Radiation Transport Calculations Research Articles

Валідація пакета програм MCPV з безперервною за енергією бібліотекою мікроскопічних констант

The results of the validation of the code package MCPV for the calculation of radiation transport within VVER-1000 reactor type near-vessel space using a continuous-energy data library are presented. The validation is carried out based on the experimental data obtained in mock-up and full-scale experiments. It is shown that the code package MCPV can be used to simulate neutrons and gamma quanta transport through the complicated heterogeneous environment of a nuclear reactor and to obtain the valid values of the functionals of the neutron and gamma fluxes within VVER-1000 near-vessel space.

Monte Carlo modelling of cyclotron and radioisotope center (CYRIC) at Tohoku University: a radiation protection study

Protection against ionizing radiations is important in laboratories with radioactive materials and high energy cyclotron beams. The Cyclotron and Radioisotope Center (CYRIC) located in Tohoku University in Miyagi prefecture, Japan and is a well-known nuclear science laboratory with cyclotron beams and substantial number of high activity radioactive materials. Considering this, it is important to perform complete radiation transport computations to ensure the safety of non-occupational and occupational workers. In the present work, we have developed a complete 3-dimensional model of the main cyclotron building and radiation labs using Monte Carlo method. We have found that the dispersed photons and neutrons inside and in the surrounding of the CYRIC building pose no significant risk to occupational and non-occupational workers. The present work and the developed models would be useful in the field of radiation protection.

Expert‐in‐the‐loop design of integral nuclear data experiments

AbstractNuclear data are fundamental inputs to radiation transport codes used for reactor design and criticality safety. The design of experiments to reduce nuclear data uncertainty has been a challenge for many years, but advances in the sensitivity calculations of radiation transport codes within the last two decades have made optimal experimental design possible. The design of integral nuclear experiments poses numerous challenges not emphasized in classical optimal design, in particular, constrained design spaces (in both a statistical and engineering sense), severely under‐determined systems, and optimality uncertainty. We present a design pipeline to optimize critical experiments that uses constrained Bayesian optimization within an iterative expert‐in‐the‐loop framework. We show a successfully completed experiment campaign designed with this framework that involved two critical configurations and multiple measurements that targeted compensating errors in 239Pu nuclear data.

Exploring Numba and CuPy for GPU-Accelerated Monte Carlo Radiation Transport

This paper examines the performance of two popular GPU programming platforms, Numba and CuPy, for Monte Carlo radiation transport calculations. We conducted tests involving random number generation and one-dimensional Monte Carlo radiation transport in plane-parallel geometry on three GPU cards: NVIDIA Tesla A100, Tesla V100, and GeForce RTX3080. We compared Numba and CuPy to each other and our CUDA C implementation. The results show that CUDA C, as expected, has the fastest performance and highest energy efficiency, while Numba offers comparable performance when data movement is minimal. While CuPy offers ease of implementation, it performs slower for compute-heavy tasks.

Comparison of transport cross-section data generated with BONAMI and TRANSX

This work compares the results of radiation transport calculations performed with VITAMIN-B7 cross section data to calculations performed with a similar library prepared with the TRANSX code. The bases for the comparisons include a simplified, one-dimensional PWR model and the industry standard H.B. Robinson Cycle 9 reactor dosimetry benchmark. Comparisons are also made with a modified TRANSX-generated library with enhanced background cross section data. The results show significant differences between VITAMIN and TRANSX-generated libraries through iron media.

Molten Salt Research Reactor (MSRR) shielding analysis using SCALE/MAVRIC sequence with continuous energy and multigroup cross sections

It is necessary to verify (and validate when experimental data are available) shielding codes and methodologies for Molten Salt Reactors (MSRs). This paper examines the impact of using a fine and coarse multigroup cross section library vs. the reference continuous energy data. Molten Salt Research Reactor (MSRR) being developed by the NEXT Research Alliance (NEXTRA) is used as a testbed. Shielding analyses are performed in support of MSRR development using the MAVRIC sequence of the SCALE 6.2.4 code package. The sequence uses deterministic forward and adjoint radiation transport calculations with FW-CADIS methodology to generate variance reduction parameters that are used by MONACO, a fixed source Monte Carlo code. Originally, MONACO was developed as a multigroup code, and a 200-group and 27-group neutron shielding-focused libraries were provided as part of the package. While the 200-group library provides adequate accuracy for many applications, it is highly desirable to confirm this for any specific analysis. In SCALE 6.2, continuous energy capability was implemented in MONACO, thus enabling direct and consistent evaluation and quantification of the impact of using a multigroup rather than the reference continuous energy library. This paper examines the impact of multigroup approximation on main radiation environment parameters in MSRR shielding analysis, including the fast flux and dpa.

Modeling and optimization of scintillating crystal layers for designing a three-layer phoswich Alpha-Beta-Gamma detector

Monitoring the level of radioactive contamination and the type of radiation in the environment is very important for the protection of facilities, employees, and people. Phoswich detector is one of the useful tools to identify different radiations and separate them from each other using different scintillating crystals. However, their design can be very diverse based on the type of particles analyzed and various parameters of scintillating crystals and needs optimization to have maximum efficiency. This work aims to optimize the scintillating crystal layers for the design of the three-layer alpha-beta-gamma phoswich detector based on Monte Carlo radiation transport calculations. The selection of the appropriate model for the type and thickness of each layer is based on the optimization of parameters such as energy accumulation, produced scintillation optical photons, attenuation of optical photons, and scintillation decay time. The results showed that the three scintillating layers of ZnS(Ag), CaF2(Eu), and LYSO(Ce) with optimal thicknesses of 25.01 μm, 3.50 mm, and 2.54 cm, respectively, have more suitable optical outputs for detecting common alpha-beta-gamma radionuclide emitters.

Radiation Protection Considerations for Cancer Patients with End-stage Renal Disease Receiving 131 I Treatment.

Differentiated thyroid cancer (DTC) is commonly treated first with a partial or complete thyroidectomy, followed by radioiodine (RAI) ablative therapy to eliminate remaining cancer cells. In such treatments, physical decay and urinary excretion are the primary means of 131 I. As such, patients with impaired urinary ability clearance, such as patients with end-stage renal disease (ESRD) whose urinary ability is impaired by dysfunction, can retain abnormally high activities of RAI, posing a concern to both the patient and those with whom the patient interacts. Additionally, ESRD patients are commonly administered dialysis therapy, wherein their blood is externally cycled through a dialyzer (hemodialysis) or filtered by instilling a dialysate fluid into the peritoneum (peritoneal dialysis) to filter uremic toxins from their blood that accumulate due to kidney dysfunction. These factors make determining release and dosing for ESRD patients receiving RAI therapy dependent on a plurality of variables. An evaluation of the current patient release guidelines, as given in US Nuclear Regulatory Commission (US NRC) Regulatory Guide 8.39 Rev. 1 for ESRD patients receiving RAI, has yet to be addressed. In this study, a biokinetic model for 131 I in ESRD patients receiving dialysis has been developed, improving on traditional two-compartment models, reflective of kinetics from multi-compartment models with updated transfer coefficients modified to reflect the different physiological functions of compartments. This updated biokinetic model was integrated with Monte Carlo radiation transport calculations using stylized computational hermaphroditic phantoms to calculate dose rate coefficients in exposure scenarios and compared with those of the point source models of NRC Reg Guide 8.39 Rev. 1 (and the proposed verbiage in Rev. 2). Results demonstrated that the baseline models of Rev. 1 and Rev. 2 overestimated the effective dose rate to an exposed individual for the majority of time post-administration, where both models overestimated the total dose to the maximally exposed individual. However, the application of several patient-specific modifying factors to the Rev. 2 model resulted in an overestimation by only a factor of 1.25, and in general, the results produced with the patient-specific modifications provide improved convergence with the dose rate coefficients computed in this study for ESRD patients.

Self-consistent integrated modeling of combined hybrid discharge-laser produced plasma devices for extreme ultraviolet metrology

Discharge- and laser-produced plasma (DLPP) devices are being used as light sources for extreme ultraviolet (EUV) generation. A key challenge for both, DPP and LPP, is achieving sufficient brightness to support the throughput requirements of nanometrology tools. To simulate the environment of a hybrid DLPP device and optimize the EUV output, we have developed an integrated HEIGHTS-DLPP computer simulation package. The package integrates simulation of two evolving plasmas (DPP and LPP) and includes modeling of a set of integrated self-consistent processes: external power source and plasma energy balance, plasma resistive magnetohydrodynamics, plasma heat conduction, detailed radiation transport (RT), and laser absorption and refraction. We simulated and optimized DLPP devices using Xe gas as a target material. We synchronized the external circuit parameters, chamber gas parameters, and laser beam temporal and spatial profiles to achieve maximum EUV output. The full 3D Monte Carlo scheme was integrated for detailed RT and EUV output calculations in Xe using more than 3600 spectral groups. The modeling results are in good agreement with Julich Forschungszentrum experimental data. Theoretical models, developed and integrated into the HEIGHTS package, showed wide capabilities and flexibility. The models and package can be used for optimization of the experimental parameters and settings, investigation of DLPP devices with complex design, analyzing the impact of integrated spatial effects and working timeline arrangement on the final EUV output, and EUV source size, shape, and angular distribution.

Large Volume and Fast Response Gamma Ray Diagnostic in the Large Helical Device

A large volume and fast response gamma ray diagnostic based on the LaBr3(Ce) scintillator was installed to obtain the gamma ray spectrum in the Large Helical Device (LHD) for understanding energetic ion confinement. The advantages of the LaBr3(Ce) scintillator are relatively sensitive to gamma rays due to its relatively heavy weight density of 5.3 g/cc, high counting operation because of a relatively short pulse width of ∼100 ns, and relatively better energy resolution of ∼3%. The gamma ray diagnostic was installed at the outboard side of LHD. The radiation shielding for the LaBr3(Ce) detector was designed to avoid unwanted signals due to stray neutrons and gamma rays using the three-dimensional radiation transport calculation MCNP6. In-situ energy calibration of the LaBr3(Ce) detector was performed using 60Co and 137Cs gamma ray sources. We surveyed a neutron effect on the LaBr3(Ce) detector in an electron-cyclotron-heated deuterium plasma discharge. The pulse counting rate of LaBr3(Ce) detector under the total neutron emission rate of 2×1011 n/s was 110 kcps. Therefore, the LaBr3(Ce) detector is expected to be utilized in most of ion cyclotron resonance frequency (ICRF) discharges, where the total neutron emission rate of ∼1011 n/s. We plan to measure the gamma ray spectrum in deuterium ICRF discharges.

Variability of Low-Z Inhomogeneity Correction in IMRT/SBRT: A Multi-Institutional Collaborative Study.

Dose-calculation algorithms are critical for radiation treatment outcomes that vary among treatment planning systems (TPS). Modern algorithms use sophisticated radiation transport calculation with detailed three-dimensional beam modeling to provide accurate doses, especially in heterogeneous medium and small fields used in IMRT/SBRT. While the dosimetric accuracy in heterogeneous mediums (lung) is qualitatively known, the accuracy is unknown. The aim of this work is to analyze the calculated dose in lung patients and compare the validity of dose-calculation algorithms by measurements in a low-Z phantom for two main classes of algorithms: type A (pencil beam) and type B (collapse cone). The CT scans with volumes (target and organs at risk, OARs) of a lung patient and a phantom build to replicate the human lung data were sent to nine institutions for planning. Doses at different depths and field sizes were measured in the phantom with and without inhomogeneity correction across multiple institutions to understand the impact of clinically used dose algorithms. Wide dosimetric variations were observed in target and OAR coverage in patient plans. The correction factor for collapsed cone algorithms was less than pencil beam algorithms in the small fields used in SBRT. The pencil beam showed ≈70% variations between measured and calculated correction factors for various field sizes and depths. For large field sizes the trends of both types of algorithms were similar. The differences in measured versus calculated dose for type-B algorithms were within ±10%. Significant variations in the target and OARs were observed among various TPS. The results suggest that the pencil beam algorithm does not provide an accurate dose and should not be considered with small fields (IMRT/SBRT). Type-B collapsed-cone algorithms provide better agreement with measurements, but still vary among various systems.

A sweep-based low-rank method for the discrete ordinate transport equation

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and computational costs. This work extends the low-rank scheme for the time-dependent radiation transport equation in 2-D and 3-D Cartesian geometries with discrete ordinates discretization in angle (SN method). The reduced system that evolves on a low-rank manifold is constructed via the “unconventional” basis update & Galerkin integrator to avoid a substep that is backward in time, which could be unstable for dissipative problems. The resulting system preserves the information on angular direction by applying separate low-rank decompositions in each octant where angular intensity has the same sign as the direction cosines. Then, transport sweeps and source iteration can efficiently solve this low-rank-SN system. The numerical results in 2-D and 3-D Cartesian geometries demonstrate that the low-rank solution requires less memory and computational time than solving the full rank equations using transport sweeps without losing accuracy.

PHSOR10 Presentation Time: 1:15 PM: Dosimetry Comparison Platform for Diffusing Alpha Emitters Radiation Therapy (DaRT) in Focal Prostate Brachytherapy

<h3>Purpose</h3> Dosimetry calculation for diffusing alpha emitters radiation therapy (DaRT) is challenging because it needs to combine both diffusion modelling and radiation transport computation. We have developed a 3D dosimetry platform to compare standard focal Ir-192 HDR and Ra-224 DaRT dosimetry for real prostate focal brachytherapy cases. <h3>Materials and Methods</h3> For DaRT dose calculation, diffusion length data on prostate tumors was based on autoradiography measurements performed 4-5 days post treatment. Leakage probability was inferred from blood and urine measurements from DaRT patients. The MIM Symphony software (MIM Software Inc, Cleveland, OH) was installed for dosimetry calculation for both standard Ir-192 source and DaRT needles (AphaTAU Medical, Jerusalem, Israel) for treatment planning. For testing purposes, the dose calculation was performed on 5 focal prostate brachytherapy cases using the standard focal dosimetry technique. <h3>Results</h3> For DaRT dose calculation, TG-43 parameters were calculated in prostate for permanent implantation of 3 microCi needles: anisotropy function, dose-rate constant, radial-dose function and geometry function. For standard dose calculation, parameters used in MIM Symphony were validated with our clinical Oncentra platform. For 5 patients, standard focal HDR brachytherapy dosimetry calculation was performed retroactively. Prescription doses were 13 or 15 Gy at the PTV. Doses to organs at risk were also evaluated: Urethra D10% (16-91%) and Rectum V75cc (0-0,6 cc), for example. <h3>Conclusions</h3> A 3D dose calculation technique was developed for DaRT based on diffusion modelling and radiation transport. With the use of this technique integrated into the MIM Symphony treatment planning software, we have developed a 3D dosimetry comparison platform for DaRT and standard (HDR or LDR) prostate brachytherapy. The advantage of DaRT for OAR protection can thus be retrospectively studied with this platform on a cohort of prostate patients from our clinic.

Built in importance estimation in forward Monte Carlo calculations

Recently, Monte Carlo code development has shown the benefits of using deterministic importance functions in radiation transport calculation; however, using Monte Carlo based importance function is less considered regarding the computational costs in this calculation.This paper offers a Monte Carlo based importance calculation method with the capability of application in forward Monte Carlo simulations. The technique uses the tracked particle’s history in the forward Monte Carlo calculation for the estimation of importance function. Moreover, the particle population, weight, and pathways can be considered for dynamic Monte Carlo calculation. The ability of the purposed method is shown by some examples in simple and complex geometries. The results show that the method can be used in the Monte Carlo code development that can benefit from a dynamic variance reduction technique in radiation transport calculations.

A new novel-1-step shutdown dose rate method combining benefits from the rigorous-2-step and direct-1-step methods

A new method for the calculation of Shutdown Dose Rates (SDDR) has been developed, the Novel-1-Step (N1S) method. The new method retains the benefits of only requiring a single radiation transport calculation, as in the use of the direct-1-step (D1S) method, while removing the need for pre-calculations to determine dominant nuclides and time correction factors. The N1S method uses a time dependent source and decay data for all nuclides. When reactions in the transport occur leading to unstable daughter nuclide, the correct contribution of photon radiation from all the decay products of a nuclide are calculated with no need for additional external activation calculations. Weights of these decay photons are calculated for each decay time of interest and are analytically determined based on the solutions to the Bateman equations.The N1S method has been implemented into MCNP and preliminary verification calculations performed. These calculations included the FNG ITER shutdown dose rate benchmark and the ITER SDDR cross comparison. For the FNG ITER SDDR benchmark the N1S method showed good agreement, within experimental error, for the first campaign apart from the first decay time where a C/E value of 1.34 was obtained. This overestimation was shown to be due to the decay of 64Cu inside the copper cup of the neutron generator. For the second campaign the N1S method showed an under prediction of up to 20% at short decay times and an over prediction up to 20% at longer decay times. These times are dominated by 56Mn and 58Co respectively and it is likely the difference is due to under and over predictions in the reaction rates leading to these nuclides. The ITER cross comparison showed good agreement between the N1S method and MCR2S (and by association other D1S and R2S codes). Differences seen in the results were shown to be due to difference in the calculated reaction rates using EAF2010, TENDL2019 and FENDL3.2.

A comprehensive evaluation of the thermal neutron detection efficiency by a single crystal CVD diamond detector with a LiF thermal neutron converter

Thermal neutron detection efficiency of the single crystal CVD diamond detector (SDD) equipping 1.9 μm-thick 6LiF thermal neutron converter, which induces the energetic ions through the 6Li(n,α)3H reaction, was evaluated comprehensively using a charge-integral based pulse shape discrimination (PSD) method and radiation transport calculation by PHITS. The PSD method applied in this work successfully separated the pulses induced by energetic tritons, alpha particles and other types of radiation. The detection efficiency of tritons was consistent with the radiation transport calculation, although that of alpha particles was lower than the estimation. The overall thermal neutron detection efficiency was obtained by summing detection efficiencies of tritons and alpha particles. Approximately 29% of 6Li(n,α)3H reaction occurred in an effective 1.9 μm-thick 6LiF thermal neutron converter could be detectable as the pulses of tritons (∼ 73%) and alpha particles (23%).

Simulation model criteria for a synchrotron radiation based MBRS/MRT clinical facility

MicroBeam Radiosurgery (MBRS, also referred to as Microbeam Radiation Therapy, MRT) is a potential clinical technique for the treatment of solid tumors. MBRS utilizes a series of narrow 30 to 50μm beams of ultra-high, lethal dose synchrotron x-ray radiation (peaks) separated by relatively wide spaces of no radiation (valleys) with spacings of 200 to 400μm center-to-center. It has been observed that healthy small animal tissue, including neurologic tissue (brain and spinal cord), can recover quickly, but solid tumors take a prolonged time of many months to regrow. This vast difference in recovery period is the basis for the therapeutic effect of MBRS on tumors. The interactions of X rays and tissue cells in alignment with the microbeams cause some deposited dose to be delivered to the tissue between the peak region of the microbeams and spill into the valley regions. It is generally believed that the dose delivered between the microbeam peak regions must be maintained at a low level to maximize the efficacy of MBRS. To date the most widely used criterion for the efficacy of MBRS is known as the Peak-to-Valley Dose Ratio (PVDR). This ratio depends on the geometry of the system along with the X-ray spectra. As most of the experimental work to date has used polychromatic microbeams of X rays, the PVDR will change with the energy range and spectrum. We are reporting novel investigations and present data suggesting considerations additional to the PVDR are needed for the design of a human clinical facility. In this paper we studied X-ray interactions in simulated human biologic material (Water - H2O) using the MCNP6 radiation transport computer code. The new slit geometry dependent information includes: (1) rounding of peak shape; (2) decrease of the maximum peak height with decreasing peak slit width; (3) qualitative and quantitative changes to the “skirt” radiation dose delivered in the valley regions adjacent to the peak regions. All these effects were highly dependent on incident X-ray energy because of the transition of the dominant X-ray interaction from the photo-electric effect to atomic Compton scattering with increasing energy in the 50 to 300 keV range. Changes in the radiation dose distributions, as a function of X-ray energy, delivered to both the peak and valley regions after the X-ray interactions were investigated in detail. Insights from understanding how the dose is delivered in the valley regions have implications for the calculations of the clinical radiation dose planning. Accurate dose distribution calculations are necessary in human clinical treatment since it is anticipated that most patients will have received prior radiation therapy treatments that need to be considered in microbeam dose planning so that radiation side-effects and toxicity are accounted for and minimized.This work suggests an X-ray energy range of 130–250 keV is the most appropriate range for a human clinical facility. Using the results of this work, the authors suggest that the PVDR may not be the only criteria one should consider for determining the energy range needed for a human clinical facility; analysis of the data presented demonstrates the benefit of also using the full width at 10% maximum of the distribution.

Fitting XMM-Newton observations of the AXP 1RXS J170849.0−400910 with four magnetar surface emission models, and predictions for X-ray polarization observations with IXPE

Context. Phase-resolved spectral and spectropolarimetric X-ray observations of magnetars present us with the opportunity to test models of the origin of the X-ray emission from these objects, and to constrain the properties of the neutron star surface and atmosphere. Aims. Our first aim is to use archival XMM-Newton observations of the magnetar 1RXS J170849.0−400910 to ascertain how well four emission models describe the phase-resolved XMM-Newton energy spectra. Our second aim is to evaluate the scientific potential of future spectropolarimetric observations of 1RXS J170849.0−400910 with the Imaging X-ray Polarimetry Explorer (IXPE) scheduled for launch in late 2021. The most salient questions are whether IXPE is able to distinguish between the different emission models, and whether IXPE can unambiguously detect the signatures of quantum electrodynamics (QED) effects in strong magnetic fields. Methods. We used numerical radiation transport calculations for a large number of different system parameters to predict the X-ray flux and polarization energy spectra of the source 1RXS J170849.0−400910. Based on the numerical results, we developed a new model to fit phase-resolved and phase-averaged X-ray spectral (i.e., XMM-Newton and IXPE) and spectropolarimetric (IXPE) data. In order to test the sensitivity of IXPE to strong-field QED effects, we fit a simulated IXPE observation with two versions of the model, i.e., with and without QED effects accounted for. Results. The fixed-ions condensed surface model gives the best description of the phase-resolved XMM-Newton spectra, followed by the blackbody and free-ions condensed surface models. The magnetized atmosphere model gives a poor description of the data and seems to be largely excluded. Simulations show that the IXPE observations of sources such as 1RXS J170849.0−400910 will allow us to cleanly distinguish between high-polarization (blackbody, magnetized atmosphere) and low-polarization (condensed surface) models. If the blackbody or magnetized atmosphere models apply, IXPE can easily prove QED effects based on ∼200 ksec observations as studied here; longer IXPE observation times will be needed for a clear detection in the case of the condensed surface models. Conclusions. The XMM-Newton data have such a good signal-to-noise ratio that they reveal some limitations of the theoretical models. Notwithstanding this caveat, the fits clearly favor the fixed-ions condensed surface and blackbody models over the free-ions condensed surface and magnetized atmosphere models. The IXPE polarization information will greatly help us to figure out how to improve the models. The first detection of strong-field QED effects in the signal from astrophysical sources seems possible if an adequate amount of time is dedicated to the observations.

Shielding conceptual designs of ITER TCP ports to protect electronics

Critical electronics of ITER Tokamak, hosted in the shielded corners (SC) of the Tokamak Building (B11), must operate under acceptable neutronic flux conditions (≤10 n·cm−2·s − 1) to minimize single event effects. During machine operation and at lower level (B1), both the Torus Cryopumps (TCP) ports location within B11 and their pumping efficiency constraints are factors contributing to the radiation environment in the SC. Although previous studies have addressed the transmission of radiation out the vessel of TCP ports, none of them have assessed the impact of such radiation beyond the Port Cell. In this work, different TCP shielding configurations were evaluated at B1 level of B11 due to plasma neutrons emerging from the six TCP ports only. MCNP and dedicated computational tools were used to perform the radiation transport calculations. Albeit being a partial study, the examination of the compatibility between the TCP plasma neutron flux and the electronics limit in the SC has been addressed, while considering the combined effect of the shielding design and the building walls, lintels and doors in the results. We present a combined shielding case that reduces the neutron flux to a range of 1.3–9.3 n·cm−2·s − 1 depending on the location, which is compatible with the limit while respecting pumping efficiency and assembly difficulty constraints.

A Sweep-Based Low-Rank Method for the Discrete Ordinate Transport Equation

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and computational costs. This work extends the low-rank scheme for the time-dependent radiation transport equation in 2-D and 3-D Cartesian geometries with discrete ordinates discretization in angle (SN method). The reduced system that evolves on a low-rank manifold is constructed via an unconventional basis update and Galerkin integrator to avoid a substep that is backward in time, which could be unstable for dissipative problems. The resulting system preserves the information on angular direction by applying separate low-rank decompositions in each octant where angular intensity has the same sign as the direction cosines. Then, transport sweeps and source iteration can efficiently solve this low-rank-SN system. The numerical results in 2-D and 3-D Cartesian geometries demonstrate that the low-rank solution requires less memory and computational time than solving the full rank equations using transport sweeps without losing accuracy.