computational effort for an optimization procedure is possible through the use of efficiently determined accurate second-order design sensitivities.

Zhang, Qing↗

An Airborne Multi-Frequency Microwave Analysis of Precipitation within Two Winter Cyclones

NASA’s Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) field campaign gathered data using “satellite-simulating” (albeit with higher-resolution data than satellites currently provide) and in situ aircraft to study snowstorms, with an emphasis on banding. This study used three IMPACTS microwave instruments—two passive and one active—chosen for their sensitivity to precipitation microphysics. The 10–37-GHz passive frequencies were well suited for detecting light precipitation and differentiating rain intensities over water. The 85–183-GHz frequencies were more sensitive to cloud ice, with higher cloud tops manifesting as lower brightness temperatures, but this did not necessarily correspond well to near-surface precipitation. Over land, retrieving precipitation information from radiometer data is more difficult, requiring increased reliance on radar to assess storm structure. A dual-frequency ratio (DFR) derived from the radar’s Ku- and Ka-band frequencies provided greater insight into storm microphysics than reflectivity alone. Areas likely to contain mixed-phase precipitation (often the melting layer/bright band) generally had the highest DFR, and high-altitude regions likely to contain ice usually had the lowest DFR. The DFR of rain columns increased toward the ground, and snowbands appeared as high-DFR anomalies.

Amanda Richter↗

PMA-PhyloChip DNA Microarray to Elucidate Viable Microbial Community Structure

Since the Viking missions in the mid-1970s, traditional culture-based methods have been used for microbial enumeration by various NASA programs. Viable microbes are of particular concern for spacecraft cleanliness, for forward contamination of extraterrestrial bodies (proliferation of microbes), and for crew health/safety (viable pathogenic microbes). However, a "true" estimation of viable microbial population and differentiation from their dead cells using the most sensitive molecular methods is a challenge, because of the stability of DNA from dead cells. The goal of this research is to evaluate a rapid and sensitive microbial detection concept that will selectively estimate viable microbes. Nucleic acid amplification approaches such as the polymerase chain reaction (PCR) have shown promise for reducing time to detection for a wide range of applications. The proposed method is based on the use of a fluorescent DNA intercalating agent, propidium monoazide (PMA), which can only penetrate the membrane of dead cells. The PMA-quenched reaction mixtures can be screened, where only the DNA from live cells will be available for subsequent PCR reaction and microarray detection, and be identified as part of the viable microbial community. An additional advantage of the proposed rapid method is that it will detect viable microbes and differentiate from dead cells in only a few hours, as opposed to less comprehensive culture-based assays, which take days to complete. This novel combination approach is called the PMA-Microarray method. DNA intercalating agents such as PMA have previously been used to selectively distinguish between viable and dead bacterial cells. Once in the cell, the dye intercalates with the DNA and, upon photolysis under visible light, produces stable DNA adducts. DNA cross-linked in this way is unavailable for PCR. Environmental samples suspected of containing a mixture of live and dead microbial cells/spores will be treated with PMA, and then incubated in the dark. Thereafter, the sample is exposed to visible light for five minutes, so that the DNA from dead cells will be cross-linked. Following this PMA treatment step, the sample is concentrated by centrifugation and washed (to remove excessive PMA) before DNA is extracted. The 16S rRNA gene fragments will be amplified by PCR to screen the total microbial community using PhyloChip DNA microarray analysis. This approach will detect only the viable microbial community since the PMA intercalated DNA from dead cells would be unavailable for PCR amplification. The total detection time including PCR reaction for low biomass samples will be a few hours. Numerous markets may use this technology. The food industry uses spore detection to validate new alternative food processing technologies, sterility, and quality. Pharmaceutical and medical equipment companies also detect spores as a marker for sterility. This system can be used for validating sterilization processes, water treatment systems, and in various public health and homeland security applications.

Venkateswaran, Kasthuri J.↗

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Kane, James H.↗

Constraints on LISA Pathfinder's Self-Gravity: Design Requirements, Estimates and Testing Procedures

LISA Pathfinder satellite was launched on 3 December 2015 toward the Sun Earth first Lagrangian point (L1) where the LISA Technology Package (LTP), which is the main science payload, will be tested. LTP achieves measurements of differential acceleration of free-falling test masses (TMs) with sensitivity below 3 x 10(exp -14) m s(exp -2) Hz(exp - 1/2) within the 130 mHz frequency band in one dimension. The spacecraft itself is responsible for the dominant differential gravitational field acting on the two TMs. Such a force interaction could contribute a significant amount of noise and thus threaten the achievement of the targeted free-fall level. We prevented this by balancing the gravitational forces to the sub nm s(exp -2) level, guided by a protocol based on measurements of the position and the mass of all parts that constitute the satellite, via finite element calculation tool estimates. In this paper, we will introduce the gravitational balance requirements and design, and then discuss our predictions for the balance that will be achieved in flight.

Armano, M.↗

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition.

Thomas, A. M.↗

Sensitivity Equation Derivation for Transient Heat Transfer Problems

The focus of the paper is on the derivation of sensitivity equations for transient heat transfer problems modeled by different discretization processes. Two examples will be used in this study to facilitate the discussion. The first example is a coupled, transient heat transfer problem that simulates the press molding process in fabrication of composite laminates. These state equations are discretized into standard h-version finite elements and solved by a multiple step, predictor-corrector scheme. The sensitivity analysis results based upon the direct and adjoint variable approaches will be presented. The second example is a nonlinear transient heat transfer problem solved by a p-version time-discontinuous Galerkin's Method. The resulting matrix equation of the state equation is simply in the form of Ax = b, representing a single step, time marching scheme. A direct differentiation approach will be used to compute the thermal sensitivities of a sample 2D problem.

Hou, Gene↗

Determining Temperature Differential to Prevent Hardware Cross-Contamination in a Vacuum Chamber

When contamination-sensitive hardware must be tested in a thermal vacuum chamber, cross-contamination from other hardware present in the chamber, or residue from previous tests, becomes a concern. Typical mitigation strategies involve maintaining the temperature of the critical item above that of other hardware elements at the end of the test. A formula for relating the pumping speed of a chamber, the surface area of contamination sources, and the temperatures of the chamber, source, and contamination-sensitive items has been developed. The formula allows the determination of a temperature threshold about which contamination will not condense on the sensitive items. It defines a parameter alpha that is the fraction given by (contaminant source area)/[chamber pumping speed (time under vacuum) 0.5]. If this parameter is less than 10(exp -6), cross-contamination from common spacecraft material will not occur when the sensitive hardware is at the same temperature as the source of contamination (The chamber is isothermal within 5 C.). Knowing when it becomes safe to have the hardware isothermal permits faster and easier thermal transitions when compared with maintaining an arbitrary temperature differential between parts. Furthermore, the standard temperature differential may not be adequate under some conditions (alpha>10(exp -4)).

Hughes, David↗