Photon Phase Space Research Articles

UBES: Unified scatter correction using ultrafast Boltzmann equation solver for conebeam CT

A semi-analytical solution to the unified Boltzmann equation is constructed to exactly describe the scatter distribution on a flat-panel detector for high-quality conebeam CT (CBCT) imaging. The solver consists of three parts, including the phase space distribution estimator, the effective source constructor and the detector signal extractor. Instead of the tedious Monte Carlo solution, the derived Boltzmann equation solver achieves ultrafast computational capability for scatter signal estimation by combining direct analytical derivation and time-efficient one-dimensional numerical integration over the trajectory along each momentum of the photon phase space distribution. The execution of scatter estimation using the proposed ultrafast Boltzmann equation solver (UBES) for a single projection is finalized in around 0.4 seconds. We compare the performance of the proposed method with the state-of-the-art schemes, including a time-expensive Monte Carlo (MC) method and a conventional kernel-based algorithm using the same dataset, which is acquired from the CBCT scans of a head phantom and an abdominal patient. The evaluation results demonstrate that the proposed UBES method achieves comparable correction accuracy compared with the MC method, while exhibits significant improvements in image quality over learning and kernel-based methods. With the advantages of MC equivalent quality and superfast computational efficiency, the UBES method has the potential to become a standard solution to scatter correction in high-quality CBCT reconstruction.

Adiabatic axion-photon mixing near neutron stars

One of the promising new proposals to search for axions in astrophysical environments is to look for narrow radio lines produced from the resonant conversion of axion dark matter falling through the magnetospheres of neutron stars. For sufficiently strong magnetic fields, axion masses in the O(10 μeV) range, and axion-photon couplings gaγ≳10−12 GeV−1, the conversion can become hyperefficient, allowing axion-photon and photon-axion transitions to occur with O(1) probabilities. Despite the strong mixing between these particles, the observable radio flux emanating from the magnetosphere is expected to be heavily suppressed—this is a consequence of the fact that photons sourced by infalling axions have a high probability of converting back into axions before escaping the magnetosphere. In this work, we study the evolution of the axion and photon phase space near the surface of highly magnetized neutron stars in the adiabatic regime, quantifying for the first time the properties of the radio flux that arise at high axion-photon couplings. We show that previous attempts to mimic the scaling in this regime have been overly conservative in their treatment, and that the suppression can be largely circumvented for radio observations targeting neutron star populations. Published by the American Physical Society 2024

Application of Conditional Generative Adversarial Networks to Efficiently Generate Photon Phase Space in Medical Linear Accelerators of Different Primary Beam Parameters

Successful application of external photon beam therapy in oncology requires that the dose delivered by a medical linear accelerator and distributed within the patient’s body is accurately calculated. Monte Carlo simulation is currently the most accurate method for this purpose but is computationally too extensive for routine clinical application. A very elaborate and time-consuming part of such Monte Carlo simulation is generation of the full set (phase space) of ionizing radiation components (mainly photons) to be subsequently used in simulating dose delivery to the patient. We propose a method of generating phase spaces in medical linear accelerators through learning, by artificial intelligence models, the joint multidimensional probability density distribution of the photon properties (their location in space, energy, and momentum). The models are conditioned with respect to the parameters of the primary electron beam (unique to each medical accelerator), which, through Bremsstrahlung, generates the therapeutical beam of ionizing radiation. Two variants of conditional generative adversarial networks are chosen, trained, and compared. We also present the second-best type of deep learning architecture that we studied: a variational autoencoder. Differences between dose distributions obtained in a water phantom, in a test phantom, and in real patients using generative-adversarial-network-based and Monte-Carlo-based phase spaces are very close to each other, as indicated by the values of standard quality assurance tools of radiotherapy. Particle generation with generative adversarial networks is three orders of magnitude faster than with Monte Carlo. The proposed GAN model, together with our earlier machine-learning-based method of tuning the primary electron beam of an MC simulator, delivers a complete solution to the problem of tuning a Monte Carlo simulator against a physical medical accelerator.

Cosmological Parameters from Planck Data in SU(2)CMB, Their Local ΛCDM Values, and the Modified Photon Boltzmann Equation

AbstractA review of the spatially flat cosmological model SU(2)CMB, minimally induced by the postulate that the cosmic microwave background (CMB) is subject to an SU(2) rather than a U(1) gauge principle, is given. Cosmological parameter values, which are determined from the Planck CMB power spectra at small angular scales, are compared to their values in spatially flat ΛCDM from both local and global extractions. As a global model SU(2)CMB leans toward local ΛCDM cosmology and is in tension with some global ΛCDM parameter values. Spectral antiscreening / screening effects in SU(2)CMB radiance are presented within the Rayleigh– Jeans regime in dependence on temperature and frequency. Such radiance anomalies can cause CMB large‐angle anomalies. Therefore, it is pointed out how SU(2)CMB modifies the Boltzmann equation for the perturbations of the photon phase space distribution at low redshift and why this requires to the solve the ℓ‐hierarchy on a comoving momentum grid (q‐grid) for all z.

A phase space model of a Versa HD linear accelerator for application to Monte Carlo dose calculation in a real-time adaptive workflow.

PurposeThis study aims to develop and validate a simple geometric model of the accelerator head, from which a particle phase space can be calculated for application to fast Monte Carlo dose calculation in real‐time adaptive photon radiotherapy. With this objective in view, the study investigates whether the phase space model can facilitate dose calculations which are compatible with those of a commercial treatment planning system, for convenient interoperability.Materials and methodsA dual‐source model of the head of a Versa HD accelerator (Elekta AB, Stockholm, Sweden) was created. The model used parameters chosen to be compatible with those of 6‐MV flattened and 6‐MV flattening filter‐free photon beams in the RayStation treatment planning system (RaySearch Laboratories, Stockholm, Sweden). The phase space model was used to calculate a photon phase space for several treatment plans, and the resulting phase space was applied to the Dose Planning Method (DPM) Monte Carlo dose calculation algorithm. Simple fields and intensity‐modulated radiation therapy (IMRT) treatment plans for prostate and lung were calculated for benchmarking purposes and compared with the convolution‐superposition dose calculation within RayStation.ResultsFor simple square fields in a water phantom, the calculated dose distribution agrees to within ±2% with that from the commercial treatment planning system, except in the buildup region, where the DPM code does not model the electron contamination. For IMRT plans of prostate and lung, agreements of ±2% and ±6%, respectively, are found, with slightly larger differences in the high dose gradients.ConclusionsThe phase space model presented allows convenient calculation of a phase space for application to Monte Carlo dose calculation, with straightforward translation of beam parameters from the RayStation beam model. This provides a basis on which to develop dose calculation in a real‐time adaptive setting.

Analytic calculations of electron–nucleus bremsstrahlung cross sections above a few MeV including higher-order corrections and multiple scattering in the target

Calculations of the elementary process of electron–nucleus bremsstrahlung employing a partial–wave expansion of the initial and final electron wave functions are exact and offer results that match the experimental data, but they become impractical for increasingly higher electron energies, especially in some regions of the emitted photon phase space. Here we take the opposite approach and use analytic expressions based on the Olsen–Maximon–Wergeland additivity rule, valid above few MeV, to decouple the calculation of the screening and Coulomb corrections. The former is obtained from the first Born approximation, while the latter is evaluated within the formalism of the Furry–Sommerfeld–Maue wave functions using the leading–order expression by Elwert and Haug and the next–to–leading–order corrections by Roche, Ducos, and Proriol, which is presently the best way to calculate cross sections for electrons with energies in the range of hundreds of MeV. A detailed discussion of the approximations involved and an extensive comparison with experimental data have been published in previous works. Here we focus on the numerical procedures that have been developed and on the stringent cross checks that have been performed to ensure the accuracy of the results. Published benchmark calculations for bremsstrahlung in a pure Coulomb field, that stop at 100 keV, are extended here to 100 MeV by making available selected values that could be used by other independent researchers to validate their programs. We also discuss the numerical details of the procedure adopted to convolve the bremsstrahlung cross section with the impinging electron angular distribution due to multiple scattering in the target.

Evaluation of latent variances in Monte Carlo dose calculations with Varian TrueBeam photon phase-spaces used as a particle source

The purpose of this study was to evaluate the latent variance (LV) of Varian TrueBeam photon phase-space files (PSF) for open 10 × 10 cm2 and small stereotactic fields and estimate the number of phase spaces required to be summed up in order to maintain sub-percent LV in Monte Carlo (MC) dose calculations. BEAMnrc/DOSXYZnrc software was used to transport particles from Varian phase-space files (PSFA) through the secondary collimators. Transported particles were scored into another phase-space located under the jaws (PSFB), or transported further through the cone collimators and scored straight below, forming PSFC. Phase-space files (PSFB) were scored for 6 MV-FFF, 6 MV, 10 MV-FFF, 10 MV and 15 MV beams with 10 × 10 cm2 field size, and PSFC were scored for 6 MV beam under circular cones of 0.13, 0.25, 0.35, and 1 cm diameter. Both PSFB and PSFC were transported into a water phantom with particle recycling number ranging from 10 to 1000. For 10 × 10 cm2 fields 0.5 × 0.5 × 0.5 cm3 voxels were used to score the dose, whereas the dose was scored in 0.1 × 0.1 × 0.5 cm3 voxels for beams collimated with small cones. In addition, for small 0.25 cm diameter cone-collimated 6 MV beam, phantom voxel size varied as 0.02 × 0.02 × 0.5 cm3, 0.05 × 0.05 × 0.5 cm3 and 0.1 × 0.1 × 0.5 cm3. Dose variances were scored in all cases and LV evaluated as per Sempau et al. For the 10 × 10 cm2 fields calculated LVs were greatest at the phantom surface and decreased with depth until they reached a plateau at 5 cm depth. LVs were found to be 0.54%, 0.96%, 0.35%, 0.69% and 0.57% for the 6 MV-FFF, 6 MV, 10 MV-FFF, 10 MV and 15 MV energies, respectively at the depth of 10 cm. For the 6 MV phase-space collimated with cones of 0.13, 0.25, 0.35, 1.0 cm diameter, the LVs calculated at 1.5 cm depth were 75.6%, 25.4%, 17.6% and 8.0% respectively. Calculated LV for the 0.25 cm cone-collimated 6 MV beam were 61.2%, 40.7%, 22.5% in 0.02 × 0.02 × 0.5 cm3, 0.05 × 0.05 × 0.5 cm3 and 0.1 × 0.1 × 0.5 cm3 voxels respectively. In order to achieve sub-percent LV in open 10 × 10 cm2 field MC simulations a single PSF can be used, whereas for small SRS fields (0.13–1.0 cm) more PSFs (66–8 PSFs) would have to be summed.

Azimuthal distributions in radiative decay of a polarized τ lepton

Various distributions over the angles of the emitted photon, especially over the azimuthal angle, in the one-meson radiative decay of the polarized $\tau$ lepton, $\tau^-\to\pi^-\gamma\nu_{\tau}$, have been investigated. In connection with this, the photon phase space is discussed in more detail since in the case of the polarized $\tau$ lepton it is not trivial. The decay matrix element contains both the inner bremsstrahlung and the resonance (structural) contributions. The azimuthal dependence of some observables have been calculated. They are the asymmetry of the differential decay width caused by the $\tau$ lepton polarization, the Stokes parameters of the emitted photon itself and the correlation parameters describing the influence of $\tau$-lepton polarization on the photon Stokes parameters. The numerical estimation was done in the $\tau$ lepton rest frame for arbitrary direction of the $\tau$ lepton polarization 3-vector. The vector and axial-vector form factors describing the structure-dependent part of the decay amplitude are determined using the chiral effective theory with resonances (R$\chi$T). It was found that the features of the azimuthal distributions allows to separate various terms in the spin-dependent contribution. The so-called up-down and right-left asymmetries are also calculated.

Varian 2100C/D Clinac 18 MV photon phase space file characterization and modeling by using MCNP Code

Multiple points and a spatial mesh based surface source model (MPSMBSS) was generated for 18MV Varian 2100 C/D Clinac phase space file (PSF) and implemented in MCNP code. The generated source model (SM) was benchmarked against PSF and measurements. PDDs and profiles were calculated using the SM and original PSF for different field sizes from 5 × 5 to 20 × 20 cm2. Agreement was within 2% of the maximum dose at 100cm SSD for beam profiles at the depths of 4cm and 15cm with respect to the original PSF. Differences between measured and calculated points were less than 2% of the maximum dose or 2mm distance to agreement (DTA) at 100 cm SSD. Thus it can be concluded that the modified MCNP code can be used for radiotherapy calculations including multiple source model (MSM) and using the source biasing capability of MPSMBSS can increase the simulation speed up to 3600 for field sizes smaller than 5 × 5 cm2.

A simplified analytical dose calculation algorithm accounting for tissue heterogeneity for low-energy brachytherapy sources

The American Association of Physicists in Medicine Task Group No. 43 (AAPM TG-43) formalism is the standard for seeds brachytherapy dose calculation. But for breast seed implants, Monte Carlo simulations reveal large errors due to tissue heterogeneity. Since TG-43 includes several factors to account for source geometry, anisotropy and strength, we propose an additional correction factor, called the inhomogeneity correction factor (ICF), accounting for tissue heterogeneity for Pd-103 brachytherapy. This correction factor is calculated as a function of the media linear attenuation coefficient and mass energy absorption coefficient, and it is independent of the source internal structure. Ultimately the dose in heterogeneous media can be calculated as a product of dose in water as calculated by TG-43 protocol times the ICF. To validate the ICF methodology, dose absorbed in spherical phantoms with large tissue heterogeneities was compared using the TG-43 formalism corrected for heterogeneity versus Monte Carlo simulations. The agreement between Monte Carlo simulations and the ICF method remained within 5% in soft tissues up to several centimeters from a Pd-103 source. Compared to Monte Carlo, the ICF methods can easily be integrated into a clinical treatment planning system and it does not require the detailed internal structure of the source or the photon phase-space.

Beam stability at light sources (invited)

The level of photon beam stability required in an experiment to meet measurement resolution goals depends on the experiment-specific photon phase space acceptance and the sensitivity of measurement to electron beam motion within its six-dimensional phase space. Stability time scales range from hours to microseconds, depending on experiment sampling rate, data integration period, and scan duration. Meeting these requirements at third-generation storage ring light sources can imply micron and submicroradian electron orbit stability and energy (ΔE/E) oscillation amplitudes in the part-per-million range, presenting a formidable challenge for accelerator designers. Beam stability criteria, measures taken to meet them, and achievable levels of stability in present and future light sources, are reviewed.

ZFITTER v.6.21: A semi-analytical program for fermion pair production in e+e− annihilation

We describe ZFITTER, a Fortran program based on a semi-analytical approach to fermion pair production in e + e − annihilation at a wide range of centre-of-mass energies, including the PETRA, TRISTAN, LEP1/SLC, and LEP2 energies. A flexible treatment of complete O(α) QED corrections and of some higher order contributions is made possible with three calculational chains containing different realistic sets of restrictions in the photon phase space. Numerical integrations are at most one-dimensional. Complete O(α) weak loop corrections supplemented by selected higher-order terms may be included. The program calculates Δr, the Z width, differential cross-sections, total cross-sections, integrated forward–backward asymmetries, left–right asymmetries, and for τ pair production also final-state polarization effects. Various interfaces allow fits to be performed with different sets of free parameters.

DIRC – A particle identification system for BaBar

The Detection of Internally Reflected Cherenkov light (DIRC) is a novel type of Cherenkov imaging device that has been developed, built and installed as part of the BaBar detector at the asymmetric B-factory PEP-II at SLAC. The DIRC is based on total internal reflection of Cherenkov photons produced and guided within thin, rectangular quartz bars covering the barrel region of BaBar. The photon detector is an array of photomultiplier tubes covering the photon phase space at the backward end of the bars. In its first few months of operation the DIRC performance has been found to achieve the design requirements. This note presents results from cosmic-ray data and an analysis of the first beam collision runs.

Comparison of EGS4 and MCNP4b Monte Carlo codes for generation of photon phase space distributions for a Varian 2100C

Monte Carlo based dose calculation algorithms require input data or distributions describing the phase space of the photons and secondary electrons prior to the patient-dependent part of the beam-line geometry. The accuracy of the treatment plan itself is dependent upon the accuracy of this distribution. The purpose of this work is to compare phase space distributions (PSDs) generated with the MCNP4b and EGS4 Monte Carlo codes for the 6 and 18 MV photon modes of the Varian 2100C and determine if differences relevant to Monte Carlo based patient dose calculations exist. Calculations are performed with the same energy transport cut-off values. At 6 MV, target bremsstrahlung production for MCNP4b is approximately 10% less than for EGS4, while at 18 MV the difference is about 5%. These differences are due to the different bremsstrahlung cross sections used in the codes. Although the absolute bremsstrahlung production differs between MCNP4b and EGS4, normalized PSDs agree at the end of the patient-independent geometry (prior to the jaws), resulting in similar dose distributions in a homogeneous phantom. EGS4 and MCNP4b are equally suitable for the generation of PSDs for Monte Carlo based dose computations.

Correlated histogram representation of Monte Carlo derived medical accelerator photon-output phase space.

We present a method for condensing the photon energy and angular distributions obtained from Monte Carlo simulations of medical accelerators. This method represents the output as a series of correlated histograms and as such is well-suited for inclusion as the photon-source package for Monte Carlo codes used to determine the dose distributions in photon teletherapy. The method accounts for the isocenter-plane variations of the photon energy spectral distributions with increasing distance from the beam central axis for radiation produced in the bremsstrahlung target as well as for radiation scattered by the various treatment machine components within the accelerator head. Comparison of the isocenter energy fluence computed by this algorithm with that of the underlying full-physics Monte Carlo photon phase space indicates that energy fluence errors are less than 1% of the maximum energy fluence for a range of open-field sizes. Comparison of jaw-edge penumbrae shows that the angular distributions of the photons are accurately reproduced. The Monte Carlo sampling efficiency (the fraction of generated photons which clear the collimator jaws) of the algorithm is approximately 83% for an open 10x10 field, rising to approximately 96% for an open 40x40 field. Data file sizes for a typical medical accelerator, at a given energy, are approximately 150 kB, compared to the 1 GB size of the underlying full-physics phase space file.

W pair production in e+e- annihilation: Radiative corrections including hard bremsstrahlung.

A calculation of the hard bremsstrahlung process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}}\ensuremath{\gamma}$ is presented and combined with previous results for the electroweak radiative corrections to ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{W}^{+}{W}^{\ensuremath{-}}$ (including soft bremsstrahlung). The phase space integrations are performed by the Monte Carlo method which allows one to apply cuts in the photon phase space. Results are given for the total cross section (no cuts) as well as for cuts in the photon energy and the angle between the photon momentum and the beam axis. The full $O(\ensuremath{\alpha})$ calculation is improved by including the known leading logarithmic $O({\ensuremath{\alpha}}^{2})$ contributions. The dependence of the results on the renormalization scheme ($\ensuremath{\alpha}$ and ${G}_{\ensuremath{\mu}}$ scheme) is investigated.

Physical null zones and radiation representation

General conditions for reconstructing physical null radiation zones in single photon tree amplitudes are given. The systematic analysis has been carried out using invariant quantities. For arbitrary values of masses and charges these zones are always smaller than in the massless and equal charges case. As an application the radiative W boson decay into heavy quarks is studied. This process turns out be a rather sensitive test of the current quark masses m q( M W 2), as well as of the q qW, q q γ and W +W −γ vertices. This is to the presence of a null line in the photon phase space with a location which strongly depends on m q. A recently proposed radiation representation for single photon tree amplitudes is analyzed. Explicit examples are given for a number of cases including fermion and vector boson lines.

Analytic regularization and infra-red divergences

For the infra-red cancellation mechanism to work in the context of analytic regularization it is necessary to replace the virtual photon propagator (k2)-1 by - Gamma (z)(-k2)-z and the photon phase-space by the continuous mass distribution 2 pi integral d4k theta (ko) theta (k2)/ Gamma (1-z)(k2)z. The cancellation for charged-particle scattering in a weak external field is shown.

Hard-photon emission in e +e − reactions

The radiative corrections to lowest order for the reactions e +e − giving any final state f, different from e +e −, are calculated, taking into account the contributions coming from the photons emitted by the electrons. Then an application of these results to the process e +e − → π + π − is done in the experimental conditions of ACO. The difference with previous results arises from: (i) a rigorous calculation of Feynman diagrams without using the “quasi-réel” process approximation, (ii) the error in the Coulomb terms, and (iii) a precise evaluation of the photon phase space.