Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.Comment: 20 pages, 7 figure

Ultra-bright gamma-ray emission and dense positron production from two laser-driven colliding foils

Matter can be transferred into energy and the opposite transformation is also possible by use of high-power lasers. A laser pulse in plasma can convert its energy into γ-rays and then e −e + pairs via the multi-photon Breit-Wheeler process. Production of dense positrons at GeV energies is very challenging since extremely high laser intensity ∼ 1024 Wcm−2 is required. Here we propose an all-optical scheme for ultra-bright γ-ray emission and dense positron production with lasers at intensity of 1022−23 Wcm−2 . By irradiating two colliding elliptically-polarized lasers onto two diamondlike carbon foils, electrons in the focal region of one foil are rapidly accelerated by the laser radiation pressure and interact with the other intense laser pulse which penetrates through the second foil due to relativistically induced foil transparency. This symmetric configuration enables efficient Compton back-scattering and results in ultra-bright γ-photon emission with brightness of ∼ 1025 photons/s/mm2 /mrad2 /0.1%BW at 15 MeV and intensity of 5×1023 Wcm−2 . Our first three-dimensional simulation with quantum-electrodynamics incorporated shows that a GeV positron beam with density of 2.5×1022 cm−3 and flux of 1.6×1010/shot is achieved. Collective effects of the pair plasma may be also triggered, offering a window on investigating laboratory astrophysics at PW laser facilities

High-Energy Radiation and Pair Production by Coulomb Processes in Particle-In-Cell Simulations

We present a Monte Carlo implementation of the Bremsstrahlung, Bethe-Heitler and Coulomb Trident processes into the particle-in-cell (PIC) simulation framework. In order to address photon and electron-positron pair production in a wide range of physical conditions, we derive Bremsstrahlung and Bethe-Heitler cross sections taking account of screening effects in arbitrarily ionized plasmas. Our calculations are based on a simple model for the atomic Coulomb potential that describes shielding due to both bound electrons, free electrons and ions. We then describe a pairwise particle interaction algorithm suited to weighted PIC plasma simulations, for which we perform several validation tests. Finally, we carry out a parametric study of photon and pair production during high-energy electron transport through micrometric solid foils. Compared to the zero-dimensional model of J. Myatt et al. [Phys. Rev. E 76, 066409 (2009)], our integrated one-dimensional simulations pinpoint the importance of the electron energy losses resulting from the plasma expansion.Comment: 25 pages, 15 figure

Modelling the effects of the radiation reaction force on the interaction of thin foils with ultra-intense laser fields

The effects of the radiation reaction (RR) force on thin foils undergoing radiation pressure acceleration (RPA) are investigated. Using QED-particle-in-cell simulations, the influence of the RR force on the collective electron dynamics within the target can be examined. The magnitude of the RR force is found to be strongly dependent on the target thickness, leading to effects which can be observed on a macroscopic scale, such as changes to the distribution of the emitted radiation and the target dynamics. This suggests that such parameters may be controlled in experiments at multi-PW laser facilities. In addition, the effects of the RR force are characterized in terms of an average radiation emission angle. We present an analytical model which, for the first time, describes the effect of the RR force on the collective electron dynamics within the 'light-sail' regime of RPA. The predictions of this model can be tested in future experiments with ultra-high intensity lasers interacting with solid targets

Monte Carlo calculations of pair production in high-intensity laser-plasma interactions

Gamma-ray and electron-positron pair production will figure prominently in laser-plasma experiments with next generation lasers. Using a Monte Carlo approach we show that straggling effects arising from the finite recoil an electron experiences when it emits a high-energy photon, increase the number of pairs produced on further interaction with the laser fields. © 2011 IOP Publishing Ltd

Reduced multi-scale kinetic models for the relativistic electron transport in solid targets: Effects related to secondary electrons

AbstractA reduced mathematical model for the transport of high current relativistic electron beams in a dense collisional plasma is developed. Based on the hypothesis that the density of relativistic electrons is much less than the plasma density and their energy is much higher than the plasma temperature, a model with two energy scales is proposed, where the beam and plasma electrons are considered as two coupled sub-systems, which exchange the energy and particles due to collisions. The process of energy exchange is described in the Fokker-Planck approximation, where the pitch angle electron-ion and electron-electron collisions dominate. The process of particle exchange between populations, leading to the production of secondary energetic electrons, is described with a Boltzmann term. The electron-electron collisions with small impact parameters make an important contribution in the overall dynamics of the beam electrons.</jats:p

From quantum to classical modeling of radiation reaction: A focus on stochasticity effects

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Stochastic partial differential equations as a tool for solving the joint velocity-scalar probability density function transport equation

International audienceIn this chapter, we outline the Eulerian (Field) Monte Carlo Method (EMC) for solving the joint velocity-scalar PDF transport equation in turbulent reactive flows. The EMC method is based on stochastic Eulerian fields, which evolve according to stochastic partial differential equations (SPDEs). These SPDEs belong to the class of quasi-linear equations. Characteristic curves of the SPDEs can cross. As a result, multi-valued solutions for the velocity and scalar fields can appear. We give an example illustrating that the entropy-dissipative interpretation of these SPDEs is inadequate and introduce their entropy conservative interpretation. We show that with this interpretation, the derived SPDEs are indeed equivalent to the PDF we want to solve. Capturing multi-valued solutions of the SPDEs by efficient algorithms is an important issue. Numerical schemes which satisfy entropy increase condition are not appropriate for the multivalued solutions. A numerical scheme is therefore proposed to solve these SPDEs and is evaluated on a simplified configuration

Dense electron-positron plasmas and bursts of gamma-rays from laser-generated quantum electrodynamic plasmas

In simulations of a 12.5 PW laser (focussed intensity I = 4 × 10 23 Wcm - 2) striking a solid aluminum target, 10% of the laser energy is converted to gamma-rays. A dense electron-positron plasma is generated with a maximum density of 10 26 m - 3, seven orders of magnitude denser than pure e- e+ plasmas generated with 1PW lasers. When the laser power is increased to 320 PW (I = 10 25 Wcm - 2), 40% of the laser energy is converted to gamma-ray photons and 10% to electron-positron pairs. In both cases, there is strong feedback between the QED emission processes and the plasma physics, the defining feature of the new "QED-plasma" regime reached in these interactions. © 2013 AIP Publishing LLC

Dense Electron-Positron Plasmas and Ultraintense gamma rays from Laser-Irradiated Solids

In simulations of a 10 PW laser striking a solid, we demonstrate the possibility of producing a pure electron-positron plasma by the same processes as those thought to operate in high-energy astrophysical environments. A maximum positron density of 10(26) m(-3) can be achieved, 7 orders of magnitude greater than achieved in previous experiments. Additionally, 35% of the laser energy is converted to a burst of γ rays of intensity 10(22) W cm(-2), potentially the most intense γ-ray source available in the laboratory. This absorption results in a strong feedback between both pair and γ-ray production and classical plasma physics in the new "QED-plasma" regime