The energy loss and penetration of multi-megelectronvolt protons into a uniform deuterium-tritium (DT) plasma has been calculated. The effects of nuclear elastic scattering and Coulomb interactions are treated from a unified point of view. In general, multiple scattering enhances the proton linear-energy transfer along the initial proton direction, thus the energy deposition increases near the end of its range. The net effect of multiple scattering is to reduce the penetration from 1.20 to 1.02 g cm-2 for 12 MeV protons in a ρ=500 g cm-3 plasma at T=5 keV. These results should have relevance to proton fast ignition, specifically to energy deposition calculations that critically assess quantitative ignition requirements.
The interaction of a quasi-monoenergetic proton beam with a pre-compressed plasma is studied in the context of inertial fusion fast ignition (FI). Based on fundamental principles, a kinetic model is developed by considering hard collisions, nuclear scattering, and the contribution due to collective processes. The penetration depth, longitudinal straggling, and the transverse blooming are evaluated by solving the Boltzmann transport equation using the multiple scattering theory. The stopping power, transport scattering cross sections, and convenient expressions for the angular moments of the proton distribution function have been used in modeling the collisional proton transport in a three-dimensional (3D) Monte Carlo code. The transport of a proton beam with a quasi-monoenergetic energy ⟨E⟩=10 MeV is studied for pre-compressed deuterium-tritium plasma with an average density of ρ=400 g cm−3 and temperatures T=1 keV, 5 keV, and 10 keV. The net effects of multiple scattering are to reduce the penetration from 1.028 to 0.828 g cm−2 with range straggling ρΣR=0.044 g cm−2 and beam blooming ρΣB=0.272 g cm−2, for 10 MeV protons in a ρ=400 g cm−3 plasma at T = 5 keV. This model can be used for quantitatively assessing ignition requirements for proton fast ignition.
Self-heating condition and following ignition in an Inertial Confinement Fusion (ICF) fuel pellet is evaluated by calculating the power equations, dynamically. In fact, the self-heating condition is a criterion that determines the minimum parameters of a fuel (such as temperature, density and areal density) that can be ignited.Deuterium is the main component of ICF fuels as large amounts of it are naturally available. In addition, the use of deuterium as a fuel in ICF causes the production of tritium and helium-3. However, pure deuterium has a high ignition temperature (T≥40 keV) which makes it inefficient. In this paper, the power equations are solved, dynamically, and it has been indicated that internal tritium and helium-3 production at early evolution of compressed deuterium fuel causes ignition at lower predicted temperatures.
The Parity-Time (PT ) symmetric potentials are derived by non-Hermitian supersymmetric quantum mechanics for square well and barrier. These PTsupersymmetric square well and barrier The partners have complex partners.The partners are isospectral with real energies. PT -symmetry is only unbroken for the bound states.
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