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Simple model of the anisotropic penetration depth in high T{sub c} superconductors

Description: We present a simple model of some high {Tc} cuprates based upon superconducting (S) and normal (N) layers, which quantitatively fits the data of Bonn et al. for the low-temperature T dependence of the penetration depths {lambda}{sub a,b,c} in untwinned YBa{sub 2}Cu{sub 3}O{sub 7-{delta}}, assuming s-wave intralyer pairing. This SN model also leads to anisotropic surface states, which complicate analysis of photoemission and tunneling measurements.
Date: April 1, 1996
Creator: Klemm, R.A. & Liu, S.H.
Partner: UNT Libraries Government Documents Department

Analysis of Fragmentation and Resulting Shrapnel Penetration of Naturally Fragmenting Cylindrical Bombs

Description: Fragmentation of exploding cylinders and penetration mechanics of surrounding vessel walls were examined and a qualitative understanding was achieved. This understanding provided a basis for making simplifying approximations and assumptions that aided in creating a shrapnel penetration model. Several mathematical models were discussed, and results from 6 cylinder tests were analyzed in order to select a model that best represented the data. It was determined that the overall best mathematical model to predict shrapnel penetration uses the modified Gurney equation to calculate fragment velocity, the Mott equation to calculate largest fragment weight, and the Christman/Gehring equation to calculate penetration depth.
Date: August 1, 2000
Creator: Gardner, S.E.
Partner: UNT Libraries Government Documents Department

Agreement Between Local and Global Measurements of the London Penetration Depth

Description: Recent measurements of the superconducting penetration depth in Ba(Fe{sub 1-x}Co{sub x}){sub 2}As{sub 2} appeared to disagree on the magnitude and curvature of {delta}{lambda}{sub ab}(T), even near optimal doping. These measurements were carried out on different samples grown by different groups. To understand the discrepancy, we use scanning SQUID susceptometry and a tunnel diode resonator to measure the penetration depth in a single sample. The penetration depth observed by the two techniques is identical with no adjustments. We conclude that any discrepancies arise from differences between samples, either in growth or crystal preparation.
Date: August 29, 2012
Creator: Lippman, Thomas M.; Kalisky, Beena; Kim, Hyunsoo; Tanatar, Makariy; Budko, Sergey L.; Canfield, Paul C. et al.
Partner: UNT Libraries Government Documents Department

Calculation of the Effect of Random Superfluid Density on the Temperature Dependence of the Penetration Depth

Description: Microscopic variations in composition or structure can lead to nanoscale inhomogeneity in superconducting properties such as the magnetic penetration depth, but measurements of these properties are usually made on longer length scales. We solve a generalized London equation with a non-uniform penetration depth {lambda}(r), obtaining an approximate solution for the disorder-averaged Meissner screening. We find that the effective penetration depth is different from the average penetration depth and is sensitive to the details of the disorder. These results indicate the need for caution when interpreting measurements of the penetration depth and its temperature dependence in systems which may be inhomogeneous.
Date: July 20, 2012
Creator: Lippman, Thomas & Moler, Kathryn A.
Partner: UNT Libraries Government Documents Department

Local measurement of the superfluid density in the pnictide superconductor Ba(Fe1-xCox)2As2 across the superconducting dome

Description: We measure the penetration depth {lambda}{sub ab}(T) in Ba(Fe{sub 1-x}Co{sub x}){sub 2}As{sub 2} using local techniques that do not average over the sample. The superfluid density {rho}{sub s}(T) {triple_bond} 1/{lambda}{sub ab}(T){sup 2} has three main features. First, {rho}{sub s}(T = 0) falls sharply on the underdoped side of the dome. Second, {lambda}{sub ab}(T) is flat at low T at optimal doping, indicating fully gapped superconductivity, but varies more strongly in underdoped and overdoped samples, consistent with either a power law or a small second gap. Third, {rho}{sub s}(T) varies steeply near T{sub c} for optimal and underdoping. These observations are consistent with an interplay between magnetic and superconducting phases.
Date: August 12, 2011
Partner: UNT Libraries Government Documents Department

Penetration Experiments with Limestone Targets and Ogive-Nose Steel Projectiles

Description: We conducted three sets of depth-of-penetration experiments with limestone targets and 3.0 caliber-radius-head (CRH), ogive-nose steel rod projectiles. The limestone targets had a nominal unconfined compressive strength of 60 MPa, a density of 2.31 kg/m{sup 3}, a porosity of 15%, and a water content less than 0.4%. The ogive-nose rod projectiles with length-to-diameter ratios often were machined from 4340 R{sub c} 45 and Aer Met 100 R{sub c} 53 steel, round stock and had diameters and masses of 7.1 mm, 0.020 kg; 12.7 mm, 0.117 kg; and 25.4 mm, 0.931 kg. Powder guns or a two-stage, light-gas gun launched the projectiles at normal impacts to striking velocities between 0.4 and 1.9 km/s. For the 4340 R{sub c} 45 and Aer Met 100 R{sub c} 53 steel projectiles, penetration depth increased as striking velocity increased to a striking velocity of 1.5 and 1.7 km/s, respectively. For larger striking velocities, the projectiles deformed during penetration without nose erosion, deviated from the shot line, and exited the sides of the target. We also developed an analytical penetration equation that described the target resistance by its density and a strength parameter determined from depth of penetration versus striking velocity data.
Date: April 8, 1999
Creator: Forrestal, M.J.; Frew, D.J. & Hanchak, S.J.
Partner: UNT Libraries Government Documents Department

Capabilities of infrared weld monitor

Description: A non-obtrusive pre-aligned, solid-state device has been developed to monitor the primary infrared emissions during laser welding. The weld monitor output is a 100-1000 mV signal that depends on the beam power and weld characteristics. The DC level of this signal is related to weld penetration, while AC portions of the output can be correlated with surface irregularities and part misalignment or contamination. Changes in DC behavior are also noted for both full and deep penetration welds. Full penetration welds are signified by an abrupt reduction in the weld monitor output. Bead on plate welds were made on steel, aluminum, and magnesium with both a CW CO{sub 2} laser and a pulsed Nd:YAG laser to explore the relationships between the weld characteristics and the weld monitor output.
Date: November 1, 1997
Creator: Sanders, P.G.; Keske, J.S.; Leong, K.H. & Kornecki, G.
Partner: UNT Libraries Government Documents Department

Magnetic imaging of interlayer Josephson vortices.

Description: The authors have magnetically imaged interlayer Josephson vortices emerging parallel to the planes of single crystals of the organic superconductor {kappa}-(BEDT-TTF){sub 2} Cu(NCS){sub 2}, and the single layer cuprate high-T{sub c} superconductors Tl{sub 2}Ba{sub 2}CuO{sub 6+{delta}} (Tl-2201) and (Hg,Cu)Ba{sub 2}CuO{sub 6+{delta}} (Hg-1201), using a scanning Superconducting Quantum Interference Device (SQUID) microscope. These images provide a direct measurement of the interlayer penetration depth, which is approximately 63 {micro}m for {kappa}-(BEDT-TTF){sub 2} Cu(NCS){sub 2}, 18 {micro}m for Tl-2201 and 8 {micro}m for Hg-1201. The lengths for the cuprates are about a factor of 10 larger than originally predicted by the interlayer tunneling model for the mechanism of superconductivity in layered compounds, indicating that this mechanism alone cannot account for the high critical temperatures in these materials.
Date: January 15, 1999
Creator: Kirtley, J. A.
Partner: UNT Libraries Government Documents Department

Depth-dependent magnetism of layered superconductors : Nb/Si.

Description: We have studied magnetic field penetration and vortex line formation in a [Nb(100 {angstrom})/Si(15 {angstrom})]x20 multilayer by magnetization and polarized neutron reflection. With the magnetic field applied parallel to the surface, the magnetization revealed the presence of a kink above H{sub cl} indicative of transitions between one row of fluxoids and two rows of fluxoids parallel to the surface. The spin-dependence of neutron reflectivity below H{sub cl} was consistent with a penetration depth of 1200 {angstrom}, substantially larger than that of bulk Nb. In the mixed phase (H{sub ext} > H{sub cl}) the field was found to penetrate the surface, with a slope as found in the case of H{sub ext} < H{sub cl}. At H{sub ext} > H{sub cl} vortex forms in addition to surface penetration. A modulation of the vortex fields was found with the periodicity of the Nb/Si bilayers as evidenced by the spin dependence of the reflectivity at the first Bragg peak of the multilayer.
Date: December 2, 1997
Creator: Felcher, G. P.; Fullerton, E. E.; Osgood, R. M. & Yusuf, S. M.
Partner: UNT Libraries Government Documents Department

Plasma Treatment of Niobium SRF Cavity Surfaces

Description: Plasma based surface modification provides an excellent opportunity to eliminate non- superconductive pollutants in the penetration depth region of the SRF cavity surface and to remove mechanically damaged surface layer improving surface roughness. We have demonstrated on flat samples that plasma etching in Ar / Cl2 of bulk Nb is a viable alternative surface preparation technique to BCP and EP methods, with comparable etching rates. The geometry of SRF cavities made of bulk Nb defines the use of asymmetric RF discharge configuration for plasma etching. In a specially designed single cell cavity with sample holders, discharge parameters are combined with etched surface diagnostics to obtain optimum combination of etching rates, roughness and homogeneity in a variety of discharge types, conditions, and sequences. The optimized experimental conditions will ultimately be applied to single cell SRF cavities.
Date: May 1, 2010
Creator: J. Upadhyay, M. Raskovic, L. Vuskovic, S. Popovic, A.-M. Valente-Feliciano, L. Phillips
Partner: UNT Libraries Government Documents Department

Investigation of oil injection into brine for the strategic petroleum reserve : hydrodynamics experiments with simulant liquids.

Description: An experimental program is being conducted to study a proposed approach for oil reintroduction in the Strategic Petroleum Reserve (SPR). The goal is to assess whether useful oil is rendered unusable through formation of a stable oil-brine emulsion during reintroduction of degassed oil into the brine layer in storage caverns. This report documents the first stage of the program, in which simulant liquids are used to characterize the buoyant plume that is produced when a jet of crude oil is injected downward from a tube into brine. The experiment consists of a large transparent vessel that is a scale model of the proposed oil injection process at the SPR. An oil layer is floated on top of a brine layer. Silicon oil (Dow Corning 200{reg_sign} Fluid, 5 cSt) is used as the simulant for crude oil to allow visualization of the flow and to avoid flammability and related concerns. Sodium nitrate solution is used as the simulant for brine because it is not corrosive and it can match the density ratio between brine and crude oil. The oil is injected downward through a tube into the brine at a prescribed depth below the oil-brine interface. Flow rates are determined by scaling to match the ratio of buoyancy to momentum between the experiment and the SPR. Initially, the momentum of the flow produces a downward jet of oil below the tube end. Subsequently, the oil breaks up into droplets due to shear forces, buoyancy dominates the flow, and a plume of oil droplets rises to the interface. The interface is deflected upward by the impinging oil-brine plume. Two different diameter injection tubes were used (1/2-inch and 1-inch OD) to vary the scaling. Use of the 1-inch injection tube also assured that turbulent pipe flow was achieved, which was questionable for lower ...
Date: October 1, 2003
Creator: Castaneda, Jaime N.; Shollenberger, Kim Ann (California Polytechnic State University, San Luis Obispo, CA); Torczynski, John Robert; Cote, Raymond O.; Barney, Jeremy & O'Hern, Timothy John
Partner: UNT Libraries Government Documents Department

Interpretation of Geoelectric Structure at Hululais Prospect Area, South Sumatra

Description: Schlumberger resistivity surveys were conducted in 1993 as part of a combined geological, geophysical and geological program to investigate a geothermal prospect in the Hululais area, Southern Sumatra. These resistivity data resolved the upper conductive layer and were interpreted to define the shallow extent of a possible geothermal system. A follow-up magnetotelluric (MT) survey was carried out to probe deeper than the dc resistivity survey results achieved. However, the resistive sub-stratum below the conductive layer was still poorly resolved. Possible reasons for this include a preferential channeling of the telluric current within the thick shallow very conductive layer, thus limiting the penetration depth of the magnetotelluric signals and poor resolution due to high noise levels caused by significant rain and sferics.
Date: January 1, 1995
Creator: Mulyadi
Partner: UNT Libraries Government Documents Department

Local Measurement of the Penetration Depth in the Pnictide Superconductor Ba(Fe_0.95 Co_0.05)_2 As_2

Description: We use magnetic force microscopy (MFM) to measure the local penetration depth {lambda} in Ba(Fe{sub 0.95}Co{sub 0.05}){sub 2}As{sub 2} single crystals and use scanning SQUID susceptometry to measure its temperature variation down to 0.4 K. We observe that superfluid density {rho}{sub s} over the full temperature range is well described by a clean two-band fully gapped model. We demonstrate that MFM can measure the important and hard-to-determine absolute value of {lambda}, as well as obtain its temperature dependence and spatial homogeneity. We find {rho}{sub s} to be uniform on the submicron scale despite the highly disordered vortex pinning.
Date: January 11, 2010
Creator: Matsushita, Y.
Partner: UNT Libraries Government Documents Department

Vortex lattice structures in YNi{sub 2}B{sub 2}C

Description: The authors observe a flux lattice with square symmetry in the superconductor YNi{sub 2}B{sub 2}C when the applied field is parallel to the c-axis of the crystal. A square lattice observed previously in the isostructural magnetic analog ErNi{sub 2}B{sub 2}C was attributed to the interaction between magnetic order in that system and the flux lattice. Since the Y-based compound does not order magnetically, it is clear that the structure of the flux lattice is unrelated to magnetic order. In fact, they show that the flux lines have a square cross-section when the applied field is parallel to the c-axis of the crystal, since the measured penetration depth along the 100 crystal direction is larger than the penetration depth along the 110 by approximately 60%. This is the likely reason for the square symmetry of the lattice. Although they find considerable disorder in the arrangement of the flux lines at 2.5T, no melting of the vortex lattice was observed.
Date: December 1, 1997
Creator: Yethiraj, M.; Paul, D.M.; Tomy, C.V. & Forgan, E.M.
Partner: UNT Libraries Government Documents Department

Use of the high-energy x-ray microprobe at the Advanced Photon Source to investigate the interactions between metals and bacteria.

Description: Understanding the fate of heavy-metal contaminants in the environment is of fundamental importance in the development and evaluation of effective remediation and sequestration strategies. Among the factors influencing the transport of these contaminants are their chemical separation and the chemical and physical attributes of the surrounding medium. Bacteria and the extracellular material associated with them are thought to play a key role in determining a contaminant's speciation and thus its mobility in the environment. In addition, the microenvironment at and adjacent to actively metabolizing cell surfaces can be significantly different from the bulk environment. Thus, the spatial distribution and chemical separation of contaminants and elements that are key to biological processes must be characterized at micron and submicron resolution in order to understand the microscopic physical, geological, chemical, and biological interfaces that determine a contaminant's macroscopic fate. Hard X-ray microimaging is a powerful technique for the element-specific investigation of complex environmental samples at th needed micron and submicron resolution. An important advantage of this technique results from the large penetration depth of hard X-rays in water. This advantage minimizes the requirements for sample preparation and allows the detailed study of hydrated samples. This paper presents results of studies of the spatial distribution of naturally occurring metals and a heavy-metal contaminant (Cr) in and near hydrated bacteria (Pseudomonas fluorescens) in the early stages of biofilm development, performed at the Advanced Photon Source Sector 2 X-ray microscopy beamline.
Date: September 30, 1999
Creator: Kemner, K. M.; Lai, B.; Maser, J.; Schneegurt, M. A.; Cai, Z.; Ilinski, P. P. et al.
Partner: UNT Libraries Government Documents Department

Characteristic features of the exotic superconductors: A summary

Description: The authors summarize the results of a comprehensive examination of the characteristic features of the exotic superconductors, the superconductors so-labelled by Uemura and co-workers. In both the electronic and the crystal-chemistry properties, they find anomalous features which appear to be universal for these materials, as well as other features which are clearly not universal but common enough to be considered typical for these materials. Some implications of these anomalies are discussed.
Date: September 1, 1997
Creator: Brandow, B.
Partner: UNT Libraries Government Documents Department

Vortex penetration depth of organic superconductors: Evidence for vortex lattice melting

Description: The authors observe a crossover field H* in the temperature and magnetic field dependence of the rf vortex penetration depth in {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br for {rvec H}{sub dc}{parallel}{cflx b}-axis. They find that H* can be described quantitatively by the 3D Lindemann melting theory; thus, it corresponds to the melting of the vortex lattice in {kappa}-(ET){sub 2}Cu[N(CN){sub 2}]Br and lies very close to the irreversibility line. In the vortex-liquid state, they argue that the saturation of the vortex penetration depth in a magnetic field results from the finite size of the sample. The results do not have the scaling form predicted by the Coffey-Clem model in contrast to previous findings.
Date: July 1, 1997
Creator: Tea, N.H.; Giannetta, R.W.; Salamon, M.B.; Williams, J.M.; Wang, H.H. & Geiser, U.
Partner: UNT Libraries Government Documents Department

Josephson coupling and plasma resonance in vortex crystal

Description: The authors consider the magnetic field dependence of the plasma resonance frequency in vortex crystal state. The authors found that low magnetic field induces a small correction to the plasma frequency proportional to the field. The slope of this linear field dependence is directly related to the average distance between the pancake vortices in the neighboring layers, wandering length. This length is determined by both Josephson and magnetic couplings between layers. At higher fields the Josephson coupling is suppressed collectively and is determined by elastic energy of the vortex lattice. Analyzing experimental data, they found that (1) the wandering length becomes comparable with the London penetration depth near {Tc}, (2) at small melting fields (< 20 G) the wandering length does not change much at the melting transition demonstrating existence of the line liquid phase in this field range, and (3) the self consistent theory of pancake fluctuations describes very well the field dependence of the Josephson plasma resonance frequency up to the melting point.
Date: January 19, 2000
Creator: Bulaevskii, L. N. & Koshelev, A. E.
Partner: UNT Libraries Government Documents Department

Campbell penetration depth in Fe-based superconductors

Description: A 'true' critical current density, j{sub c}, as opposite to commonly measured relaxed persistent (Bean) current, j{sub B}, was extracted from the Campbell penetration depth, {lambda}{sub c}(T,H) measured in single crystals of LiFeAs, and optimally electron-doped Ba(Fe{sub 0.954}Ni{sub 0.046}){sub 2}As{sub 2} (FeNi122). In LiFeAs, the effective pinning potential is nonparabolic, which follows from the magnetic field - dependent Labusch parameter {alpha}. At the equilibrium (upon field - cooling), {alpha}(H) is non-monotonic, but it is monotonic at a finite gradient of the vortex density. This behavior leads to a faster magnetic relaxation at the lower fields and provides a natural dynamic explanation for the fishtail (second peak) effect. We also find the evidence for strong pinning at the lower fields.The inferred field dependence of the pinning potential is consistent with the evolution from strong pinning, through collective pinning, and eventually to a disordered vortex lattice. The value of j{sub c}(2 K) {approx_equal} 1.22 x 10{sup 6} A/cm{sup 2} provide an upper estimate of the current carrying capability of LiFeAs. Overall, vortex behavior of almost isotropic, fully-gapped LiFeAs is very similar to highly anisotropic d-wave cuprate superconductors, the similarity that requires further studies in order to understand unconventional superconductivity in cuprates and pnictides. In addition to LiFeAs, we also report the magnetic penetration depth in BaFe{sub 2}As{sub 2} based superconductors including irradiation of FeNi122. In unirradiated FeNi122, the maximum critical current value is, j{sub c}(2K) {approx_equal} 3.3 x 10{sup 6} A/cm{sup 2}. The magnetic-dependent feature was observed near the transition temperature in FeTe{sub 0.53}Se{sub 0.47} and irradiated FeNi122. Because of this feature, further studies are required in order to properly calibrate the Campbell penetration depth. Finally, we detected the crossing between the magnetic penetration depth and London penetration depth in optimally hold-doped Ba{sub 0.6}K{sub 0.4}Fe{sub 2}As{sub 2} (BaK122) and isovalent doped BaFe{sub ...
Date: August 15, 2011
Creator: Prommapan, Plegchart
Partner: UNT Libraries Government Documents Department

Flux pinning characteristics in cylindrical ingot niobium used in superconducting radio frequency cavity fabrication

Description: We present the results of from DC magnetization and penetration depth measurements of cylindrical bulk large-grain (LG) and fine-grain (FG) niobium samples used for the fabrication of superconducting radio frequency (SRF) cavities. The surface treatment consisted of electropolishing and low temperature baking as they are typically applied to SRF cavities. The magnetization data were fitted using a modified critical state model. The critical current density Jc and pinning force Fp are calculated from the magnetization data and their temperature dependence and field dependence are presented. The LG samples have lower critical current density and pinning force density compared to FG samples which implies a lower flux trapping efficiency. This effect may explain the lower values of residual resistance often observed in LG cavities than FG cavities.
Date: April 1, 2012
Creator: Dhavale Ashavai, Pashupati Dhakal, Anatolii A Polyanskii, Gianluigi Ciovati
Partner: UNT Libraries Government Documents Department

Pattern Recognition: The Importance of Dispersion in Crystal Collimation

Description: One aspect of the upcoming CRYSTAL experiment is to study the dynamics of single protons circulating the SPS in the presence of a crystal. Under some circumstances (for example under crystal channeling) a proton may hit the crystal and the neighboring silicon strip position detectors only once, before extraction from the SPS. In general (at most crystal rotation angles) it is expected that single protons will hit the crystal many times, with many accelerator turns between each hit, before escaping. Intermediate regimes are also possible (for example under volume reflection) in which a proton hits the crystal only a few times over many turns before being lost. It is crucial that the data analysis of each single proton data set be able to distinguish between these different dynamical phases, and to be able to convincingly demonstrate that the fundamental processes at play in each phase are well understood. Distinguishing between dynamical phases depends crucially on the ability to perform pattern recognition--at least visually, but preferably quantitatively--on the single proton data sets. This note shows that synchrotron oscillations significantly affect the hit pattern of a proton on the crystal. (By hit pattern we mean either the measurement vector of turn number and penetration depth, for each proton, or a vector that can be directly derived from the measurement vector, such as the vector of inferred synchrotron phase and penetration depth.) The analysis is (deliberately) as rudimentary as possible, using an elementary linear calculation which neither includes any higher order effects in the accelerator, nor any dynamical interactions between the test proton and the crystal or the silicon detectors. Single particle simulation studies need to be carried out for CRYSTAL, exploring realistic effects besides dispersion, such as multiple scattering, dead zones, energy loss, dispersion slope, and linear coupling. Only after analysis software ...
Date: September 1, 2008
Creator: Peggs,S. & Shiraishi, S.
Partner: UNT Libraries Government Documents Department

Biomolecular Origin of The Rate-Dependent Deformation of Prismatic Enamel

Description: Penetration deformation of columnar prismatic enamel was investigated using instrumented nanoindentation testing, carried out at three constant strain rates (0.05 s{sup -1}, 0.005 s{sup -1}, and 0.0005 s{sup -1}). Enamel demonstrated better resistance to penetration deformation and greater elastic modulus values were measured at higher strain rates. The origin of the rate-dependent deformation was rationalized to be the shear deformation of nanoscale protein matrix surrounding each hydroxyapatite crystal rods. And the shear modulus of protein matrix was shown to depend on strain rate in a format: G{sub p} = 0.213 + 0.021 ln {dot {var_epsilon}}. Most biological composites compromise reinforcement mineral components and an organic matrix. They are generally partitioned into multi-level to form hierarchical structures that have supreme resistance to crack growth [1]. The molecular mechanistic origin of toughness is associated with the 'sacrificial chains' between the individual sub-domains in a protein molecule [2]. As the protein molecule is stretched, these 'sacrificial chains' break to protect its backbone and dissipate energy [3]. Such fresh insights are providing new momentum toward updating our understanding of biological materials [4]. Prismatic enamel in teeth is one such material. Prismatic microstructure is frequently observed in the surface layers of many biological materials, as exemplified in mollusk shells [5] and teeth [6]. It is a naturally optimized microstructure to bear impact loading and penetration deformation. In teeth, the columnar prismatic enamel provides mechanical and chemical protection for the relatively soft dentin layer. Its mechanical behavior and reliability are extremely important to ensure normal tooth function and human health. Since enamel generally contains up to 95% hydroxyapatite (HAP) crystals and less than 5% protein matrix, it is commonly believed to be a weak and brittle material with little resistance to fracture [7]. This study is aimed at exploring the effect of the weak amelogenin-rich protein ...
Date: July 5, 2006
Creator: Zhou, J & Hsiung, L
Partner: UNT Libraries Government Documents Department

Moment-based effective transport equations for energy straggling.

Description: Ion energy straggling is accomodated in condensed history (CH) Monte Carlo simulation by sampling energy-losses at the end of a fixed spatial step from precomputed, pathlength dependent energy-loss distributions. These distributions are essentially solutions to a straight ahead transport equation given by {partial_derivative}{psi}(s,E)/{partial_derivative}s = {integral}{sub Q{sub min}}{sup Q{sub max}} dQ {sigma}{sub e}(E,Q){psi}(s, E + Q) - {sigma}{sub e}(E){psi}(s,E), 8 {ge} 0, with monoenergetic incidence {psi}(0, E) = {delta}(E{sub 0} - E). In Eq.(1), s is the pathlength variable, {sigma}{sub e}(E,Q) is the differential cross section for energy loss Q, typically given by the relativistic Rutherford cross section for hard collisions, {sigma}{sub e}(E) is the total ion-electron scattering cross section, and Q{sub min} and Q{sub max} are, respectively, the minimum and maximum energy transfer per collision. Direct solution of Eq.( 1) by stochastic or deterministic numerical techniques is not feasible because of the very small energy transfers and very small mean free paths that characterize charged particle interactions. Condensed history codes typically employ an approximate solution due to Vavilov, obtained assuming a constant mean free path and thus restricted to short step sizes. This solution is formal and its numerical evaluation can be computationally laborious, especially for small step sizes. In practice, Monte Carlo codes have incorporated the Vavilov theory through elaborate numerical approximations, such as truncated Edgeworth expansions, curve-fitting approximations using Moyal functions for small penetration depths or higher energies, and special treatments for the large energy-loss tail of the distribution. In this paper we propose an alternative approach which is also valid under the conditions of the Vavilov theory but has the potential of being computationally more efficient.
Date: January 1, 2002
Creator: Prinja, A. K. (Anil K.); Klein, V. (Veronica) & Hughes, H. G. (Henry Grady)
Partner: UNT Libraries Government Documents Department