The Coefficient of Bohm Diffusion in Fully Ionized Plasma and its Theoretical Proof
|
|
- Peter Moody
- 5 years ago
- Views:
Transcription
1 Utah State University Graduate Student Presentations Browse all Graduate Research The Coefficient of Bohm Diffusion in Fully Ionized Plasma and its Theoretical Proof Ahmad Talaei Utah State University Reza Amrollahi Follow this and additional works at: Part of the Physics Commons Recommended Citation Ahmad Talaei and R. Amrollahi Coefficient of Bohm diffusion in fully ionized plasma and its theoretical proof Proceeding of 2th IPM international conference on plasma dynamics, Tehran, Iran, 2006 This Presentation is brought to you for free and open access by the Browse all Graduate Research at It has been accepted for inclusion in Graduate Student Presentations by an authorized administrator of For more information, please contact
2 The Coe cient of Bohm Di usion in Fully Ionized Plasma and its Theoretical Proof Ahmad Talaei a,, Reza Amrollahi a a Department of Nuclear Engineering and Physics, Amirkabir University of Technology, No. 424, Hafez Ave., P.O.Box , Tehran, Iran 2 th IPM International Conference on Plasma Dynamics, Tehran, Iran, Abstract As we know, the classical di usion can not be able to respond the experimental results of the diffusion in the fully ionized and isothermal plasma. In this article, we purpose to extract the empirical coe cients of the Bohm di usion and its confinement time, theoretically, in the fully ionized plasma, using the single fluid MHD equations. Keywords: Classical di usion, Bohm di usion, Bohm time, Single fluid MHD equations, Fick s low. 1 Introduction As we know, in the weakly ionized plasma in the absence of magnetic fields, charged particles collide primarily with neutral atoms rather that with one another. But considering the weakly ionized plasma in a existence of the magnetic field, charged particles will move along by di usion and mobility. In this case, we can write the perpendicular coe cient of the di usion to the magnetic field as [1]: D? / r2? (1.1) Where r? is the Larmor radius and the mean time between collisions for particles. In fully ionized plasmas (composed of ions and electrons alone), all collisions are Coulomb collisions between charged particles. In the absence of gravity, for a steady state plasma, the perpendicular coe cient of the di usion to the magnetic field using the single fluid MHD equations, becomes[1]: D? /?n P KT B 2 (1.2) Corresponding author. addresses: ahmad.talaei@gmail.com (Ahmad Talaei) 1
3 D? is so called the classical di usion coe cient for a fully ionized gases where n is the plasma density and? the perpendicular resistance to the magnetic field. As we see Eq.(1.2), D? is proportional to B 2, just like in the case of weakly ionized plasma. But the laboratory verification of the B 2 dependence of the D? in a fully ionized plasma elude from the all experiments. In almost previous experiments, D? scaled as B 1, rather than B 2, and the decay of plasma was found to be exponential, rather than reciprocal with time. Furthermore, the absolute value of D? was far larger than that given by Eq.(1.2). Bohm, gave the coe cient of this poor magnetic confinement di usion empirical as [1]: D? = 1 KT e 16 eb D B (1.3) Di usion following this law is called Bohm di usion. This formula was obeyed in a surprising number of di erent experiments. As we see, D B is independent of density and proportional to B 1. The confinement time in a cylindrical plasma column of radius R and length L can be estimated from Eq.(1.3) as follows [1]: The B is often called the Bohm time. = R2 2D B B (1.4) 2 Therotical Equation of Bohm Di usion in Fully Ionized Plasma We use the single fluid MHD equations for obtaining Eqs.(1.3) and = j B rp + g (2.1) E + V B = + r ( V ) = + r ( j ) = 0 (2.4) Where is the mass density of plasma, V the velocity of one phase plasma, j the current density of plasma, B the magnetic field, p the Maxwellian pressure, g gravitational field,? specific resistivity and charge density in one phase plasma. We write the perpendicular component to B in Eq.(2.1), as V? = j? B rp + g In the absence of gravity, for a steady state plasma, we have: Taking the cross product with B, we have: j? B rp = 0 (2.6) 2
4 ( j? B ) B rp B = 0 (2.7) The scalar product of current density perpendicular to magnetic field with B is zero, thus: j? = As we know, j? = ne V?. Thus, we have: rp B B 2 (2.8) rp B V? = neb 2 ) V? = ( ekt e + i KT i ) rn B neb 2 (2.9) For simplicity, we assumed e KT e = i KT i (for an isothermal plasma) so we have: V? = 2 e KT e rn B neb 2 (2.10) The perpendicular component of the flux associated with di usion to magnetic field,? is as:? = n V? = 2 e KT e rn B eb 2 (2.11) On the other hand, Fick s low of di usion is equal: = D rn (2.12) Where D is di usion coe cient. We compare Eq.(2.11), with the perpendicular component of the flux in Eq.(2.12) so we can write the perpendicular di usion coe cient to B as: D? =2 KT e eb (2.13) As we obtained, D? is proportional to B 1, and it is not proportional to n. Also, the absolute value of D? in Eq.(2.13) is nearly equal to value of coe cient of the Bohm di usion. For obtaining the Bohm time, we use the equation of continuity + r = 0 (2.14) For perpendicular component of Eq.(2.14) to B, and using Fick s law (that we assume D? is independent of geometry), we D? r 2 n = 0 Eq.(2.15) can be solved by using the method of separation of variables. Therefore, we consider: Combining Eqs.(2.15) and (2.16), we have: n(r, t) =T (t)s(r) (2.16) 1 dt (t) = D? T (t) dt S(r) r2 S(r) (2.17) 3
5 Since the left side is a function of time alone and the right side a function of space alone, they must both be equal to the same constant, which we shall call 1. The function T(t) obeys the equation: 1 dt (t) = D? T (t) dt S(r) r2 S(r) = 1 (2.18) 1 dt (t) = 1 T (t) dt ) T (t) =T e t (2.19) Therefore, density decays exponentially with time, as one would expect. Also, the spatial part of Eq.(2.18), S(r), in cylindrical geometry obeys the equation: D? S(r) r2 S(r) = 1 ) d2 S(r) dr r ds(r) dr + S(r) D? = 0 (2.20) As we know, S(r) is called a Bessel function of order of zero, and Eq.(2.20) is called Bessel s equation of order zero. With the solution we have: r S(r) =AJ ( p D? )+BY ( r p D? ) (2.21) We would expect the density to be finite at the center of cylinder (r=0). condition {S(r 0) = finite} requires: This boundary r S(r) =AJ ( p D? ) (2.22) Also, we would expect the density to be nearly zero at the walls. Since once ions and electrons reach the wall, they recombine there. The density near the wall, therefore, is essentially zero. Thus: R S(r R) =0) AJ ( p D? )=0) R p D? = n (2.23) n is points that the Bessel function of order of zero is zero in these points, such as 2.408,5.87,etc.. R For satisfying the boundary condition {n(r R, t) =0}, we must set p D? equal to the first zero of J, namely, Therefore, for the decay time, we have: R p D? =2.408 ) = R 2 (2.24) 5.798D? The valve of confinement time in Eq.(2.24) is nearly equal to value of the Bohm time. As one sees, we extract the empirical coe cients of the Bohm di usion and Bohm time, theoretically, using the single fluid MHD equations. Consequently, by combining Eqs.(2.16),(2.19),(2.22) and (2.24), the density of plasma as function of time and space in the cylindrical geometry is equal: n(r, t) =T (t)s(r) =n J ( 2.408r R )e t (2.25) 4
6 3 Conclusion In this work, we extract Bohm di usion and Bohm time in fully ionized plasma for a steady state (that Bohm gave the empirical formulas for them) using the single fluid MHD equations. Consequently, we suggested a plasma density with time and space components in a cylindrical column of radius R and length L. References [1] Francis F.Chen, Introduction to Plasma Physics and Controlled Fusion, Plennum Press, New York, Second Edition, Vol. 1, Plasma Physics,
Diffusion equation, flux, diffusion coefficient scaling. Diffusion in fully ionized plasma vs. weakly ionized plasma. n => Coulomb collision frequency
Last Time Diffusion in plasma: the main reason why we need to control it (i.e. using magnetic field) Diffusion equation, flux, diffusion coefficient scaling o o t nx,t Dn D2 nx,t o D ~ L 2 T Diffusion
More informationFundamentals of Plasma Physics Transport in weakly ionized plasmas
Fundamentals of Plasma Physics Transport in weakly ionized plasmas APPLAuSE Instituto Superior Técnico Instituto de Plasmas e Fusão Nuclear Luís L Alves (based on Vasco Guerra s original slides) 1 As perguntas
More informationPlasma Physics Prof. Vijayshri School of Sciences, IGNOU. Lecture No. # 38 Diffusion in Plasmas
Plasma Physics Prof. Vijayshri School of Sciences, IGNOU Lecture No. # 38 Diffusion in Plasmas In today s lecture, we will be taking up the topic diffusion in plasmas. Diffusion, why do you need to study
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 informationChapter 5 MAGNETIZED PLASMAS. 5.1 Introduction. 5.2 Diamagnetic current
Chapter 5 MAGNETIZED PLASMAS 5.1 Introduction We are now in a position to study the behaviour of plasma in a magnetic field. In the first instance we will re-examine particle diffusion and mobility with
More informationGalaxy Inclination and Surface Brightness
Utah State University DigitalCommons@USU Student Showcase Browse Undergraduate Research Events 1-1-2013 Galaxy Inclination and Surface Brightness Jordan C. Rozum Utah State University Shane L. Larson Utah
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 informationThe ideal Maxwellian plasma
The ideal Maxwellian plasma Dr. L. Conde Departamento de Física Aplicada. E.T.S. Ingenieros Aeronáuticos Universidad Politécnica de Madrid Plasmas are,... The plasma state of matter may be defined as a
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 information18 The Electromagnetic Wave Equation
Utah State University DigitalCommons@USU Foundations of Wave Phenomena Physics, Department of 1-1-2004 18 The Electromagnetic Wave Equation Charles G. Torre Department of Physics, Utah State University,
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 informationMODERN PHYSICS OF PLASMAS (19 lectures)
UNIT OF STUDY OUTLINE (PHYS 3021, 3921, 3024, 3924, 3025, 3925) MODERN PHYSICS OF PLASMAS (19 lectures) Course coordinator and principal lecturer: Dr Kostya (Ken) Ostrikov Lecturer (normal student stream,
More informationPhysics of fusion power. Lecture 13 : Diffusion equation / transport
Physics of fusion power Lecture 13 : Diffusion equation / transport Many body problem The plasma has some 10 22 particles. No description is possible that allows for the determination of position and velocity
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 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 informationIntegrated Particle Transport Simulation of NBI Plasmas in LHD )
Integrated Particle Transport Simulation of NBI Plasmas in LHD Akira SAKAI, Sadayoshi MURAKAMI, Hiroyuki YAMAGUCHI, Arimitsu WAKASA, Atsushi FUKUYAMA, Kenichi NAGAOKA 1, Hiroyuki TAKAHASHI 1, Hirohisa
More informationCharged particle motion in external fields
Chapter 2 Charged particle motion in external fields A (fully ionized) plasma contains a very large number of particles. In general, their motion can only be studied statistically, taking appropriate averages.
More informationChapter 18 Thermal Properties of Matter
Chapter 18 Thermal Properties of Matter In this section we define the thermodynamic state variables and their relationship to each other, called the equation of state. The system of interest (most of the
More informationSimple examples of MHD equilibria
Department of Physics Seminar. grade: Nuclear engineering Simple examples of MHD equilibria Author: Ingrid Vavtar Mentor: prof. ddr. Tomaž Gyergyek Ljubljana, 017 Summary: In this seminar paper I will
More informationDiffusion of Arc Plasmas across a Magnetic Field
P366 USA Diffusion of Arc Plasmas across a Magnetic Field By Albert Simon* The effect of a magnetic field В is to reduce the coefficients of diffusion, ) p, across the magnetic field to the values equations
More informationComparing Experimental Apples and Oranges with Quantile-Quantile Plots
Utah State University DigitalCommons@USU Presentations Materials Physics Fall 10-2015 Comparing Experimental Apples and Oranges with Quantile-Quantile Plots Allen Andersen Utah State University JR Dennison
More informationPLASMA: WHAT IT IS, HOW TO MAKE IT AND HOW TO HOLD IT. Felix I. Parra Rudolf Peierls Centre for Theoretical Physics, University of Oxford
1 PLASMA: WHAT IT IS, HOW TO MAKE IT AND HOW TO HOLD IT Felix I. Parra Rudolf Peierls Centre for Theoretical Physics, University of Oxford 2 Overview Why do we need plasmas? For fusion, among other things
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 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 informationMacroscopic plasma description
Macroscopic plasma description Macroscopic plasma theories are fluid theories at different levels single fluid (magnetohydrodynamics MHD) two-fluid (multifluid, separate equations for electron and ion
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 informationNeutral beam plasma heating
Seminar I b 1 st year, 2 nd cycle program Neutral beam plasma heating Author: Gabrijela Ikovic Advisor: prof.dr. Tomaž Gyergyek Ljubljana, May 2014 Abstract For plasma to be ignited, external heating is
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 informationWaves in plasma. Denis Gialis
Waves in plasma Denis Gialis This is a short introduction on waves in a non-relativistic plasma. We will consider a plasma of electrons and protons which is fully ionized, nonrelativistic and homogeneous.
More informationDiffusion in cylindrical geometry
4/30/0 Random walk, etc. iffusion, cylindrical iffusion in cylindrical geometry In this exercise we will solve the diffusion equation in cylindrical geometry. We will use the same approach that was used
More informationxkcd.com It IS about physics. It ALL is.
xkcd.com It IS about physics. It ALL is. Introduction to Space Plasmas The Plasma State What is a plasma? Basic plasma properties: Qualitative & Quantitative Examples of plasmas Single particle motion
More informationThe low-field density peak in helicon discharges
PHYSICS OF PLASMAS VOLUME 10, NUMBER 6 JUNE 2003 Francis F. Chen a) Electrical Engineering Department, University of California, Los Angeles, Los Angeles, California 90095-1597 Received 10 December 2002;
More informationModélisation de sources plasma froid magnétisé
Modélisation de sources plasma froid magnétisé Gerjan Hagelaar Groupe de Recherche Energétique, Plasma & Hors Equilibre (GREPHE) Laboratoire Plasma et Conversion d Énergie (LAPLACE) Université Paul Sabatier,
More information02 Coupled Oscillators
Utah State University DigitalCommons@USU Foundations of Wave Phenomena Physics, Department of --4 Coupled Oscillators Charles G. Torre Department of Physics, Utah State University, Charles.Torre@usu.edu
More informationFast Ion Confinement in the MST Reversed Field Pinch
Fast Ion Connement in the MST Reversed Field Pinch Gennady Fiksel B. Hudson, D.J. Den Hartog, R.M. Magee, R. O'Connell, S.C. Prager MST Team - University of Wisconsin - Madison Center for Magnetic Self-Organization
More informationPHYSICS BASIS FOR THE GASDYNAMIC MIRROR (GDM) FUSION ROCKET. Abstract
PHYSICS BASIS FOR THE GASDYNAMIC MIRROR (GDM) FUSION ROCKET T. Kammash Department of Nuclear Engineering and Radiological Sciences University of Michigan Ann Arbor, MI 48109 (313) 764-0205 W. Emrich Jr.
More information02 Coupled Oscillators
Utah State University DigitalCommons@USU Foundations of Wave Phenomena Library Digital Monographs 8-04 0 Coupled Oscillators Charles G. Torre Department of Physics, Utah State University, Charles.Torre@usu.edu
More informationPoiseuille Advection of Chemical Reaction Fronts
Utah State University DigitalCommons@USU All Physics Faculty Publications Physics 8- Poiseuille Advection of Chemical Reaction Fronts Boyd F. Edwards Utah State University Follow this and additional works
More informationIntroduction. Chapter Plasma: definitions
Chapter 1 Introduction 1.1 Plasma: definitions A plasma is a quasi-neutral gas of charged and neutral particles which exhibits collective behaviour. An equivalent, alternative definition: A plasma is a
More informationMAGNETOHYDRODYNAMICS
Chapter 6 MAGNETOHYDRODYNAMICS 6.1 Introduction Magnetohydrodynamics is a branch of plasma physics dealing with dc or low frequency effects in fully ionized magnetized plasma. In this chapter we will study
More informationMAGNETIC NOZZLE PLASMA EXHAUST SIMULATION FOR THE VASIMR ADVANCED PROPULSION CONCEPT
MAGNETIC NOZZLE PLASMA EXHAUST SIMULATION FOR THE VASIMR ADVANCED PROPULSION CONCEPT ABSTRACT A. G. Tarditi and J. V. Shebalin Advanced Space Propulsion Laboratory NASA Johnson Space Center Houston, TX
More informationTHE SHEARED-FLOW STABILIZED Z-PINCH
THE SHEARED-FLOW STABILIZED Z-PINCH U. Shumlak* J. Chadney R.P. Golingo D.J. Den Hartog M.C. Hughes S.D. Knecht W. Lowrie V.S. Lukin B.A. Nelson R.J. Oberto J.L. Rohrbach M.P. Ross and G.V. Vogman *University
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 informationxkcd.com It IS about physics. It ALL is.
xkcd.com It IS about physics. It ALL is. Introduction to Space Plasmas! The Plasma State What is a plasma? Basic plasma properties: Qualitative & Quantitative Examples of plasmas! Single particle motion
More informationCharacteristics of Positive Ions in the Sheath Region of Magnetized Collisional Electronegative Discharges
Plasma Science and Technology, Vol.6, No.6, Jun. 204 Characteristics of Positive Ions in the Sheath Region of Magnetized Collisional Electronegative Discharges M. M. HATAMI, A. R. NIKNAM 2 Physics Department
More informationLecture 6: High Voltage Gas Switches
Lecture 6: High Voltage Gas Switches Switching is a central problem in high voltage pulse generation. We need fast switches to generate pulses, but in our case, they must also hold off high voltages before
More informationConvection Heat Transfer. Introduction
Convection Heat Transfer Reading Problems 12-1 12-8 12-40, 12-49, 12-68, 12-70, 12-87, 12-98 13-1 13-6 13-39, 13-47, 13-59 14-1 14-4 14-18, 14-24, 14-45, 14-82 Introduction Newton s Law of Cooling Controlling
More informationPlasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi
Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi Module No. # 01 Lecture No. # 02 Plasma Response to Fields: Fluid Equations Well, friends today I am going
More informationFormation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas )
Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas ) Yasutomo ISHII and Andrei SMOLYAKOV 1) Japan Atomic Energy Agency, Ibaraki 311-0102, Japan 1) University
More informationPlasma Optimization in a Multicusp Ion Source by Using a Monte Carlo Simulation
Journal of the Korean Physical Society, Vol. 63, No. 7, October 2013, pp. 0 0 Plasma Optimization in a Multicusp Ion Source by Using a Monte Carlo Simulation M. Hosseinzadeh and H. Afarideh Nuclear Engineering
More informationPHYSICS - CLUTCH CH 19: KINETIC THEORY OF IDEAL GASSES.
!! www.clutchprep.com CONCEPT: ATOMIC VIEW OF AN IDEAL GAS Remember! A gas is a type of fluid whose volume can change to fill a container - What makes a gas ideal? An IDEAL GAS is a gas whose particles
More informationFluid equations, magnetohydrodynamics
Fluid equations, magnetohydrodynamics Multi-fluid theory Equation of state Single-fluid theory Generalised Ohm s law Magnetic tension and plasma beta Stationarity and equilibria Validity of magnetohydrodynamics
More informationAMSC 663 Project Proposal: Upgrade to the GSP Gyrokinetic Code
AMSC 663 Project Proposal: Upgrade to the GSP Gyrokinetic Code George Wilkie (gwilkie@umd.edu) Supervisor: William Dorland (bdorland@umd.edu) October 11, 2011 Abstract Simulations of turbulent plasma in
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 informationIntegrated Heat Transport Simulation of High Ion Temperature Plasma of LHD
1 TH/P6-38 Integrated Heat Transport Simulation of High Ion Temperature Plasma of LHD S. Murakami 1, H. Yamaguchi 1, A. Sakai 1, K. Nagaoka 2, H. Takahashi 2, H. Nakano 2, M. Osakabe 2, K. Ida 2, M. Yoshinuma
More informationImpact of neutral atoms on plasma turbulence in the tokamak edge region
Impact of neutral atoms on plasma turbulence in the tokamak edge region C. Wersal P. Ricci, F.D. Halpern, R. Jorge, J. Morales, P. Paruta, F. Riva Theory of Fusion Plasmas Joint Varenna-Lausanne International
More informationThe Equivalence Problem: EinsteinMaxwell Solutions
Utah State University DigitalCommons@USU Physics Capstone Project Physics Student Research 5-6-2016 The Equivalence Problem: EinsteinMaxwell Solutions Rebecca Whitney Utah State University Follow this
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 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 informationTURBULENT TRANSPORT THEORY
ASDEX Upgrade Max-Planck-Institut für Plasmaphysik TURBULENT TRANSPORT THEORY C. Angioni GYRO, J. Candy and R.E. Waltz, GA The problem of Transport Transport is the physics subject which studies the physical
More informationElectrical Transport. Ref. Ihn Ch. 10 YC, Ch 5; BW, Chs 4 & 8
Electrical Transport Ref. Ihn Ch. 10 YC, Ch 5; BW, Chs 4 & 8 Electrical Transport The study of the transport of electrons & holes (in semiconductors) under various conditions. A broad & somewhat specialized
More informationIonization Detectors. Mostly Gaseous Detectors
Ionization Detectors Mostly Gaseous Detectors Introduction Ionization detectors were the first electrical devices developed for radiation detection During the first half of the century: 3 basic types of
More informationRadiative & Magnetohydrodynamic Shocks
Chapter 4 Radiative & Magnetohydrodynamic Shocks I have been dealing, so far, with non-radiative shocks. Since, as we have seen, a shock raises the density and temperature of the gas, it is quite likely,
More informationMagnetic Reconnection Propulsion
The Space Congress Proceedings 2016 (44th) The Journey: Further Exploration for Universal Opportunities May 24th, 7:30 AM Magnetic Reconnection Propulsion D. L. Chesny Magnetic Reconnection Propulsion
More informationChapter 2 HEAT CONDUCTION EQUATION
Heat and Mass Transfer: Fundamentals & Applications 5th Edition in SI Units Yunus A. Çengel, Afshin J. Ghajar McGraw-Hill, 2015 Chapter 2 HEAT CONDUCTION EQUATION Mehmet Kanoglu University of Gaziantep
More informationChapter 2 HEAT CONDUCTION EQUATION
Heat and Mass Transfer: Fundamentals & Applications Fourth Edition Yunus A. Cengel, Afshin J. Ghajar McGraw-Hill, 2011 Chapter 2 HEAT CONDUCTION EQUATION Mehmet Kanoglu University of Gaziantep Copyright
More informationNotes on the Magnetic Mirror Effect*' **
737 Progress of Theoretical Physics, Vol. 20, No.5, November 1958 Notes on the Magnetic Mirror Effect*' ** Masatomo SA TO Department of Physics, College of Science and Engineering, Nihon University, Tokyo
More informationBunno, M.; Nakamura, Y.; Suzuki, Y. Matsunaga, G.; Tani, K. Citation Plasma Science and Technology (
Title The Finite Beta Effects on the Toro Tokamak Plasma Author(s) Bunno, M.; Nakamura, Y.; Suzuki, Y. Matsunaga, G.; Tani, K. Citation Plasma Science and Technology (2013 Issue Date 2013-02 URL http://hdl.handle.net/2433/173038
More informationImportance of Accurate Computation of Secondary Electron Emission for ModelingSpacecraft Charging
Utah State University DigitalCommons@USU All Physics Faculty Publications Physics 1-1-2005 Importance of Accurate Computation of Secondary Electron Emission for ModelingSpacecraft Charging Sebastien Clerc
More informationSpring Not-Break Review Assignment
Name AP Physics B Spring Not-Break Review Assignment Date Mrs. Kelly. A kilogram block is released from rest at the top of a curved incline in the shape of a quarter of a circle of radius R. The block
More informationSelf-Organization of Plasmas with Flows
Self-Organization of Plasmas with Flows ICNSP 2003/ 9/10 Graduate School of Frontier Sciences,, National Institute for Fusion Science R. NUMATA, Z. YOSHIDA, T. HAYASHI ICNSP 2003/ 9/10 p.1/14 Abstract
More informationFundamentals of Magnetic Island Theory in Tokamaks
Fundamentals of Magnetic Island Theory in Tokamaks Richard Fitzpatrick Institute for Fusion Studies University of Texas at Austin Austin, TX, USA Talk available at http://farside.ph.utexas.edu/talks/talks.html
More informationThe Physics of Fluids and Plasmas
The Physics of Fluids and Plasmas An Introduction for Astrophysicists ARNAB RAI CHOUDHURI CAMBRIDGE UNIVERSITY PRESS Preface Acknowledgements xiii xvii Introduction 1 1. 3 1.1 Fluids and plasmas in the
More informationPhysics For Scientists and Engineers A Strategic Approach 3 rd Edition, AP Edition, 2013 Knight
For Scientists and Engineers A Strategic Approach 3 rd Edition, AP Edition, 2013 Knight To the Advanced Placement Topics for C *Advanced Placement, Advanced Placement Program, AP, and Pre-AP are registered
More informationwhere the index 2 indicates the particle species (electrons and different ion species if present). With
hapter 3 Magnetohydrodynamics luid equations are probably the most widely used equations for the description of inhomogeneous plasmas. While the phase fluid which is governed by the Boltzmann equation
More informationGA A24016 PHYSICS OF OFF-AXIS ELECTRON CYCLOTRON CURRENT DRIVE
GA A6 PHYSICS OF OFF-AXIS ELECTRON CYCLOTRON CURRENT DRIVE by R. PRATER, C.C. PETTY, R. HARVEY, Y.R. LIN-LIU, J.M. LOHR, and T.C. LUCE JULY DISCLAIMER This report was prepared as an account of work sponsored
More informationThermal Equilibrium in Nebulae 1. For an ionized nebula under steady conditions, heating and cooling processes that in
Thermal Equilibrium in Nebulae 1 For an ionized nebula under steady conditions, heating and cooling processes that in isolation would change the thermal energy content of the gas are in balance, such that
More informationA note on the plasma sheath and the Bohm Criterion
A note on the plasma sheath and the Bohm Criterion G.D. Severn Dept. of Physics, University of San Diego, San Diego CA 92110 (Dated: April 6, 2006) PACS numbers: 52.27.Aj, 52.27.Cm The word sheath in connection
More informationPREDICTIVE MODELING OF PLASMA HALO EVOLUTION IN POST-THERMAL QUENCH DISRUPTING PLASMAS
GA A25488 PREDICTIVE MODELING OF PLASMA HALO EVOLUTION IN POST-THERMAL QUENCH DISRUPTING PLASMAS by D.A. HUMPHREYS, D.G. WHYTE, M. BAKHTIARI, R.D. DERANIAN, E.M. HOLLMANN, A.W. HYATT, T.C. JERNIGAN, A.G.
More informationRadioactivity. PC1144 Physics IV. 1 Objectives. 2 Equipment List. 3 Theory
PC1144 Physics IV Radioactivity 1 Objectives Investigate the analogy between the decay of dice nuclei and radioactive nuclei. Determine experimental and theoretical values of the decay constant λ and the
More informationSawtooth mixing of alphas, knock on D, T ions and its influence on NPA spectra in ITER plasma
Sawtooth mixing of alphas, knock on D, T ions and its influence on NPA spectra in ITER plasma F.S. Zaitsev 1, 4, N.N. Gorelenkov 2, M.P. Petrov 3, V.I. Afanasyev 3, M.I. Mironov 3 1 Scientific Research
More informationElectrical Discharges Characterization of Planar Sputtering System
International Journal of Recent Research and Review, Vol. V, March 213 ISSN 2277 8322 Electrical Discharges Characterization of Planar Sputtering System Bahaa T. Chaid 1, Nathera Abass Ali Al-Tememee 2,
More informationProbing the Cosmos with light and gravity: multimessenger astronomy in the gravitational wave era
Utah State University DigitalCommons@USU Colloquia and Seminars Astrophysics 9-7-2011 Probing the Cosmos with light and gravity: multimessenger astronomy in the gravitational wave era Shane L. Larson Utah
More informationOn existence of resistive magnetohydrodynamic equilibria
arxiv:physics/0503077v1 [physics.plasm-ph] 9 Mar 2005 On existence of resistive magnetohydrodynamic equilibria H. Tasso, G. N. Throumoulopoulos Max-Planck-Institut für Plasmaphysik Euratom Association
More informationIs plasma important? Influence molecule formation?
Is plasma important? Influence molecule formation? Plasma Structure (space & time) Influence? Daan Schram Eindhoven University of Technology d.c.schram@tue.nl http://www.tue.nl/en/employee/ep/e/d/ep-uid/19780797/?no_cache=1&chash=e23e831cf0c6bebeac6023f04dd3c4b6
More informationPlasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi
Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi Lecture No. # 03 DC Conductivity and Negative Differential Conductivity Well friends, in this lecture, I
More informationIonosphères planétaires (introduction)
Ionosphères planétaires (introduction) email: arnaud.zaslavsky@obspm.fr Structure de l atmosphère terrestre Temperature gradients determined by IR radiation from Earth (low altitude Troposhere) And from
More informationEquilibrium and transport in Tokamaks
Equilibrium and transport in Tokamaks Jacques Blum Laboratoire J.-A. Dieudonné, Université de Nice Sophia-Antipolis Parc Valrose 06108 Nice Cedex 02, France jblum@unice.fr 08 septembre 2008 Jacques Blum
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 informationA MIRROR FUSION DEVICE FOR ADVANCED SPACE PROPULSION
A MIRROR FUSION DEVICE FOR ADVANCED SPACE PROPULSION Terry Kammash and Myoung-Jae Lee Department of Nuclear Engineering The University of Michigan Ann Arbor, M148109 (313) 764-0205 Abstract An open-ended
More informationHelium-3 transport experiments in the scrape-off layer with the Alcator C-Mod omegatron ion mass spectrometer
PHYSICS OF PLASMAS VOLUME 7, NUMBER 11 NOVEMBER 2000 Helium-3 transport experiments in the scrape-off layer with the Alcator C-Mod omegatron ion mass spectrometer R. Nachtrieb a) Lutron Electronics Co.,
More informationIntroduction. Statement of Problem. The governing equations for porous materials with Darcy s law can be written in dimensionless form as:
Symbolic Calculation of Free Convection for Porous Material of Quadratic Heat Generation in a Circular Cavity Kamyar Mansour Amirkabir University of technology, Tehran, Iran, 15875-4413 mansour@aut.ac.ir
More informationComparison of plasma breakdown with a carbon and ITER-like wall
Comparison of plasma breakdown with a carbon and ITER-like wall P.C. de Vries, A.C.C. Sips, H.T. Kim, P.J. Lomas, F. Maviglia, R. Albanese, I. Coffey, E. Joffrin, M. Lehnen, A. Manzanares, M. O Mulane,
More informationThe Riemann curvature tensor, its invariants, and their use in the classification of spacetimes
DigitalCommons@USU Presentations and Publications 3-20-2015 The Riemann curvature tensor, its invariants, and their use in the classification of spacetimes Follow this and additional works at: http://digitalcommons.usu.edu/dg_pres
More informationρ c (2.1) = 0 (2.3) B = 0. (2.4) E + B
Chapter 2 Basic Plasma Properties 2.1 First Principles 2.1.1 Maxwell s Equations In general magnetic and electric fields are determined by Maxwell s equations, corresponding boundary conditions and the
More information13 Spherical Coordinates
Utah State University DigitalCommons@USU Foundations of Wave Phenomena Library Digital Monographs 8-204 3 Spherical Coordinates Charles G. Torre Department of Physics, Utah State University, Charles.Torre@usu.edu
More informationChapter 27. Current and Resistance
Chapter 27 Current and Resistance Electric Current Most practical applications of electricity deal with electric currents. The electric charges move through some region of space. The resistor is a new
More informationLecture 28. Key words: Heat transfer, conduction, convection, radiation, furnace, heat transfer coefficient
Lecture 28 Contents Heat transfer importance Conduction Convection Free Convection Forced convection Radiation Radiation coefficient Illustration on heat transfer coefficient 1 Illustration on heat transfer
More informationPlasma Spectroscopy Inferences from Line Emission
Plasma Spectroscopy Inferences from Line Emission Ø From line λ, can determine element, ionization state, and energy levels involved Ø From line shape, can determine bulk and thermal velocity and often
More informationCalculation of alpha particle redistribution in sawteeth using experimentally reconstructed displacement eigenfunctions
Calculation of alpha particle redistribution in sawteeth using experimentally reconstructed displacement eigenfunctions R. Farengo, H. E. Ferrari,2, M.-C. Firpo 3, P. L. Garcia-Martinez 2,3, A. F. Lifschitz
More information