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Results for “EXPONENTIAL FUNCTION”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

The dynamics of photoinduced defect creation in amorphous chalcogenides: The origin of the stretched exponential function

The article discusses the dynamics of photoinduced defect creations (PDC) in amorphous chalcogenides, which is described by the stretched exponential function (SEF), while the well known photodarkening (PD) and photoinduced volume expansion (PVE) are governed only by the exponential function. It is shown that the exponential distribution of the thermal activation barrier produces the SEF in PDC, suggesting that thermal energy, as well as photon energy, is incorporated in PDC mechanisms. The differences in dynamics among three major photoinduced effects (PD, PVE, and PDC) in amorphous chalcogenides are now well understood.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Calculating the divided differences of the exponential function by addition and removal of inputs

We introduce a method for calculating the divided differences of the exponential function by means of addition and removal of items from the input list to the function. Our technique exploits a new identity related to divided differences recently derived by F. Zivcovich. We show that upon adding an item to or removing an item from the input list of an already evaluated exponential, the re-evaluation of the divided differences can be done with only O(sn) floating point operations and O(sn) bytes of memory, where [z 0 ,...,z n ] are the inputs and s ∝ max i,j |z i – z j |. We demonstrate our algorithm’s ability to deal with input lists that are orders-of-magnitude longer than the maximal capacities of the current state-of-the-art. Here, we discuss in detail one practical application of our method: the efficient calculation of weights in the off-diagonal series expansion quantum Monte Carlo algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Time-resolved photoluminescence spectroscopy of localized exciton magnetic polarons in Cd{sub 0.70}Mn{sub 0.30}Te spin glass compound

We have investigated dynamics of different localized exciton magnetic polarons (LEMPs) in Cd{sub 0.70}Mn{sub 0.30}Te spin glass (SG) compound below the freezing temperature T{sub f} in the crystal regions, where various microscopic magnetic spin states (MMSSs), namely, “loose” spins, finite, and infinite clusters, are formed. It was shown that there is a broad distribution of the LEMPs lifetimes. The presence of the long-lived LEMPs is caused by the admixture of the optically active bright exciton states to the dark exciton states, i.e., the “brightening” of the dark LEMPs which exist along with the bright LEMPs. The lifetimes of the dark LEMPs correspond to hundreds of nanoseconds. It was found that the time decay of photoluminescence band intensity is approximated by the sum of two functions: a single exponential function and the Kohlrausch–Williams–Watts stretched exponential function. The stretched exponential function describes the recombination processes of the LEMPs formed in the crystal regions of the finite clusters as well as the infinite cluster. This reflects the appearance of spatially heterogeneous dynamics in Cd{sub 0.70}Mn{sub 0.30}Te SG compound below T{sub f} which is due to the disorder in the spin distribution caused by the formation of different MMSSs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

SU-E-T-259: Particle Swarm Optimization in Radial Dose Function Fitting for a Novel Iodine-125 Seed

Purpose: To determine the coefficients of bi- and tri-exponential functions for the best fit of radial dose functions of the new iodine brachytherapy source: Iodine-125 Seed AgX-100. Methods: The particle swarm optimization (PSO) method was used to search for the coefficients of the biand tri-exponential functions that yield the best fit to data published for a few selected radial distances from the source. The coefficients were encoded into particles, and these particles move through the search space by following their local and global best-known positions. In each generation, particles were evaluated through their fitness function and their positions were changed through their velocities. This procedure was repeated until the convergence criterion was met or the maximum generation was reached. All best particles were found in less than 1,500 generations. Results: For the I-125 seed AgX-100 considered as a point source, the maximum deviation from the published data is less than 2.9% for bi-exponential fitting function and 0.2% for tri-exponential fitting function. For its line source, the maximum deviation is less than 1.1% for bi-exponential fitting function and 0.08% for tri-exponential fitting function. Conclusion: PSO is a powerful method in searching coefficients for bi-exponential and tri-exponential fitting functions. The bi- and tri-exponential models of Iodine-125 seed AgX-100 point and line sources obtained with PSO optimization provide accurate analytical forms of the radial dose function. The tri-exponential fitting function is more accurate than the bi-exponential function.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Transconvolution and the virtual positron emission tomograph-A new method for cross calibration in quantitative PET/CT imaging

Purpose: Positron emission tomography (PET)/computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET/CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET/CT in the context of multicenter trials. Methods: To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET/CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET/CT systems, a dedicated solid-state phantom incorporating {sup 68}Ge/{sup 68}Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET/CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. Results: The proposed Transconvolution method matched different PET/CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. Conclusions: By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Experimental observations of bifurcated power decay lengths in the near Scrape-Off Layer of ST40 High Field Spherical Tokamak

The scrape-off layer parallel heat flux decay lengths measured at ST40, a high field, low aspect ratio spherical tokamak, have been observed to bifurcate into two groups. The wide group follows established H-mode scalings (ranging between 2 to 8 mm) while the narrow group falls up to 10 times below these scalings (between 0.2 and 0.8 mm), being comparable to the ion total Larmor radius rather than the ion poloidal Larmor radius. The heat flux profiles of the latter group can only be described by a multi-exponential function, rather than the single exponential function convoluted with a Gaussian. The onset of the narrow scrape-off layer width is observed to be associated with suppressed magnetic fluctuations, suggesting reduced electromagnetic turbulence levels in the SOL.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

A novel conformity index for intensity modulated radiation therapy plan evaluation

Purpose: Intensity modulated radiation therapy (IMRT) has gained popularity in the treatment of cancers. Manual evaluation of IMRT plans for head-and-neck cancers has been especially challenging necessitating efficient and objective assessment tools. In this work, the authors address this issue by developing a personalized conformity index (CI) for comparison of IMRT plans for head-and-neck cancers and evaluating its plan quality discerning power in comparison with other widely used CIs. Methods: A two-dimensional CI with dose and distance incorporated (CI{sub DD}) was developed using the MATLAB program language, to quantify the planning target volume (PTV) coverage. Valuable information contained in the digital imaging and communication in medicine (DICOM) RT objects were harvested for computation of each of the CI{sub DD} components. Apart from the dose penalty factor, a distance-based exponential function was employed by varying the penalty weight associated with the location of cold spots within the PTV. With the goal of deriving a customized penalty factor, the distances between individual pixel and its nearest PTV boundary was found. Using the exponential function, the impact of distance penalty was substantially larger for cold spots closer to the PTV centroid but petered out quickly wherever they were situated in the vicinity of PTV border. In order to evaluate the CI{sub DD} scoring system, three CT image data sets of nasopharyngeal carcinoma (NPC) patients were collected. Ten IMRT plans with degrading qualities were generated from each dataset and were ranked based on CI{sub DD} and other existing indices. The coefficient of variance was calculated for each dataset to compare the degree of variation. Results: The CI{sub DD} scoring system that considered spatial importance of each voxel within the PTV was successfully developed. The results demonstrated that the CI{sub DD} including four discrete factors could provide accurate rankings of plan quality by examining the relative importance of each cold spot within the PTVs. Apart from the dose penalty factor, a distance-based exponential function was employed taking the specific tumor geometry into account. Compared with other commonly used CIs, the CI{sub DD} resulted in the largest coefficient of variance among the ten IMRT plans for each dataset, indicating that its discerning power was the best among the CIs being compared. Conclusions: The CI{sub DD} scoring system was successfully developed to incorporate patient-specific spatial dose information and provide a geometry-based physical index for comparison of IMRT plans for head-and-neck cancers. By taking individual tumor geometry into account, the superiority of CI{sub DD} in plan discerning power was demonstrated. The use of CI{sub DD} could provide an effective means of benchmarking performance, reducing treatment plan variability, and advancing the quality of current IMRT planning.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Fracture length data for geothermal applications

Fracture lengths govern permeability and are unknowns in geothermal assessment. Along their lengths, fracture widths vary due to growth by linkage. Under the influence of diagenesis, narrow widths seal, breaking porosity continuity and reducing open length. The largest range of widths and thus susceptibility to fill occurs where fractures are linked by narrow segments. Outcrops of a geothermal target, Cambrian Potsdam quartz arenite, contain opening-mode fractures having lengths spanning five orders of magnitude from 0.082 mm to 17.9 m. Combined lengths measured at a range of scales can be described by power laws, but at a given image resolution, lengths are best fit by exponential functions. Owing to preferential sealing of small fractures, open fractures follow exponential functions, but values depend on rules for designating fractures as continuous. En échelon segments, offset 10 mm, are connected by narrow fractures or microfractures (hard linked) not evident on outcrop 1 m-elevation LiDAR or 30 m-height drone images. A rule that identifies where narrow and likely connected segments are located can yield lengths meaningful for flow simulation. Depending on diagenesis, continuity rules can halve or double average and maximum length values. Length values from outcrop for geothermal applications should be adjusted based on wellsite-specific diagenesis information.

15 GEOTHERMAL ENERGY↗
DOE OSTI2015

Translational diffusion of water inside hydrophobic carbon micropores studied by neutron spectroscopy and molecular dynamics simulation

When water molecules are confined to nanoscale spacings, such as in the nanometer-size pores of activated carbon fiber (ACF), their freezing point gets suppressed down to very low temperatures (~150 K), leading to a metastable liquid state with remarkable physical properties. Here we have investigated the ambient pressure diffusive dynamics of water in microporous Kynol ACF-10 (average pore size ~11.6 Å, with primarily slit-like pores) from temperature T = 280 K in its stable liquid state down to T = 230 K into the metastable supercooled phase. The observed characteristic relaxation times and diffusion coefficients are found to be, respectively, higher and lower than those in bulk water, indicating a slowing down of the water mobility with decreasing temperature. The observed temperature-dependent average relaxation time (${{\tau}}$) when compared to previous findings indicate that it is the width of the slit pores-not their curvature-that primarily affects the dynamics of water for pore sizes larger than 10 Å. The experimental observations are compared to complementary molecular dynamics simulations of a model system, in which we studied the diffusion of water within the 11.6 Å gap of two parallel graphene sheets. We find generally a reasonable agreement between the observed and calculated relaxation times at the low momentum transfer Q (Q ≤ 0.9 Å -1) . At high Q, however, where localized dynamics becomes relevant, this ideal system does not satisfactorily reproduce the measurements. Consequently, the simulations are compared to the experiments at low Q, where the two can be best reconciled. The best agreement is obtained for the diffusion parameter D associated with the hydrogen-site when a representative stretched exponential function, rather than the standard bimodal exponential model, is used to parametrize the self-correlation function I (Q,t).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Parameterization of photon beam dosimetry for a linear accelerator

Purpose: In radiation therapy, accurate data acquisition of photon beam dosimetric quantities is important for (1) beam modeling data input into a treatment planning system (TPS), (2) comparing measured and TPS modeled data, (3) the quality assurance process of a linear accelerator’s (Linac) beam characteristics, (4) the establishment of a standard data set for comparison with other data, etcetera. Parameterization of the photon beam dosimetry creates a data set that is portable and easy to implement for different applications such as those previously mentioned. The aim of this study is to develop methods to parameterize photon beam dosimetric quantities, including percentage depth doses (PDDs), profiles, and total scatter output factors (S{sub cp}). Methods: S{sub cp}, PDDs, and profiles for different field sizes, depths, and energies were measured for a Linac using a cylindrical 3D water scanning system. All data were smoothed for the analysis and profile data were also centered, symmetrized, and geometrically scaled. The S{sub cp} data were analyzed using an exponential function. The inverse square factor was removed from the PDD data before modeling and the data were subsequently analyzed using exponential functions. For profile modeling, one halfside of the profile was divided into three regions described by exponential, sigmoid, and Gaussian equations. All of the analytical functions are field size, energy, depth, and, in the case of profiles, scan direction specific. The model’s parameters were determined using the minimal amount of measured data necessary. The model’s accuracy was evaluated via the calculation of absolute differences between the measured (processed) and calculated data in low gradient regions and distance-to-agreement analysis in high gradient regions. Finally, the results of dosimetric quantities obtained by the fitted models for a different machine were also assessed. Results: All of the differences in the PDDs’ buildup and the profiles’ penumbra regions were less than 2 and 0.5 mm, respectively. The differences in the low gradient regions were 0.20% ± 0.20% (<1% for all) and 0.50% ± 0.35% (<1% for all) for PDDs and profiles, respectively. For S{sub cp} data, all of the absolute differences were less than 0.5%. Conclusions: This novel analytical model with minimum measurement requirements was proved to accurately calculate PDDs, profiles, and S{sub cp} for different field sizes, depths, and energies.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2018

Luminescence Decay of Colloidal Quantum Dots and Stretched Exponential (Kohlrausch) Relaxation Function

The room temperature non-exponential luminescence decay of colloidal quantum dots is investigated theoretically in an attempt to identify the underlying physical mechanisms responsible for the shape of the decay. It is shown that a stretched exponential functional form of the luminescence decay can be understood in terms of long-range resonance energy transfer from quantum dots to acceptors (molecules, quantum dots, or anharmonic molecular vibrations) or by contact quenching by quenchers (surface traps, molecules or quantum dots) distributed statistically (Poisson distribution) on the surface of the dots. These non-radiative transition processes are assigned to different ranges of the stretching parameter β.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb-Zn Deposit in Dangchang County, Gansu Province

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb-Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seen as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.

58 GEOSCIENCES↗
DOE OSTI2019

Electrical and Optical Characteristics of Si-Nanoparticle Films Deposited onto Substrates by High-Voltage Electrospraying from Ethanol Sols

The optical and electrical characteristics of films consisting of nanocrystalline silicon (nc-Si) deposited onto substrates by the high-voltage electrospraying of nc-Si sols in ethanol are investigated. It is found that the interaction of ethanol droplets carrying Si nanoparticles with a corona-discharge electric field leads to the polymerization of ethanol and the formation of a polymer layer on the Si-nanoparticle surface. A high-voltage facility for depositing the films using an additional focusing electrode allows one to change the geometry of the electric field and intensity in the region of the ethanol droplet flow. As a result, nc-Si films with qualitatively different properties of the polymer on the nanoparticle surface are formed, specifically, nc-Si-A and nc-Si-B, obtained without a focusing electrode and with it, respectively. Upon annealing at temperatures of up to 400°С, the optical band gap E{sub g} of the nc-Si-A films increases from ~1.9 to ~2.2 eV, while the E{sub g} value of the nc-Si-B films remains constant and amounts to 1.85 eV. The constant E{sub g} value of the nc-Si-B films is explained by the properties of the polymer on the Si-nanoparticle surface and the more effective blocking of oxygen penetration from the surrounding environment upon annealing at temperatures of up to 400°C than in the case of a polymer in nc-Si-A films. The temperature dependences of the dark and photoinduced conductivity of nc-Si-A films are approximated with good accuracy by two activation-type exponential functions and the dark activation energies are ~0.75 and 0.1 eV, respectively. The conductivity of the nc-Si-A films noticeably decreases under irradiation of the samples at wavelengths of 460–470 nm. The temperature dependences of the conductivity of the nc-Si-B films are approximated with good accuracy by exponential functions with activation energies of 0.73 (in the dark) and 0.59 eV (under photoexcitation). In contrast to the case of nc-Si-A films, the photoconductivity of nc-Si-B films grows more than fourfold relative to the dark conductivity under analogous illumination. The nc-Si-B films are photoactive and sandwich-like Al/nc-Si-B/Al structures can generate a voltage. The dark conductivity and photoconductivity of the nc-Si-A films in the voltage range of V > 2 V are determined by the two-center Poole–Frenkel effect; the concentration of the centers affecting the Poole–Frenkel conductivity is ~3 × 10{sup 17} cm{sup –3}. In nc-Si-B films in the voltage range of 2–5 V, electron transport is determined by space-charge-limited currents and, at high voltages, by the two-center Poole–Frenkel effect. The concentration of traps contributing to the space-charge-limited currents is ~4 × 10{sup 16} cm{sup –3}. The concentration of Poole–Frenkel centers affecting the conductivity decreases according to the activation law with an activation energy of 0.7 eV from 3 × 10{sup 16} to 2 × 10{sup 14} cm{sup –3} with a decrease in temperature from 120°C to 40°C.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

SU-G-TeP1-10: Predicting Photon Percentage Depth Dose From Profile Due to Changes in Beam Quality

Purpose: To predict photon percentage depth dose (PDD) from profile due to a change in flattened (FF) and flattening-filter-free (FFF) beam quality. Methods: 6MV photon beam PDDs and profiles in a 3D water tank (3DW) and profiles in an ionization chamber array (ICP) were collected for different field sizes and depths with FF and FFF beams in a Versa HD (Elekta Ltd.). The energy was adjusted by changing the bending magnet current (BMC) ±15% from the clinical beam (6MV) in 5% increments. For baseline establishment, PDDs(depth≥3cm) were parameterized with bi-exponential functions and the PDD 20 to 10cm ratios (PDD{sub 20,10}) were calculated. Then, the FF profile at 10cm from the central axis (Pr{sub 10}) and the slope of the FFF central linear region (SFFF) were calculated. Calibration curves were established: (1) change in Pr{sub 10} and SFFF as functions of the change in PDD{sub 20,10} and (2) change in PDD(depth=3, 15 and 30cm) as function of the change in PDD{sub 20,10}. The differences between Pr{sub 10} and SFFF from baseline were calculated and, from calibration curves, changes in PDD{sub 20,10} and PDD(depth=3, 15 and 30cm) were obtained. Then, absolute PDD(depth=3, 15 and 30cm) values were input into a least-square-optimization algorithm to calculate the bi-exponential function’s optimal coefficients and generate the PDD(depths≥3cm). Results: The change in PDD{sub 20,10} relative to baseline increased (<±4%) with BMC. Pr{sub 10} increased (±6%) and SFFF decreased (±11%) with BMC. Relative differences between measured and calculated (i.e. PDD calculation from Pr{sub 10} and SFFF) PDDs were less than 1%. Results apply to FF and FFF beams measured in 3DW and ICP. Conclusion: Pr{sub 10} and SFFF are more sensitive than PDD to changes in beam energy and PDD information can be accurately generated from them. With known 3DW and ICP profile relationship, ICP can be used to obtain PDD for current photon beam.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2013

Dependence of diode sensitivity on the pulse rate of delivered radiation

Purpose: It has been reported that diode sensitivity decreases by as much as 2% when the average dose rate set at the accelerator console was decreased from 600 to 40 MU/min. No explanation was given for this effect in earlier publications. This work is a detailed investigation of this phenomenon: the change of diode sensitivity versus the rate of delivery of dose pulses in the milliseconds and seconds range. Methods: X-ray beams used in this work had nominal energies of 6 and 15 MV and were generated by linear accelerators. The average dose rate was varied from 25 to 600 MU/min, which corresponded to time between microsecond-long dose pulses of 60-2.7 ms, respectively. The dose-per-pulse, dpp, was changed by positioning the detector at different source-to-detector distance. A variety of diodes fabricated by a number of manufacturers were tested in this work. Also, diodes in three different MapCHECKs (Sun Nuclear, Melbourne, FL) were tested. Results: For all diodes tested, the diode sensitivity decreases as the average dose rate is decreased, which corresponds to an increase in the pulse period, the time between radiation pulses. A sensitivity decrease as large as 5% is observed for a 60-ms pulse period. The diode sensitivity versus the pulse period is modeled by an empirical exponential function. This function has a fitting parameter, t{sub eff}, defined as the effective lifetime. The values of t{sub eff} were found to be 1.0-14 s, among the various diodes. For all diodes tested, t{sub eff} decreases as the dpp decreases and is greater for 15 MV than for 6 MV x rays. The decrease in diode sensitivity after 20 s without radiation can be reversed by as few as 60 radiation pulses. Conclusions: A decrease in diode sensitivity occurs with a decrease in the average dose rate, which corresponds to an increase in the pulse period of radiation. The sensitivity decrease is modeled by an empirical exponential function that decreases with an effective lifetime, t{sub eff}, of 1.0-14 s. t{sub eff} varies widely for different diodes, dpp, and x-ray energy. It is hypothesized that the capture of excess minority carriers by charge traps, cause the observed decrease in diode sensitivity. Also, it is hypothesized that the slow reopening of these traps occurs in the hundreds of milliseconds to seconds range at ambient temperature and this underlies the slow decrease in the diode sensitivity. Calibration of a diode is best done at the average dose rate with which it will be used. This is easily accomplished for radiation deliveries in which the average dose rate is a constant. However, for a VMAT delivery the average dose rate is a variable. For measurements made under these conditions diodes can be calibrated with a median or average dose rate which splits the difference in diode sensitivity that is known to occur with changes in average dose rate.

60 APPLIED LIFE SCIENCES↗