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Shells, orbit bifurcations, and symmetry restorations in Fermi systems

The periodic-orbit theory based on the improved stationary-phase method within the phase-space path integral approach is presented for the semiclassical description of the nuclear shell structure, concerning themain topics of the fruitful activity ofV.G. Soloviev. We apply this theory to study bifurcations and symmetry breaking phenomena in a radial power-law potential which is close to the realistic Woods–Saxon one up to about the Fermi energy. Using the realistic parametrization of nuclear shapes we explain the origin of the double-humped fission barrier and the asymmetry in the fission isomer shapes by the bifurcations of periodic orbits. The semiclassical origin of the oblate–prolate shape asymmetry and tetrahedral shapes is also suggested within the improved periodic-orbit approach. The enhancement of shell structures at some surface diffuseness and deformation parameters of such shapes are explained by existence of the simple local bifurcations and new non-local bridge-orbit bifurcations in integrable and partially integrable Fermi-systems. We obtained good agreement between the semiclassical and quantum shell-structure components of the level density and energy for several surface diffuseness and deformation parameters of the potentials, including their symmetry breaking and bifurcation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Shock revival in core-collapse supernovae: A phase-diagram analysis

We examine the conditions for the revival of the stalled accretion shock in core-collapse supernovae, in the context of the neutrino heating mechanism. We combine one-dimensional simulations of the shock revival process with a derivation of a quasi-stationary approximation, which is both accurate and efficient in predicting the flow. In particular, this approach is used to explore how the evolution of the accretion shock depends on the shock radius, R{sub S}, and velocity, V{sub S} (in addition to other global properties of the system). We do so through a phase-space analysis of the shock acceleration, a{sub S}, in the R{sub S}--V{sub S} plane, shown to provide quantitative insights into the initiation and nature of runaway expansion. In the particular case of an initially stationary (V{sub S}=0, a{sub S}=0) profile, the prospects for an explosion can be assessed by the initial signs of the partial derivatives of the shock acceleration, in analogy to a linear damped/anti-damped oscillator. If ∂a{sub S}/∂R{sub S}<0 and ∂a{sub S}/∂V{sub S}>0, runaway will likely occur after several oscillations, while if ∂a{sub S}/∂R{sub S}>0, runaway expansion will commence in a non-oscillatory fashion. These two modes of runaway correspond to low and high mass accretion rates, respectively. We also use the quasi-stationary approximation to assess the advection-to-heating timescale ratio in the gain region, often used as an explosion proxy. Indeed, this ratio does tend to ∼1 in conjunction with runaway conditions, but neither this unit value nor the specific choice of the gain region as a point of reference appear to be unique in this regard.

79 ASTRONOMY AND ASTROPHYSICS↗

The shape of the inner Milky Way halo from observations of the Pal 5 and GD-1 stellar streams

We constrain the shape of the Milky Way’s halo by dynamical modeling of the observed phase-space tracks of the Pal 5 and GD–1 tidal streams. We find that the only information about the potential gleaned from the tracks of these streams are precise measurements of the shape of the gravitational potential—the ratio of vertical to radial acceleration—at the location of the streams, with weaker constraints on the radial and vertical accelerations separately. The latter will improve significantly with precise proper-motion measurements from Gaia. We measure that the overall potential flattening is 0.95 ± 0.04 at the location of GD–1 ([R,Z]≈[12.5,6.7] kpc) and 0.94 ± 0.05 at the position of Pal 5 ([R,Z]≈[8.4,16.8] kpc). Combined with constraints on the force field near the Galactic disk, we determine that the axis ratio of the dark-matter halo’s density distribution is 1.05 ± 0.14 within the inner 20 kpc, with a hint that the halo becomes more flattened near the edge of this volume. The halo mass within 20 kpc is (1.1±0.1)×10{sup 11} M{sub ⊙}. A dark-matter halo this close to spherical is in tension with the predictions from numerical simulations of the formation of dark-matter halos.

79 ASTRONOMY AND ASTROPHYSICS↗

Doping Effect of Fe Ions on the Structural, Electrical, and Magnetic Properties of SrTiO{sub 3} Nanoceramic Matrix

In the present investigation, strontium titanate nanoceramic was synthesized by incorporating iron (Fe) ion with general formula SrTi{sub 1−x}Fe{sub x}O{sub 3} (x = 0.0, 0.1, 0.2, and 0.4) using sol-gel autocombustion method. The effect of Fe ions on the structural, morphological, electrical, dielectric, and magnetic properties of the prepared matrix has been investigated by various characterization techniques with the appropriate formulation. The structural properties such as phase space, crystallite size (D), and lattice parameter (a) of prepared matrix are calculated by X-ray diffraction (XRD) technique. The functional groups were analyzed by Fourier transform infrared spectroscopy (FT-IR). The surface morphology of the prepared nanoceramic matrix has been determined by using field emission scanning electron microscopy (FE-SEM) analysis. Calculation of average particle size and diffraction patterns was confirmed by using images from transmission electron microscopy (TEM) and selected area electron diffraction pattern (SAED), respectively. An energy dispersive spectrum analysis (EDS) confirmed the compositional stoichiometry in the investigated matrix. Electrical conductivity increased the prepared sample due to the increasing in the Fe concentration and temperature. The dielectric parameters in the frequency range of 30 Hz to 1 MHz were found higher at lower frequencies. The pure SrTiO{sub 3} matrix shows a paramagnetic nature at room temperature, but for a higher concentration of Fe doping was used to observe the weak ferromagnetic nature. Therefore, due to Fe ion concentration, the properties of the prepared matrix have been completely varied and enhancement in the magnetic properties was observed.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

MCNP 6.2.0 Delayed-Particle Production Improvements

Development began on a delayed-particle physics package for the Monte Carlo Radiation transport code MCNPX in 2004 incorporating the CINDER90 depletion code and delayed particle libraries. When MCNP5 was merged with MCNPX to form MCNP6 in 2010, this delayed-particle capability was passed on and has been continuously improved in subsequent versions of MCNP6. Today, the delayed-particle feature in MCNP6 allows for the production of delayed neutrons, gammas, betas, and alpha particles. Future development includes the addition of delayed-positron production in the next release of MCNP6. Delayed particles can be sampled with MCNP using the ACT card in conjunction with the FISSION and NONFISS keywords. The user can specify one or more of the four available delayed-particle types mentioned above on one or both of the FISSION and NONFISS keywords. If a delayed-particle type is selected on the FISSION keyword, then delayed production of that particle from fission products and their progeny will be produced. Likewise, if a delayed-particle type is selected on the NONFISS keyword then delayed production of that particle from non-fission interactions and spontaneous decay will be produced. In some cases, the sheer number of delayed particles that can be produced from nuclear reactions and spontaneous decay (i.e. hundreds of delayed gamma lines when spontaneous fission is possible) can make it difficult to achieve converged solutions in an efficient and timely manner. Truncation methods are the simplest form of variance reduction and can be used to decrease convergence times by limiting calculations to the phase space of interest. This paper introduces several such truncation methods that allow the user to restrict the number of possible delayed particles available for sampling to only those of interest in the problem. It is important to stress that the use of any truncation method should be verified by first assessing the impact of the truncated particles (i.e. by disabling the truncation) for one or more baseline cases. In addition to these new methods, a new delayed-gamma sampling algorithm implemented in MCNP 6.2.0 is introduced. Comparisons to ENDF data and analytical benchmarking with the new algorithm show a substantial improvement in accuracy over previous versions. New improvements to the delayed-particle capability have been added to MCNP 6.2.0. These improvements include an updated treatment of the THRESH keyword which omits delayed-particle lines below a set amplitude, and addition of the PECUT and HLCUT keywords which allow the user to truncate delayed-particles lines based on energy and half-life, respectively. The delayed-gamma sampling algorithm has also been improved to allow exact energy sampling. Comparisons of MCNP calculations directly to ENDF data and analytical benchmarks have verified the significant improvement in the new delayed gamma sampling algorithm. (authors)

97 MATHEMATICS AND COMPUTING↗

SU-E-T-358: Monte Carlo Dose Calculation of Small Field Electron Beams

Purpose: Dynamic radiotherapy involving electron beams such as Dynamic Electron Arc Radiotherapy (DEAR) requires accurate dose modelling of small field sizes, similar to the requirement of IMRT field on the small photon field. The current commercial electron Monte Carlo algorithms such as eMC v11 in Eclipse were developed for standard field sizes and do not support the planning of dynamic therapy yet. The purpose of this study is to develop a method to accurately model small field electron beam dosimetry using Monte Carlo simulations. Methods: Comparison between eMC, phantom measurements (diode), and Monte Carlo (MC) simulations (BEAMnrc/DOSYZnrc) were performed for a Varian TrueBeam linac. MC simulations utilized Varian TrueBeam phase space files which had been validated in another study. Static single small field was assessed by comparing dose distributions in water for a 16 MeV beam for circular (2 cm diameter) and rectangular (1×10 cm{sup 2}) cut-out. MC was performed with a resolution of 2.5×2.5×2 mm{sup 2} and statistical uncertainty < 4%. The dose distribution was averaged over adjacent bins to improve precision. Depth dose and orthogonal profiles were evaluated. Results: Small field PDDs differ from those with standard cones. For both circular and rectangular cutouts, the difference in range R8 0-R1 0 is less than 2 mm and in dose within 2%. For the orthogonal profiles, field size and penumbra differences were within 1 mm at depth of maximum dose. The eMC displayed a distinctive “step” in the out-field dose profile in disagreement with both measurement and MC results and needs further investigation. Conclusion: MC was able to characterize the small field dosimetry with good agreement with the measurement data, and thus offers the opportunity for treatment planning of dynamic radiotherapy. Analyses for all other electron energies and cut-out sizes are under way and results will be included in the presentation.

07 ISOTOPE AND RADIATION SOURCES↗

SU-E-T-349: Verification of a Monte Carlo Simulation Tool as a Second Check for TomoTherapy Treatment Planning

Purpose: To verify a virtual source model used in Monte Carlo (MC) TomoTherapy simulations and to provide a tool for the dose distribution second check for TomoTherapy treatment planning. Methods: Published studies adopted the full MC model to simulate helical TomoTherapy which use phase space files (PSFs) at different scoring planes to facilitate patient dose calculations. We have developed a simple virtual source model (VSM) based on the commissioning data of helical TomoTherapy unit which can be exported from the treatment planning station (TPS). To calculate the patient dose distribution, TPS-generated sinograms are extracted from archived patient XML files and fluence maps are created by incorporating the openclose leaf time with leaf filter, jaw penumbra, and leaf latency. The VSM has been validated for various geometrical set-ups including open fields, heterogeneous media and clinical DQA cases. Results: Good agreement was obtained between our VSM and a published full MC model for the test case of heterogeneous media. For the complex clinical head and neck (HN) case, the MC simulation of the DQA plan agreed with the film measurement with 98% of planar dose pixels passing the 2%/2 mm gamma value test. For the patient treatment plan itself, the MC simulation showed comparable DVHs for the planning target volumes (PTVs) and organs-at-risk (OARs). Deviations observed were consistent with literature. Conclusion: The proposed VSM can be used in the MC method to accurately simulate the patient dose distributions for helical TomoTherapy.

60 APPLIED LIFE SCIENCES↗

SU-E-T-424: Dosimetric Verification of Modulated Electron Radiation Therapy Delivered Using An Electron Specific Multileaf Collimator for Treatment of Scalp Cases

Purpose: Modulated electron radiotherapy (MERT) has the potential to achieve better treatment outcome for shallow tumors such as those of breast and scalp. In a separate study with scalp lesions, MERT was compared to volumetric modulated arc therapy. Our results showed a reduction in the dose reaching the brain with MERT. However dose calculation accuracy and delivery efficiency challenges remain. Thus in the current study we proceed to add more cases to demonstrate MERT beneficial outcome and its delivery accuracy using an electron specific multileaf collimator (eMLC). Methods: We have used the MCBEAM code for treatment head simulation and for generating phase space files to be used as radiation source input for our Monte Carlo based treatment planning system (MC TPS). MCPLAN code is used for calculation of patient specific dose deposition coefficient and for final MERT plan dose calculation. An in-house developed optimization code is used for the optimization process. MERT plans were generated for real patients and head and neck phantom. Film was used for dosimetric verification. The film was cut following the contour of the curved phantom surface and then sealed with black masking tape. In the measurement, the sealed film packet was sandwiched between two adjacent slabs of the head and neck phantom. The measured 2D dose distribution was then compared with calculations. Results: The eMLC allows effective treatment of scalps with multi-lesions spreading around the patient head, which was usually difficult to plan or very time consuming with conventional applicators. MERT continues to show better reduction in the brain dose. The dosimetric measurements showed slight discrepancy, which was attributed to the film setup. Conclusion: MERT can improve treatment plan quality for patients with scalp cancers. Our in-house MC TPS is capable of performing treatment planning and accurate dose calculation for MERT using the eMLC.

60 APPLIED LIFE SCIENCES↗

Stochastic Averaging Principle for Spatial Birth-and-Death Evolutions in the Continuum

We study a spatial birth-and-death process on the phase space of locally finite configurations Γ{sup +}×Γ{sup −} over ℝ{sup d}. Dynamics is described by an non-equilibrium evolution of states obtained from the Fokker-Planck equation and associated with the Markov operator L{sup +}(γ{sup −})+(1/ε)L{sup −}, ε>0. Here L{sup −} describes the environment process on Γ{sup −} and L{sup +}(γ{sup −}) describes the system process on Γ{sup +}, where γ{sup −} indicates that the corresponding birth-and-death rates depend on another locally finite configuration γ{sup −}∈Γ{sup −}. We prove that, for a certain class of birth-and-death rates, the corresponding Fokker-Planck equation is well-posed, i.e. there exists a unique evolution of states μ{sub t}{sup ε} on Γ{sup +}×Γ{sup −}. Moreover, we give a sufficient condition such that the environment is ergodic with exponential rate. Let μ{sub inv} be the invariant measure for the environment process on Γ{sup −}. In the main part of this work we establish the stochastic averaging principle, i.e. we prove that the marginal of μ{sub t}{sup ε} onto Γ{sup +} converges weakly to an evolution of states on Γ{sup +} associated with the averaged Markov birth-and-death operator L̄=∫{sub Γ{sup −}}L{sup +}(γ{sup −})dμ{sub inv}(γ{sup −}).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Properties of galactic dark matter: Constraints from astronomical observations

The distributions of normal matter and of dark matter in the Galaxy are coupled to each other as they both move in the common gravitational potential. In order to fully exploit this interplay and to derive the various properties of dark matter relevant to their direct and indirect detection, we have comprehensively reviewed the astronomical observations of the spatial and velocity distributions of the components of normal matter. We then postulate that the phase-space distribution of dark matter follows a lowered-isothermal form and self-consistently solve Poisson's equation to construct several models for the spatial and velocity distributions of dark matter. In this paper, we compute the total gravitational potential of the normal and dark matter components and investigate their consistency with current observations of the rotation curve of the Galaxy and of the spatial and velocity distributions of blue horizontal-branch and blue straggler stars. Even with this demand of consistency, a large number of models with a range of parameters characterizing the dark matter distribution remain. We find that the best choice of parameters, within the range of allowed values for the surface density of the disk 55 M {sub ☉} pc{sup –2}, are the following: the dark matter density at the Galactic center ρ{sub DM,} {sub c} ≈ 100-250 GeV cm{sup –3}, the local dark matter density ρ{sub DM}(R {sub 0}) ≈ 0.56-0.72 GeV cm{sup –3}, and the rms speed of dark matter particles 〈v{sub DM}{sup 2}(R{sub 0})〉{sup 1/2}≈490−−550 km s{sup –1}. We also discuss possible astronomical observations that may further limit the range of the allowed models. The predictions of the allowed models for direct and indirect detection will be discussed separately in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗

Extragalactic synchrotron transients in the era of wide-field radio surveys. I. Detection rates and light curve characteristics

The impending era of wide-field radio surveys has the potential to revolutionize our understanding of astrophysical transients. Here we evaluate the prospects of a wide range of planned and hypothetical radio surveys using the properties and volumetric rates of known and hypothetical classes of extragalactic synchrotron radio transients (e.g., on-axis and off-axis gamma-ray bursts (GRBs), supernovae, tidal disruption events, compact object mergers). Utilizing these sources and physically motivated considerations we assess the allowed phase space of radio luminosity and peak timescale for extragalactic transients. We also include for the first time effects such as redshift evolution of the rates, K-corrections, and non-Euclidean luminosity distance, which affect the detection rates of the most sensitive surveys. The number of detected events is calculated by means of a Monte Carlo method, using the various survey properties (depth, cadence, area) and realistic detection criteria that include a cut on the minimum variability of the transients during the survey and an assessment of host galaxy contamination. We find that near-term GHz frequency surveys (ASKAP/VAST, Very Large Array Sky Survey) will detect few events: ≲30−50 on- and off-axis long GRBs (LGRBs) and off-axis tidal disruption events, and ∼50−100 neutron star binary mergers if ∼0.5% of the mergers result in a stable millisecond magnetar. Low-frequency surveys (e.g., LOFAR) are unlikely to detect any transients, while a hypothetical large-scale mm survey may detect ∼40 on-axis LGRBs. On the other hand, we find that SKA1 surveys at ∼0.1−1 GHz have the potential to uncover thousands of transients, mainly on-axis and off-axis LGRBs, on-axis short GRBs, off-axis TDEs, and neutron star binary mergers with magnetar remnants.

79 ASTRONOMY AND ASTROPHYSICS↗

Integrated system modeling analysis of a cryogenic multi-cell deflecting-mode cavity resonator

A deflecting mode cavity is the integral element for six-dimensional phase-space beam control in bunch compressors and emittance transformers at high energy beam test facilities. RF performance of a high-Q device is, however, highly sensitive to operational conditions, in particular in a cryo-cooling environment. Using analytic calculations and RF simulations, we examined cavity parameters and deflecting characteristics of TM{sub 110,π} mode of a 5 cell resonator in a liquid nitrogen cryostat, which has long been used at the Fermilab A0 Photoinjector (A0PI). The sensitivity analysis indicated that the cavity could lose 30%–40% of deflecting force due to defective input power coupling accompanying non-uniform field distribution across the cells with 40 ∼ 50 MeV electron beam and 70–80 kW klystron power. Vacuum-cryomodules of the 5 cell cavity are planned to be installed at the Fermilab Advanced Superconducting Test Accelerator facility. Comprehensive modeling analysis integrated with multi-physics simulation tools showed that RF loading of 1 ms can cause a ∼5 K maximum temperature increase, corresponding to a ∼4.3 μm/ms deformation and a 1.32 MHz/K maximum frequency shift. The integrated system modeling analysis will improve design process of a high-Q cavity with more accurate prediction of cryogenic RF performance under a high power pulse operation.

43 PARTICLE ACCELERATORS↗

SU-G-BRC-10: Feasibility of a Web-Based Monte Carlo Simulation Tool for Dynamic Electron Arc Radiotherapy (DEAR)

Purpose: DEAR is a radiation therapy technique utilizing synchronized motion of gantry and couch during delivery to optimize dose distribution homogeneity and penumbra for treatment of superficial disease. Dose calculation for DEAR is not yet supported by commercial TPSs. The purpose of this study is to demonstrate the feasibility of using a web-based Monte Carlo (MC) simulation tool (VirtuaLinac) to calculate dose distributions for a DEAR delivery. Methods: MC simulations were run through VirtuaLinac, which is based on the GEANT4 platform. VirtuaLinac utilizes detailed linac head geometry and material models, validated phase space files, and a voxelized phantom. The input was expanded to include an XML file for simulation of varying mechanical axes as a function of MU. A DEAR XML plan was generated and used in the MC simulation and delivered on a TrueBeam in Developer Mode. Radiographic film wrapped on a cylindrical phantom (12.5 cm radius) measured dose at a depth of 1.5 cm and compared to the simulation results. Results: A DEAR plan was simulated using an energy of 6 MeV and a 3×10 cm{sup 2} cut-out in a 15×15 cm{sup 2} applicator for a delivery of a 90° arc. The resulting data were found to provide qualitative and quantitative evidence that the simulation platform could be used as the basis for DEAR dose calculations. The resulting unwrapped 2D dose distributions agreed well in the cross-plane direction along the arc, with field sizes of 18.4 and 18.2 cm and penumbrae of 1.9 and 2.0 cm for measurements and simulations, respectively. Conclusion: Preliminary feasibility of a DEAR delivery using a web-based MC simulation platform has been demonstrated. This tool will benefit treatment planning for DEAR as a benchmark for developing other model based algorithms, allowing efficient optimization of trajectories, and quality assurance of plans without the need for extensive measurements.

60 APPLIED LIFE SCIENCES↗

ON GALACTIC DENSITY MODELING IN THE PRESENCE OF DUST EXTINCTION

Inferences about the spatial density or phase-space structure of stellar populations in the Milky Way require a precise determination of the effective survey volume. The volume observed by surveys such as Gaia or near-infrared spectroscopic surveys, which have good coverage of the Galactic midplane region, is highly complex because of the abundant small-scale structure in the three-dimensional interstellar dust extinction. We introduce a novel framework for analyzing the importance of small-scale structure in the extinction. This formalism demonstrates that the spatially complex effect of extinction on the selection function of a pencil-beam or contiguous sky survey is equivalent to a low-pass filtering of the extinction-affected selection function with the smooth density field. We find that the angular resolution of current 3D extinction maps is sufficient for analyzing Gaia sub-samples of millions of stars. However, the current distance resolution is inadequate and needs to be improved by an order of magnitude, especially in the inner Galaxy. We also present a practical and efficient method for properly taking the effect of extinction into account in analyses of Galactic structure through an effective selection function. We illustrate its use with the selection function of red-clump stars in APOGEE using and comparing a variety of current 3D extinction maps.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-E-T-313: Dosimetric Deviation of Misaligned Beams for a 6 MV Photon Linear Accelerator Using Monte Carlo Simulations

Purpose: To quantify the dosimetric variations of misaligned beams for a linear accelerator by using Monte Carlo (MC) simulations. Method and Materials: Misaligned beams of a Varian 21EX Clinac were simulated to estimate the dosimetric effects. All the linac head components for a 6 MV photon beam were implemented in BEAMnrc/EGSnrc system. For incident electron beam parameters, 6 MeV with 0.1 cm full-width-half-max Gaussian beam was used. A phase space file was obtained below the jaw per each misalignment condition of the incident electron beam: (1) The incident electron beams were tilted by 0.5, 1.0 and 1.5 degrees on the x-axis from the central axis. (2) The center of the incident electron beam was off-axially moved toward +x-axis by 0.1, 0.2, and 0.3 cm away from the central axis. Lateral profiles for each misaligned beam condition were acquired at dmax = 1.5 cm and 10 cm depth in a rectangular water phantom. Beam flatness and symmetry were calculated by using the lateral profile data. Results: The lateral profiles were found to be skewed opposite to the angle of the incident beam for the tilted beams. For the displaced beams, similar skewed lateral profiles were obtained with small shifts of penumbra on the +x-axis. The variations of beam flatness were 3.89–11.18% and 4.12–42.57% for the tilted beam and the translated beam, respectively. The beam symmetry was separately found to be 2.95 −9.93% and 2.55–38.06% separately. It was found that the percent increase of the flatness and the symmetry values are approximated 2 to 3% per 0.5 degree tilt or per 1 mm displacement. Conclusion: This study quantified the dosimetric effects of misaligned beams using MC simulations. The results would be useful to understand the magnitude of the dosimetric deviations for the misaligned beams.

60 APPLIED LIFE SCIENCES↗

THE INNER STRUCTURE OF DWARF-SIZED HALOS IN WARM AND COLD DARK MATTER COSMOLOGIES

By means of N-body + hydrodynamic zoom-in simulations we study the evolution of the inner dark matter and stellar mass distributions of central dwarf galaxies formed in halos of virial masses M{sub v} = (2–3) × 10{sup 10} h{sup −1} M{sub ⊙} at z = 0, both in a warm dark matter (WDM) and cold dark matter (CDM) cosmology. The half-mode mass in the WDM power spectrum of our simulations is M{sub f} = 2 × 10{sup 10} h{sup −1} M{sub ⊙}. In the dark matter (DM) only simulations halo density profiles are well described by the Navarro–Frenk–White parametric fit in both cosmologies, though the WDM halos have concentrations lower by factors of 1.5–2.0 than their CDM counterparts. In the hydrodynamic simulations, the effects of baryons significantly flatten the inner density, velocity dispersion, and pseudo phase space density profiles of the WDM halos but not of the CDM ones. The density slope, measured at ≈0.02R{sub v}, α{sub 0.02}, becomes shallow in periods of 2–5 Gyr in the WDM runs. We explore whether this flattening process correlates with the global star formation (SF), M{sub s}/M{sub v} ratio, gas outflow, and internal specific angular momentum histories. We do not find any clear trends, but when α{sub 0.02} is shallower than −0.5, M{sub s}/M{sub v} is always between 0.25% and 1%. We conclude that the main reason for the formation of the shallow core is the presence of strong gas mass fluctuations inside the inner halo, which are a consequence of the feedback driven by a very bursty and sustained SF history in shallow gravitational potentials. Our WDM halos, which assemble late and are less concentrated than the CDM ones, obey these conditions. There are also (rare) CDM systems with extended mass assembly histories that obey these conditions and form shallow cores. The dynamical heating and expansion processes behind the DM core flattening apply also to the stars in such a way that the stellar age and metallicity gradients of the dwarfs are softened, their stellar half-mass radii strongly grow with time, and their central surface densities decrease.

79 ASTRONOMY AND ASTROPHYSICS↗

Higher-order massive neutrino perturbations in large-scale structure

We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is applicable also to a single warm dark matter species. In order to capture the suppressed growth of neutrino density perturbations on small scales, we account for the full momentum dependence of the phase space distribution using the Vlasov equation, and derive from it a formal closed-form nonlinear equation for the neutrino density. Using a systematic perturbative expansion of this equation we compute high-order corrections to the neutrino density contrast without the explicit need to track the perturbed neutrino momentum distribution. We calculate the leading-order total matter bispectrum for several neutrino masses. Using our result as a benchmark, we test the accuracy of the fluid approximation and a linear approximation used in perturbative and N-body analyses, as well as a new hybrid approach that combines the exact linear evolution with the nonlinear structure of the fluid equations. Aiming at ∼< 1% accuracy, we find that the total matter bispectrum with a low neutrino mass m = 0.046 eV can be reproduced by all but the fluid approximation, while for larger neutrino masses m=0.46 → 0.93 eV only the hybrid approach has the desired accuracy on a large range of scales. This result serves as a cautionary note that approximate nonlinear models of neutrino clustering that reproduce the gross features of some observables may not suffice for precision calculations, nor are they guaranteed to apply to other observables. All of the approximation schemes fail to reproduce the bispectrum of the neutrino density perturbations at better than 20% accuracy across all scales, indicating that an exact treatment of nonlinear neutrino perturbations is necessary.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-E-T-632: Preliminary Study On Treating Nose Skin Using Energy and Intensity Modulated Electron Beams with Monte Carlo Based Dose Calculations

Purpose: Uneven nose surfaces and air cavities underneath and the use of bolus present complexity and dose uncertainty when using a single electron energy beam to plan treatments of nose skin with a pencil beam-based planning system. This work demonstrates more accurate dose calculation and more optimal planning using energy and intensity modulated electron radiotherapy (MERT) delivered with a pMLC. Methods: An in-house developed Monte Carlo (MC)-based dose calculation/optimization planning system was employed for treatment planning. Phase space data (6, 9, 12 and 15 MeV) were used as an input source for MC dose calculations for the linac. To reduce the scatter-caused penumbra, a short SSD (61 cm) was used. Our previous work demonstrates good agreement in percentage depth dose and off-axis dose between calculations and film measurement for various field sizes. A MERT plan was generated for treating the nose skin using a patient geometry and a dose volume histogram (DVH) was obtained. The work also shows the comparison of 2D dose distributions between a clinically used conventional single electron energy plan and the MERT plan. Results: The MERT plan resulted in improved target dose coverage as compared to the conventional plan, which demonstrated a target dose deficit at the field edge. The conventional plan showed higher dose normal tissue irradiation underneath the nose skin while the MERT plan resulted in improved conformity and thus reduces normal tissue dose. Conclusion: This preliminary work illustrates that MC-based MERT planning is a promising technique in treating nose skin, not only providing more accurate dose calculation, but also offering an improved target dose coverage and conformity. In addition, this technique may eliminate the necessity of bolus, which often produces dose delivery uncertainty due to the air gaps that may exist between the bolus and skin.

62 RADIOLOGY AND NUCLEAR MEDICINE↗