Monte Carlo Collisions in Particle in Cell simulations
|
|
- Vivian Lyons
- 5 years ago
- Views:
Transcription
1 Monte Carlo Collisions in Particle in Cell simulations Konstantin Matyash, Ralf Schneider HGF-Junior research group COMAS : Study of effects on materials in contact with plasma, either with fusion or low-temperature plasmas; Development of computational multi-scale tools
2 Particle in Cell model dx = v dt dv q = E + v B dt m ( ) Δt E = ϕ 1 Δ ϕ = ε E ρ ( x ) E qi ρ = S x x i i ΔxΔy x y 1 1 S( x) Δx Δy = x Δx and y Δy ( ) E E
3 Two-particle interaction (1D) David Tskhakaya, Heraeus-Sommer School "Computational Many Particle Physics, Greifswald
4 Coulomb collisions Motivation: 1. Classical PIC simulates only 5 4 PIC 1D D 3D macro fields and neglects particle collisions. 3 ~1/r ~1/r. Inside grid cells the interaction between particles deviates from the Coulomb law 1 ~r ~const r/ Δr Interaction force between two particles inside the grid cell
5 Fokker-Planck Coulomb collision model Test particle hitting the field particles with distribution function f ( v ) friction Δ v = + ( 1 m ) L φ v and diffusion Δv Δ v = L ϕ v v φ ( v ) 1 = 4π f v ( v) 3 d v v v 1 8 v v π f v d v, ( ) = ( ) 3 ψ are Rosenbluth potentials ( ε ) L = e e / m lnλ ln Λ Coulomb logarithm B. A. Trubnikov, Particle interactions in a fully ionized plasma, Reviews of Plasma Physics 1 (1965) M. N. Rosenbluth, W. M. MacDonald and D. L. Judd, Fokker-Planck Equation for an Inverse-Square Force, Phys. Rev. 17 (1957) 1-6
6 Fokker-Planck Coulomb collision model If the distribution of the field particles is Maxwellian : the friction and diffusion coefficients can be calculated analytically: mv 3 f (v ) = ( π kt m ) exp kt friction: ( 1 m ) ( ) Δ v = A + n G l v A Δ v = n l G( l v) Δ v = n H ( l v) diffusion:, v = v v A v G( x) erf ( x ) x erf ( x ) = H ( x) = erf ( x) G( x) x ln Λ,,, 4 A = 8π e m l = m T R. Chodura, Particle simulation of the plasma-wall transition. Proceedings of the 8th Europhysics Conference on Computational Physics, Computing in Plasma Physics, Garmisch, 1986
7 Fokker-Planck Coulomb collision model Treating diffusion as a Brownian motion we can calculate the change of particle velocity : Δ v = Δv Δ t + R Δv Δt Δ v = R 3 5. Δv Δt x 1 y,z, Δt is the time step Random numbers R 13,, are taken from Gaussian distribution with R i = R = 1 i If distribution is not Maxwellian the energy and momentum are not conserved! for particles of the same kind = after collision velocity of Center of Mass and the temperature are not the same u u T 1 T 1 CM CM Solution force the momentum and the energy conservation by hand: after collisions for every particle we subtract the difference in the center of mass velocities v ( 1,i = v,i ucm ucm ) and scale it to ensure energy conservation v,i = ucm + ( v,i ucm ) T T 1 Introducing large error if distribution is far from Maxwellian!
8 Takizuka-Abe binary Coulomb collision model Takizuka-Abe approach nonlinear collisional operator! T. Takizuka, H. Abe, A binary collision model plasma simulation with a particle code, J. Comput. Phys. 5 (1977) 5. Binary collision model 1. grouping the particle in cells. randomly changing the particles order inside the cells 3. colliding the particles (3a. the same type; 3b. - different types)
9 Takizuka-Abe binary Coulomb collision model v 1 v Sampling Fokker-Planck collisional operator: θ θ P( θ ) = exp θ θ Δt u = v v 1 Δt relative velocity θ μ = qqn lnλ = Δt 3 8πε m u R. Shanny, J. M. Dawson, and J. M. Greene, One-dimensional model of a Lorentz plasma, Phys. Fluids, 1 (1967) 181 m mm + m reduced mass u ϕ u t+δt θ = θ ln R Δt 1 ϕ=π R scattering angle azimuth angle Random numbers R 1, are taken from uniform distribution with m = + Δ m v 1 = v Δu m + m v1 v1 u m1 + m 1 1 R i θ Scheme explicitly conserves energy and momentum! qqn lnλ Limitation: ν νc = cδt 1 θ 1 3 πεmvt
10 Takizuka-Abe binary Coulomb collision model Relaxation of non-maxwellian distribution Relaxation of Maxwellian distribution with different parallel and perpendicular temperatures m(v + v ) 3 mv f (v ) = ( π k m e ) T T exp kt kt e x y e z EVDF, a.u ν t = ν t =. ν t = 1 ν t = 3 Gauss ΔT/ΔT 1..8 PIC MCC result analytical result v ex, v te ν i t
11 Nanbu binary Coulomb collision model Nanbu approach optimization of Takizuka-Abe scheme ( accumulation of many small angle collisions ) K. Nanbu, Theory of cumulative small-angle collisions in plasmas Phys. Rev. E 55 (1997). u = v 1 v u,u,u...u 1 N uu cos( θ N ) = u coth N ( A) A 1 = exp ( s) relative velocity after N collisions accumulated scattering angle after N collisions Accumulated scattering angle is sampled from the distribution allows larger Δt initial relative velocity qqn lnλ s = Δt 3 4πε m u in practice, in order to resolve relaxation dynamics νcδt 1 f ( N ) ( θ ) = exp A cos ( θ ) N A 4π sinh( A) Pro: lower computational cost Contra: complicated implementation
12 Collision happens with probability σ ( E ) Sampling the collision event: Max-Planck Institut für Plasmaphysik, EURATOM Association, Greifswald, Germany - cross-section of the process R Collisions with neutrals 1 < ( ( ) ) P = exp un σ E Δt P 1 col Random number is taken from uniform distribution 1 R 1 R i u ϕ u t+δt u = v v 1 Elastic collisions relative velocity energy in the Center of Mass system: E CM = m, u μ = as no energy is lost in the elastic collision we just need to rotate the relative velocity m mm + m - reduced mass no scattering angle distribution data is available for most of the species we use isotropic scattering θ cos ( ) θ = 1 R ϕ=π R 3 scattering angle for isotropic scattering azimuth angle Random numbers R 3 are taken from uniform distribution with, 1 R i m = + Δ m v 1 = v Δu m + m v1 v1 u m1 + m 1
13 Collisions with neutrals Ionization collision e - + N => e - + N + Splitting 3-body process in two -body processes: u ϕ θ u t+δt 1. Inelastic uniform isotropic electron-neutral collision with loss of energy E i mm mm u = u + E e n e n t+δt i e n e n ( m + M ) ( m + M ) cos ( ) θ = 1 R ϕ=π R 3 electron velocity after 1st step: scattering angle for isotropic scattering azimuth angle energy conservation in the Center of Mass system Random numbers R 3 are taken from uniform distribution with, dividing neutral into the ion and the secondary electron: 1 * M i t+δt m e ve = ve + Δu neutral velocity: vn = vn u me + M Δ n me + Mn t t t t v +Δ +Δ = v v = v t+δt i n e" n R i final velocity of primary electron:. Elastic uniform isotropic electron-electron collision * u = v e ve" u is rotated according to isotropic scattering t t * v +Δ e = v 1 t t e + Δu v +Δ e" = v 1 final velocity of secondary electron: e" Δu Scheme explicitly conserves particles, energy and momentum!
14 Reactions included in methane model ee CH CH 4 4 CH CH e e - - ee CH CH 3 3 CH CH e e - - ee CH CH CH CH e e - - ee CH CH CH CH + + +e +e - - ee CH CH 4 4 CH CH H + e e - - ee CH CH 3 3 CH CH H + e e - - ee CH CH CH CH + + H + e e - - ee CH CH C + + H + e e - - ee CH CH C + H + + e e - - ee CH CH 4 4 CH CH H + ee - - ee CH CH 3 3 CH CH + H + ee - - ee CH CH CH CH + H + ee - - ee CH CH C + H + ee - - ee CH CH CH CH H + + ee - - ee CH CH CH CH H + ee - - ee CH CH CH CH + H + + ee - - ee CH CH CH CH H + ee - - ee CH CH + + CH CH + H + + ee - - ee CH CH + + CH CH + + H + ee - - ee CH CH + + C + H + + ee - - ee CH CH + + C + + H + ee - - ee CH CH CH CH H ee CH CH CH CH + H H ee CH CH CH CH + H ee CH CH + + CH CH + H ee CH CH + + C + H ee C C + + e e - - H + + CH CH 4 4 CH CH H H + + CH CH 3 3 CH CH H H + + CH CH CH CH H H + + CH CH CH CH + + H H + + C C + + H ee H H e e - - ee H H + H + ee - - ee H H + + e e - -
15 PIC simulation: capacitive RF discharge Parallel plate RF discharge (Univesity of Bochum) f RF = MHz, RF peak-to-peak voltage ~ -16 V Gas : CH 4 H mixture, pressure p = 1-1Pa, electron density n e ~ cm -3 potential
16 PIC simulation: capacitive RF discharge electron and CH 4+ ion density CH 4+ ion energy distribution electrons reach electrode only during sheaths collapse energetic ions at the wall due to acceleration in the sheath
17 PIC simulation: capacitive RF discharge n H = cm -3, n CH4 = cm -3, p = 11 Pa Stochastic (Fermi) heating n H = cm -3, n CH4 = cm -3 p = 11 Pa Ohmic heating
18 PIC simulation: capacitive RF discharge simulation electron energy probability function experiment eepf (ev -3/ cm -3 ) T 1 =.39 ev, n 1 = 1 1 cm -3 T = 3 ev, n = 1 9 cm -3 T T electron energy (ev) V.A. Godyak, et al., Phys. Rev. Lett., 65 (199) 996. bi-maxwellian distribution due to stochastic heating
19 Capacitive RF discharge high pressure n e = 1 1 cm -3, n H = cm -3,n CH4 = cm -3, p = 11 Pa potential n' ei, cm -3 c -1 1.x1 16 electron-impact ionization rate 1.x x x x1 15.x Y, λ D field reversal after sheath collapse ionization localized in the sheaths
20 Capacitive RF discharge high pressure Y, mm electron-impact ionization rate simulation n' ei, cm -3 c -1 7E16 6E16 4.8E16 3.6E16.4E16 1.E nm excitation rate experiment time, ns C.M.O. Mahony et al., Appl. Phys. Lett. 71 (1997) 68. double peak structure due to sheath reversal
4 Modeling of a capacitive RF discharge
4 Modeling of a capacitive discharge 4.1 PIC MCC model for capacitive discharge Capacitive radio frequency () discharges are very popular, both in laboratory research for the production of low-temperature
More informationThe Role of Secondary Electrons in Low Pressure RF Glow Discharge
WDS'05 Proceedings of Contributed Papers, Part II, 306 312, 2005. ISBN 80-86732-59-2 MATFYZPRESS The Role of Secondary Electrons in Low Pressure RF Glow Discharge O. Brzobohatý and D. Trunec Department
More informationPIC-MCC simulations for complex plasmas
GRADUATE SUMMER INSTITUTE "Complex Plasmas August 4, 008 PIC-MCC simulations for complex plasmas Irina Schweigert Institute of Theoretical and Applied Mechanics, SB RAS, Novosibirsk Outline GRADUATE SUMMER
More informationPIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma
PIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma Kallol Bera a, Shahid Rauf a and Ken Collins a a Applied Materials, Inc. 974 E. Arques Ave., M/S 81517, Sunnyvale, CA 9485, USA
More informationKinetic simulation of the stationary HEMP thruster including the near field plume region
Kinetic simulation of the stationary HEMP thruster including the near field plume region IEPC-2009-110 Presented at the 31st International Electric Propulsion Conference, University of Michigan Ann Arbor,
More informationUltra-Cold Plasma: Ion Motion
Ultra-Cold Plasma: Ion Motion F. Robicheaux Physics Department, Auburn University Collaborator: James D. Hanson This work supported by the DOE. Discussion w/ experimentalists: Rolston, Roberts, Killian,
More informationPIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma
PIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma Kallol Bera a, Shahid Rauf a and Ken Collins a a Applied Materials, Inc. 974 E. Arques Ave., M/S 81517, Sunnyvale, CA 9485, USA
More informationKINETIC DESCRIPTION OF MAGNETIZED TECHNOLOGICAL PLASMAS
KINETIC DESCRIPTION OF MAGNETIZED TECHNOLOGICAL PLASMAS Ralf Peter Brinkmann, Dennis Krüger Fakultät für Elektrotechnik und Informationstechnik Lehrstuhl für Theoretische Elektrotechnik Magnetized low
More informationParticle-In-Cell Simulations of a Current-Free Double Layer
Particle-In-Cell Simulations of a Current-Free Double Layer S. D. Baalrud 1, T. Lafleur, C. Charles and R. W. Boswell American Physical Society Division of Plasma Physics Meeting November 10, 2010 1Present
More informationComparison of SPT and HEMP thruster concepts from kinetic simulations
Comparison of SPT and HEMP thruster concepts from kinetic simulations K. Matyash, R. Schneider, A. Mutzke, O. Kalentev Max-Planck-Institut für Plasmaphysik, EURATOM Association, Greifswald, D-1749, Germany
More informationSimulation of Coulomb Collisions in Plasma Accelerators for Space Applications
Simulation of Coulomb Collisions in Plasma Accelerators for Space Applications D. D Andrea 1, W.Maschek 1 and R. Schneider 2 Vienna, May 6 th 2009 1 Institut for Institute for Nuclear and Energy Technologies
More informationNARROW GAP ELECTRONEGATIVE CAPACITIVE DISCHARGES AND STOCHASTIC HEATING
NARRW GAP ELECTRNEGATIVE CAPACITIVE DISCHARGES AND STCHASTIC HEATING M.A. Lieberman, E. Kawamura, and A.J. Lichtenberg Department of Electrical Engineering and Computer Sciences University of California
More informationScattering in Cold- Cathode Discharges
Simulating Electron Scattering in Cold- Cathode Discharges Alexander Khrabrov, Igor Kaganovich*, Vladimir I. Demidov**, George Petrov*** *Princeton Plasma Physics Laboratory ** Wright-Patterson Air Force
More informationPhysique des plasmas radiofréquence Pascal Chabert
Physique des plasmas radiofréquence Pascal Chabert LPP, Ecole Polytechnique pascal.chabert@lpp.polytechnique.fr Planning trois cours : Lundi 30 Janvier: Rappels de physique des plasmas froids Lundi 6 Février:
More informationOverview of Accelerated Simulation Methods for Plasma Kinetics
Overview of Accelerated Simulation Methods for Plasma Kinetics R.E. Caflisch 1 In collaboration with: J.L. Cambier 2, B.I. Cohen 3, A.M. Dimits 3, L.F. Ricketson 1,4, M.S. Rosin 1,5, B. Yann 1 1 UCLA Math
More information12. MHD Approximation.
Phys780: Plasma Physics Lecture 12. MHD approximation. 1 12. MHD Approximation. ([3], p. 169-183) The kinetic equation for the distribution function f( v, r, t) provides the most complete and universal
More informationDOE WEB SEMINAR,
DOE WEB SEMINAR, 2013.03.29 Electron energy distribution function of the plasma in the presence of both capacitive field and inductive field : from electron heating to plasma processing control 1 mm PR
More informationExperimental evaluation of nonlinear collision effect on the beam slowing-down process
P-2 Experimental evaluation of nonlinear collision effect on the beam slowing-down process H. Nuga R. Seki,2 S. Kamio M. Osakabe,2 M. Yokoyama,2 M. Isobe,2 K. Ogawa,2 National Institute for Fusion Science,
More informationLectures on basic plasma physics: Introduction
Lectures on basic plasma physics: Introduction Department of applied physics, Aalto University Compiled: January 13, 2016 Definition of a plasma Layout 1 Definition of a plasma 2 Basic plasma parameters
More information14. Energy transport.
Phys780: Plasma Physics Lecture 14. Energy transport. 1 14. Energy transport. Chapman-Enskog theory. ([8], p.51-75) We derive macroscopic properties of plasma by calculating moments of the kinetic equation
More informationCurrent sheath formation in the plasma focus
Plasma Science and Applications (ICPSA 2013) International Journal of Modern Physics: Conference Series Vol. 32 (2014) 1460321 (8 pages) The Author DOI: 10.1142/S2010194514603214 Current sheath formation
More informationIonization Detectors
Ionization Detectors Basic operation Charged particle passes through a gas (argon, air, ) and ionizes it Electrons and ions are collected by the detector anode and cathode Often there is secondary ionization
More informationContents Motivation Particle In Cell Method Projects Plasma and Ion Beam Simulations
PIC Method for Numerical Simulation Ninad Joshi NNP Group 1 Contents Motivation Particle In Cell Method Projects Plasma and Ion Beam Simulations Motivation 3 Particle simulation Ion beams and Plasmas Accelerators
More informationPhysical models for plasmas II
Physical models for plasmas II Dr. L. Conde Dr. José M. Donoso Departamento de Física Aplicada. E.T.S. Ingenieros Aeronáuticos Universidad Politécnica de Madrid Physical models,... Plasma Kinetic Theory
More informationA theoretical study of the energy distribution function of the negative hydrogen ion H - in typical
Non equilibrium velocity distributions of H - ions in H 2 plasmas and photodetachment measurements P.Diomede 1,*, S.Longo 1,2 and M.Capitelli 1,2 1 Dipartimento di Chimica dell'università di Bari, Via
More informationEffects of fast atoms and energy-dependent secondary electron emission yields in PIC/ MCC simulations of capacitively coupled plasmas
(14pp) Plasma Sources Science and Technology doi:10.1088/0963-0252/24/3/034002 Effects of fast atoms and energy-dependent secondary electron emission yields in PIC/ MCC simulations of capacitively coupled
More informationAssessment of fluctuation-induced and wall-induced anomalous electron transport in HET
Assessment of fluctuation-induced and wall-induced anomalous electron transport in HET IEPC-2015-418 Presented at Joint Conference of 30th International Symposium on Space Technology and Science 34th International
More informationFundamentals of Plasma Physics
Fundamentals of Plasma Physics Definition of Plasma: A gas with an ionized fraction (n i + + e ). Depending on density, E and B fields, there can be many regimes. Collisions and the Mean Free Path (mfp)
More informationHong Young Chang Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea
Hong Young Chang Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea Index 1. Introduction 2. Some plasma sources 3. Related issues 4. Summary -2 Why is
More informationKinetic Solvers with Adaptive Mesh in Phase Space for Low- Temperature Plasmas
Kinetic Solvers with Adaptive Mesh in Phase Space for Low- Temperature Plasmas Vladimir Kolobov, a,b,1 Robert Arslanbekov a and Dmitry Levko a a CFD Research Corporation, Huntsville, AL 35806, USA b The
More informationPLASMA-NEUTRAL MODELING IN NIMROD. Uri Shumlak*, Sina Taheri*, Jacob King** *University of Washington **Tech-X Corporation April 2016
PLASMA-NEUTRAL MODELING IN NIMROD Uri Shumlak*, Sina Taheri*, Jacob King** *University of Washington **Tech-X Corporation April 2016 Plasma-Neutral Model Physical Model is derived by E. Meier and U. Shumlak*
More informationSolution of time-dependent Boltzmann equation for electrons in non-thermal plasma
Solution of time-dependent Boltzmann equation for electrons in non-thermal plasma Z. Bonaventura, D. Trunec Department of Physical Electronics Faculty of Science Masaryk University Kotlářská 2, Brno, CZ-61137,
More informationCHAPTER 8. SUMMARY AND OUTLOOK 90 Under the operational conditions used in the present work the translation temperatures can be obtained from the Dopp
Chapter 8 Summary and outlook In the present work reactive plasmas have been investigated by comparing experimentally obtained densities with the results from a simple chemical model. The studies have
More informationCollision Processes. n n The solution is 0 exp x/ mfp
Collision Processes Collisions mediate the transfer of energy and momentum between various species in a plasma, and as we shall see later, allow a treatment of highly ionized plasma as a single conducting
More information16.55 Ionized Gases Problem Set #5
16.55 Ionized Gases Problem Set #5 Problem 1: A probe in a non-maxellian plasma The theory of cold probes, as explained in class, applies to plasmas with Maxwellian electron and ion distributions. However,
More informationCharacteristics and classification of plasmas
Characteristics and classification of plasmas PlasTEP trainings course and Summer school 2011 Warsaw/Szczecin Indrek Jõgi, University of Tartu Partfinanced by the European Union (European Regional Development
More informationModeling and Simulation of Plasma Based Applications in the Microwave and RF Frequency Range
Modeling and Simulation of Plasma Based Applications in the Microwave and RF Frequency Range Dr.-Ing. Frank H. Scharf CST of America What is a plasma? What is a plasma? Often referred to as The fourth
More informationarxiv: v1 [physics.plasm-ph] 10 Nov 2014
arxiv:1411.2464v1 [physics.plasm-ph] 10 Nov 2014 Effects of fast atoms and energy-dependent secondary electron emission yields in PIC/MCC simulations of capacitively coupled plasmas A. Derzsi 1, I. Korolov
More informationChapter 3. Coulomb collisions
Chapter 3 Coulomb collisions Coulomb collisions are long-range scattering events between charged particles due to the mutual exchange of the Coulomb force. Where do they occur, and why they are of interest?
More informationPlasma Astrophysics Chapter 1: Basic Concepts of Plasma. Yosuke Mizuno Institute of Astronomy National Tsing-Hua University
Plasma Astrophysics Chapter 1: Basic Concepts of Plasma Yosuke Mizuno Institute of Astronomy National Tsing-Hua University What is a Plasma? A plasma is a quasi-neutral gas consisting of positive and negative
More informationPIC/MCC Simulation of Radio Frequency Hollow Cathode Discharge in Nitrogen
PIC/MCC Simulation of Radio Frequency Hollow Cathode Discharge in Nitrogen HAN Qing ( ), WANG Jing ( ), ZHANG Lianzhu ( ) College of Physics Science and Information Engineering, Hebei Normal University,
More informationBeams and magnetized plasmas
Beams and magnetized plasmas 1 Jean-Pierre BOEUF LAboratoire PLAsma et Conversion d Energie LAPLACE/ CNRS, Université Paul SABATIER, TOULOUSE Beams and magnetized plasmas 2 Outline Ion acceleration and
More informationLow Temperature Plasma Technology Laboratory
Low Temperature Plasma Technology Laboratory CENTRAL PEAKING OF MAGNETIZED GAS DISCHARGES Francis F. Chen and Davide Curreli LTP-1210 Oct. 2012 Electrical Engineering Department Los Angeles, California
More informationNonlinear Diffusion in Magnetized Discharges. Francis F. Chen. Electrical Engineering Department
Nonlinear Diffusion in Magnetized Discharges Francis F. Chen Electrical Engineering Department PPG-1579 January, 1998 Revised April, 1998 Nonlinear Diffusion in Magnetized Discharges Francis F. Chen Electrical
More informationLinear Momentum, Center of Mass, Conservation of Momentum, and Collision.
PHYS1110H, 2011 Fall. Shijie Zhong Linear Momentum, Center of Mass, Conservation of Momentum, and Collision. Linear momentum. For a particle of mass m moving at a velocity v, the linear momentum for the
More informationPlasmas as fluids. S.M.Lea. January 2007
Plasmas as fluids S.M.Lea January 2007 So far we have considered a plasma as a set of non intereacting particles, each following its own path in the electric and magnetic fields. Now we want to consider
More informationThe dynamics of small particles whose size is roughly 1 µmt or. smaller, in a fluid at room temperature, is extremely erratic, and is
1 I. BROWNIAN MOTION The dynamics of small particles whose size is roughly 1 µmt or smaller, in a fluid at room temperature, is extremely erratic, and is called Brownian motion. The velocity of such particles
More informationThe distorting effect of the ion current on electron temperature measured by an electric probe
The distorting effect of the ion current on electron temperature measured by an electric probe A. Kudryavtsev 1, S.A. Gutsev 1, V.I. Demidov 2,1 1 St.Petersburg State University, St. Petersburg, Russia
More informationProduction and Damping of Runaway Electrons in a Tokamak
International Sherwood Fusion Theory Conference Madison, WI, April 4-6, 2016 Production and Damping of Runaway Electrons in a Tokamak Boris Breizman 1) and Pavel Aleynikov 2) 1) Institute for Fusion Studies,
More informationElectron Transport Behavior in a Mirror Magnetic Field and a Non-uniform Electric Field
Commun. Theor. Phys. (Beijing, China) 35 (2001) pp. 207 212 c International Academic Publishers Vol. 35, No. 2, February 15, 2001 Electron Transport Behavior in a Mirror Magnetic Field and a Non-uniform
More informationPlasma-Wall Interaction: A Multi-Scale Problem
Plasma-Wall Interaction: A Multi-Scale Problem R. Schneider 1 Max-Planck-Institut für Plasmaphysik, EURATOM Association, Teilinstitut Greifswald, Wendelsteinstr.1, D-17491 Greifswald, Germany Abstract
More information1.0. T (ev) 0.5. z [m] y [m] x [m]
W7-X edge modelling with the 3D SOL fluid code BoRiS M. Borchardt, J. Riemann, R. Schneider, X. Bonnin Max-Planck-Institut für Plasmaphysik, Teilinstitut Greifswald EURATOM Association, D 17491 Greifswald,
More informationA Kinetic Theory of Planar Plasma Sheaths Surrounding Electron Emitting Surfaces
A Kinetic Theory of Planar Plasma Sheaths Surrounding Electron Emitting Surfaces J. P. Sheehan1, I. Kaganovich2, E. Barnat3, B. Weatherford3, H. Wang2, 4 1 2 D. Sydorenko, N. Hershkowitz, and Y. Raitses
More informationTwo-dimensional Fluid Simulation of an RF Capacitively Coupled Ar/H 2 Discharge
Two-dimensional Fluid Simulation of an RF Capacitively Coupled Ar/H 2 Discharge Lizhu Tong Keisoku Engineering System Co., Ltd., Japan September 18, 2014 Keisoku Engineering System Co., Ltd., 1-9-5 Uchikanda,
More informationLecture 6 Plasmas. Chapters 10 &16 Wolf and Tauber. ECE611 / CHE611 Electronic Materials Processing Fall John Labram 1/68
Lecture 6 Plasmas Chapters 10 &16 Wolf and Tauber 1/68 Announcements Homework: Homework will be returned to you on Thursday (12 th October). Solutions will be also posted online on Thursday (12 th October)
More informationP. Diomede, D. J. Economou and V. M. Donnelly Plasma Processing Laboratory, University of Houston
P. Diomede, D. J. Economou and V. M. Donnelly Plasma Processing Laboratory, University of Houston 1 Outline Introduction PIC-MCC simulation of tailored bias on boundary electrode Semi-analytic model Comparison
More informationTwo-Dimensional Particle-in-Cell Simulation of a Micro RF Ion Thruster
Two-Dimensional Particle-in-Cell Simulation of a Micro RF Ion Thruster IEPC--7 Presented at the nd International Electric Propulsion Conference, Wiesbaden Germany September 5, Yoshinori Takao, Koji Eriguchi,
More informationDiffusion during Plasma Formation
Chapter 6 Diffusion during Plasma Formation Interesting processes occur in the plasma formation stage of the Basil discharge. This early stage has particular interest because the highest plasma densities
More informationParticle Transport and Density Gradient Scale Lengths in the Edge Pedestal
Particle Transport and Density Gradient Scale Lengths in the Edge Pedestal W. M. Stacey Fusion Research Center, Georgia Institute of Technology, Atlanta, GA, USA Email: weston.stacey@nre.gatech.edu Abstract
More informationOn the locality of parallel transport of heat carrying electrons in the SOL
P1-068 On the locality of parallel transport of heat carrying electrons in the SOL A.V. Chankin* and D.P. Coster Max-Planck-Institut für Pasmaphysik, 85748 Garching, Germany Abstract A continuum Vlasov-Fokker-Planck
More informationOverview of FRC-related modeling (July 2014-present)
Overview of FRC-related modeling (July 2014-present) Artan Qerushi AFRL-UCLA Basic Research Collaboration Workshop January 20th, 2015 AFTC PA Release# 15009, 16 Jan 2015 Artan Qerushi (AFRL) FRC modeling
More informationDual-RadioFrequency Capacitively-Coupled Plasma Reactors. Tomás Oliveira Fartaria nº58595
Dual-RadioFrequency Capacitively-Coupled Plasma Reactors Tomás Oliveira Fartaria nº58595 Index Capacitive Reactors Dual Frequency Capacitively-Coupled reactors o Apparatus for improved etching uniformity
More informationLow Temperature Plasma Technology Laboratory
Low Temperature Plasma Technology Laboratory Equilibrium theory for plasma discharges of finite length Francis F. Chen and Davide Curreli LTP-6 June, Electrical Engineering Department Los Angeles, California
More informationIncoherent Scatter theory and its application at the magnetic Equator
Incoherent Scatter theory and its application at the magnetic Equator Marco A. Milla Radio Observatorio de Jicamarca Instituto Geofísico del Perú JIREP Seminar, June 2018 Jicamarca Radio Observatory Jicamarca
More informationSimulation of Low Pressure Plasma Processing Reactors: Kinetics of Electrons and Neutrals
Simulation of Low Pressure Plasma Processing Reactors: Kinetics of Electrons and Neutrals R. R. Arslanbekov and V. I. Kolobov CFD Research Corporation, Huntsville, AL, USA Abstract. In this paper, we illustrate
More informationPenning Traps. Contents. Plasma Physics Penning Traps AJW August 16, Introduction. Clasical picture. Radiation Damping.
Penning Traps Contents Introduction Clasical picture Radiation Damping Number density B and E fields used to increase time that an electron remains within a discharge: Penning, 936. Can now trap a particle
More informationStopping, blooming, and straggling of directed energetic electrons in hydrogenic and arbitrary-z plasmas
Stopping, blooming, and straggling of directed energetic electrons in hydrogenic and arbitrary-z plasmas This model Monte Carlo 1 MeV e 1 MeV e C. K. Li and R. D. Petrasso MIT 47th Annual Meeting of the
More informationModeling of Negative Ion Transport in Cesium-Seeded Volume Negative Ion Sources
Modeling of Negative Ion Transport in Cesium-Seeded Volume Negative Ion Sources Osamu Fukumasa and Ryo Nishida Department of Electrical and Electronic Engineering, Faculty of Engineering, Yamaguchi University,
More informationEffect of Applied Electric Field and Pressure on the Electron Avalanche Growth
Effect of Applied Electric Field and Pressure on the Electron Avalanche Growth L. ZEGHICHI (), L. MOKHNACHE (2), and M. DJEBABRA (3) () Department of Physics, Ouargla University, P.O Box.5, OUARGLA 3,
More informationIncoherent Scatter theory and its application at the magnetic Equator
Incoherent Scatter theory and its application at the magnetic Equator Marco A. Milla Radio Observatorio de Jicamarca Instituto Geofísico del Perú JIREP Seminar, June 3, 2013 Jicamarca Radio Observatory
More informationSensors Plasma Diagnostics
Sensors Plasma Diagnostics Ken Gentle Physics Department Kenneth Gentle RLM 12.330 k.gentle@mail.utexas.edu NRL Formulary MIT Formulary www.psfc.mit.edu/library1/catalog/ reports/2010/11rr/11rr013/11rr013_full.pdf
More informationImprovement of Propulsion Performance by Gas Injection and External Magnetic Field in Electrodeless Plasma Thrusters
Improvement of Propulsion Performance by Gas Injection and External Magnetic Field in Electrodeless Plasma Thrusters IEPC-217-249 Presented at the th International Electric Propulsion Conference Georgia
More informationCollisionless electron heating by capacitive radio-frequency plasma sheaths 2 and Lieberman[2, 3, 4], where the electrons moving towards the sheath ar
Collisionless electron heating by capacitive radio-frequency plasma sheaths G. Gozadinosyx, D. Vendery, M.M. Turnery and M.A. Liebermanz yplasma Research Laboratory, School of Physical Sciences Dublin
More informationPlasma collisions and conductivity
e ion conductivity Plasma collisions and conductivity Collisions in weakly and fully ionized plasmas Electric conductivity in non-magnetized and magnetized plasmas Collision frequencies In weakly ionized
More informationSimulation of alpha particle current drive and heating in spherical tokamaks
Simulation of alpha particle current drive and heating in spherical tokamaks R. Farengo 1, M. Zarco 1, H. E. Ferrari 1, 1 Centro Atómico Bariloche and Instituto Balseiro, Argentina. Consejo Nacional de
More informationAnalysis of recombination and relaxation of non-equilibrium air plasma generated by short time energetic electron and photon beams
22 nd International Symposium on Plasma Chemistry July 5-10, 2015; Antwerp, Belgium Analysis of recombination and relaxation of non-equilibrium air plasma generated by short time energetic electron and
More informationIntegrated Modeling of Fast Ignition Experiments
Integrated Modeling of Fast Ignition Experiments Presented to: 9th International Fast Ignition Workshop Cambridge, MA November 3-5, 2006 R. P. J. Town AX-Division Lawrence Livermore National Laboratory
More informationAlgebraic Analysis Approach for Multibody Problems
Algebraic Analysis Approach for Multibody Problems Shun-ichi OIKAWA and Hideo FUNASAKA Graduate School of Engineering, Hokkaido University, N-13, W-8, Sapporo 6-8628, Japan (Received 15 November 27 / Accepted
More informationControl of ion and electron distribution functions by the Electrical Asymmetry Effect. U. Czarnetzki
Control of ion and electron distribution functions by the Electrical Asymmetry Effect U. Czarnetzki 64t h GEC, Salt Lake City, 14-18 November 2011 Institute for Plasma and Atomic Physics 1 Ion energy:
More informationPhysics and Modelling of a Negative Ion Source Prototype for the ITER Neutral Beam Injection
1 ITR/P1-37 Physics and Modelling of a Negative Ion Source Prototype for the ITER Neutral Beam Injection J.P. Boeuf a, G. Fubiani a, G. Hagelaar a, N. Kohen a, L. Pitchford a, P. Sarrailh a, and A. Simonin
More information182 ms 184 ms ARENA. ln(flux/e ) [ster cm ev s ] E (kev)
TH/8- On the Physics of Runaway Particles in JET and MAST P. Helander, L.-G. Eriksson, F. Andersson 3, R.J. Akers, C. Byrom ;4, C.G. Gimblett, M.R. Tournianski EURATOM/UKAEA Fusion Association, Culham
More information3. Gas Detectors General introduction
3. Gas Detectors 3.1. General introduction principle ionizing particle creates primary and secondary charges via energy loss by ionization (Bethe Bloch, chapter 2) N0 electrons and ions charges drift in
More informationThe electron diffusion into the channel of stationary plasma thruster
The electron diffusion into the channel of stationary plasma thruster IEPC-215-397 Presented at Joint Conference of 3th International Symposium on Space Technology and Science 34th International Electric
More informationInvestigation of rotating spoke instabilities in a wall-less Hall thruster. Part II: Simulation.
Investigation of rotating spoke instabilities in a wall-less Hall thruster. Part II: Simulation. IEPC-2017-403 Presented at the 35th International Electric Propulsion Conference Georgia Institute of Technology
More informationFIG. 1. "Flower-like" configuration of filaments used for modelling. Magnetic field values for this configuration can be described analytically. Induc
Ion Motion Modelling within Dynamic Filamentary PF-Pinch Column A. Gaψlkowski 1), A. Pasternak 2), M. Sadowski 2) 1) Institute of Plasma Physics and Laser Microfusion, Warsaw, Poland 2) The Andrzej Soltan
More informationAPPENDIX Z. USEFUL FORMULAS 1. Appendix Z. Useful Formulas. DRAFT 13:41 June 30, 2006 c J.D Callen, Fundamentals of Plasma Physics
APPENDIX Z. USEFUL FORMULAS 1 Appendix Z Useful Formulas APPENDIX Z. USEFUL FORMULAS 2 Key Vector Relations A B = B A, A B = B A, A A = 0, A B C) = A B) C A B C) = B A C) C A B), bac-cab rule A B) C D)
More informationTH/P4-9. T. Takizuka 1), K. Shimizu 1), N. Hayashi 1), M. Hosokawa 2), M. Yagi 3)
1 Two-dimensional Full Particle Simulation of the Flow Patterns in the Scrape-off-layer Plasma for Upper- and Lower- Null Point Divertor Configurations in Tokamaks T. Takizuka 1), K. Shimizu 1), N. Hayashi
More informationUniversity of Oslo. Department of Physics. Interaction Between Ionizing Radiation And Matter, Part 2 Charged-Particles.
Interaction Between Ionizing Radiation And Matter, Part Charged-Particles Audun Sanderud Excitation / ionization Incoming charged particle interact with atom/molecule: Ionization Excitation Ion pair created
More informationHeating and current drive: Radio Frequency
Heating and current drive: Radio Frequency Dr Ben Dudson Department of Physics, University of York Heslington, York YO10 5DD, UK 13 th February 2012 Dr Ben Dudson Magnetic Confinement Fusion (1 of 26)
More informationKinetic simulations of SPT and HEMP thrusters including the near-field plume region
This work was presented at 21st International Conference on Numerical Simulation of Plasmas (ICNSP'09) 1 Kinetic simulations of SPT and HEMP thrusters including the near-field plume region K. Matyash,
More informationTransduction Based on Changes in the Energy Stored in an Electrical Field
Lecture 6-1 Transduction Based on Changes in the Energy Stored in an Electrical Field Electric Field and Forces Suppose a charged fixed q 1 in a space, an exploring charge q is moving toward the fixed
More informationMWP MODELING AND SIMULATION OF ELECTROMAGNETIC EFFECTS IN CAPACITIVE DISCHARGES
MWP 1.9 MODELING AND SIMULATION OF ELECTROMAGNETIC EFFECTS IN CAPACITIVE DISCHARGES Insook Lee, D.B. Graves, and M.A. Lieberman University of California Berkeley, CA 9472 LiebermanGEC7 1 STANDING WAVES
More informationSimulation of a two-dimensional sheath over a flat insulator conductor interface on a radio-frequency biased electrode in a high-density plasma
JOURNAL OF APPLIED PHYSICS VOLUME 95, NUMBER 7 1 APRIL 2004 Simulation of a two-dimensional sheath over a flat insulator conductor interface on a radio-frequency biased electrode in a high-density plasma
More informationPlasma parameter evolution in a periodically pulsed ICP
Plasma parameter evolution in a periodically pulsed ICP V. Godyak and B. Alexandrovich OSRAM SYLVANIA, 71 Cherry Hill Drive, Beverly, MA 01915, USA The electron energy probability function (EEPF) has been
More informationOne dimensional hybrid Maxwell-Boltzmann model of shearth evolution
Technical collection One dimensional hybrid Maxwell-Boltzmann model of shearth evolution 27 - Conferences publications P. Sarrailh L. Garrigues G. J. M. Hagelaar J. P. Boeuf G. Sandolache S. Rowe B. Jusselin
More informationCONSEQUENCES OF RADIATION TRAPPING ON ELECTRON ENERGY DISTRIBUTIONS IN LOW PRESSURE INDUCTIVELY COUPLED Hg/Ar DISCHARGES*
CONSEQUENCES OF RADIATION TRAPPING ON ELECTRON ENERGY DISTRIBUTIONS IN LOW PRESSURE INDUCTIVELY COUPLED Hg/Ar DISCHARGES* Kapil Rajaraman**, Alex Vasenkov*** and Mark J. Kushner*** **Department of Physics
More informationSelf consistent kinetic simulations of SPT and HEMP thrusters including the near-field plume region
Self consistent kinetic simulations of SPT and HEMP thrusters including the near-field plume region K. Matyash 1, R. Schneider, A. Mutzke, O. Kalentev Max-Planck-Institut für Plasmaphysik, EURATOM Association,
More informationExtremely far from equilibrium: the multiscale dynamics of streamer discharges
Extremely far from equilibrium: the multiscale dynamics of streamer discharges Ute Ebert 1,2 1 Centrum Wiskunde & Informatica Amsterdam 2 Eindhoven University of Technology http://www.cwi.nl/~ebert www.cwi.nl/~ebert
More informationChapter V: Interactions of neutrons with matter
Chapter V: Interactions of neutrons with matter 1 Content of the chapter Introduction Interaction processes Interaction cross sections Moderation and neutrons path For more details see «Physique des Réacteurs
More informationWall-induced Cross-field Electron Transport with Oblique Magnetic Field Lines
Wall-induced Cross-field Electron Transport with Oblique Magnetic Field Lines IEPC-213-77 Presented at the 33 rd International Electric Propulsion Conference, The George Washington University, Washington,
More information