scholarly journals Study of the slowing down of high energy proton shots through metals via a Monte Carlo simulation of the Fokker-Planck equation

2005 ◽  
Vol 20 (2) ◽  
pp. 23-27
Author(s):  
Francesco Teodori ◽  
Vincenzo Molinari
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Planck Equation ◽  
High Energy ◽  
High Energy Proton ◽  
Slowing Down ◽  
Energy Proton ◽  
Fokker Planck Equation ◽  
Multi Body ◽  
Fokker Planck

The aim of this work is to analyze the diffusion and the slowing down of high energy proton shots through a target. Analyzing the phenomenon rigorously with the full transport equations, means tack ling many difficulties, most of which arise from the long range nature of the Coulomb interactions involving more than one particle simultaneously. The commonly used approach of neglecting the multi-body collisions, though correct for rarefied neutral gases, of ten leads to very poor approximations when charged particles moving through dense matter are considered. Here we present a Monte Carlo simulation of the Fokker-Planck equation where the multi-body collisions are taken into account. The model al lows the calculation of a point-wise distribution of energy and momentum transferred to the tar get.

EXACT SOLUTIONS AND MONTE CARLO SIMULATIONS OF SELF-CONSISTENT LANGEVIN EQUATIONS: A CASE STUDY FOR THE COLLECTIVE DYNAMICS OF STOCK PRICES

2007 ◽  
Vol 21 (07) ◽  
pp. 1099-1112 ◽  
Author(s):  
T. D. FRANK
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Langevin Equation ◽  
Analytical Solutions ◽  
Planck Equation ◽  
Collective Dynamics ◽  
Fokker Planck Equation ◽  
Self Consistent ◽  
Fokker Planck

In a case study, the exact solution of a self-consistent Langevin equation associated with a nonlinear Fokker–Planck equation is derived. On the basis of this solution, a Monte Carlo simulation scheme for the Langevin equation is proposed. The case study addresses a generalized geometric Brownian walk that describes the collective dynamics of a large set of interacting stocks. Numerical results obtained from the Monte Carlo simulation are compared with analytical solutions derived from the nonlinear Fokker–Planck equation. The power of the Monte Carlo simulation is demonstrated for situations in which analytical solutions are not available.

Semi-analytical inspection of the quasi-linear absorption of lower hybrid wave in presence of -particles in tokamak reactor

2018 ◽  
Vol 84 (5) ◽  
Author(s):  
A. Cardinali ◽  
C. Castaldo ◽  
R. Ricci
Keyword(s):  
Distribution Function ◽  
Planck Equation ◽  
Current Drive ◽  
Dielectric Tensor ◽  
Lower Hybrid ◽  
Linear Diffusion ◽  
Tokamak Reactor ◽  
Slowing Down ◽  
Fokker Planck Equation ◽  
Fokker Planck

In a reactor plasma like demonstration power station (DEMO), when using the radio frequency (RF) for heating or current drive in the lower hybrid (LH) frequency range (Frankeet al.,Fusion Engng Des., vol. 96–97, 2015, p. 46; Cardinaliet al.,Plasma Phys. Control. Fusion, vol. 59, 2017, 074002), a large fraction of the ion population (the continuously born$\unicode[STIX]{x1D6FC}$-particle, and/or the neutral beam injection (NBI) injected ions) is characterized by a non-thermal distribution function. The interaction (propagation and absorption) of the LH wave must be reformulated by considering the quasi-linear approach for each species separately. The collisional slowing down of such an ion population in a background of an electron and ion plasma is balanced by a quasi-linear diffusion in velocity space due to the propagating electromagnetic wave. In this paper, both propagations are considered by including the ion distribution function, solution of the Fokker–Planck equation, which describes the collisional dynamics of the$\unicode[STIX]{x1D6FC}$-particles including the effects of frictional slowing down, energy diffusion and pitch-angle scattering. Analytical solutions of the Fokker–Planck equation for the distribution function of$\unicode[STIX]{x1D6FC}$-particles with a background of ions and electrons at steady state are included in the calculation of the dielectric tensor. In the LH frequency domain, ray tracing (including quasi-linear damping), can be analytically solved by iterating with the Fokker–Planck solution, and the interaction of the LH wave with$\unicode[STIX]{x1D6FC}$-particles, thermal ions and electrons can be accounted self-consistently and the current drive efficiency can be evaluated in this more general scenario.

scholarly journals Alignment of Dust Grains by Magnetic Relaxation: A Comparison Between Results Obtained by Two Different Methods

1973 ◽  
Vol 52 ◽  
pp. 187-189
Author(s):  
P. Cugnon
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Magnetic Relaxation ◽  
Planck Equation ◽  
Dust Grains ◽  
Fokker Planck Equation ◽  
The Monte Carlo Method ◽  
Good Agreement ◽  
Fokker Planck

This paper is devoted to a comparison between results obtained by Purcell and Spitzer (1971) using a Monte-Carlo method and by the author (1971) using a Fokker-Planck equation. It is shown that there is a good agreement between the results within the dispersion expected from the Monte-Carlo method.

Monte Carlo simulations of a nozzle for the treatment of ocular tumours with high-energy proton beams

2005 ◽  
Vol 50 (22) ◽  
pp. 5229-5249 ◽  
Author(s):  
Wayne Newhauser ◽  
Nicholas Koch ◽  
Stephen Hummel ◽  
Matthias Ziegler ◽  
Uwe Titt
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
High Energy ◽  
High Energy Proton ◽  
Proton Beams ◽  
Energy Proton ◽  
Ocular Tumours
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