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2b Coulomb collisions in plasmas
2b Coulomb collisions in plasmas
Published: 2015/09/15
Channel: Plasma Physics and Applications
Coulomb collision Meaning
Coulomb collision Meaning
Published: 2015/04/22
Channel: SDictionary
14A Coulomb Collisions | Introduction to Plasma Physics by J D Callen
14A Coulomb Collisions | Introduction to Plasma Physics by J D Callen
Published: 2015/12/24
Channel: Lucius Fox
collision response with coulomb friction
collision response with coulomb friction
Published: 2013/03/23
Channel: Glenn Fiedler
Special collision between 2 Protons entering inside the range of strong Coulomb force
Special collision between 2 Protons entering inside the range of strong Coulomb force
Published: 2010/08/17
Channel: Bengt Nyman
Energy & Chemistry: Crash Course Chemistry #17
Energy & Chemistry: Crash Course Chemistry #17
Published: 2013/06/11
Channel: CrashCourse
When Protons Collide
When Protons Collide
Published: 2016/05/04
Channel: Boston University
Proton collision and penetration into the range of strong Coulomb force
Proton collision and penetration into the range of strong Coulomb force
Published: 2010/10/08
Channel: Bengt Nyman
Robust Treatment of Simultaneous Collisions
Robust Treatment of Simultaneous Collisions
Published: 2012/12/26
Channel: Walt Disney Animation Studios
Collisions (Momentum Activity, CP Physics)
Collisions (Momentum Activity, CP Physics)
Published: 2013/12/09
Channel: Dan Welty
Physics: How many electrons are in 1 coulomb?
Physics: How many electrons are in 1 coulomb?
Published: 2014/05/17
Channel: Smoleny1
Coulomb
Coulomb's Law, Force of a Proton and an Electron in Hydrogen Atom
Published: 2014/01/26
Channel: Step-by-Step Science
Conservation of momentum: Concept of Collision CBSE 11th 12th IIT JEE physics AIEEE BITSAT PMT ISEET
Conservation of momentum: Concept of Collision CBSE 11th 12th IIT JEE physics AIEEE BITSAT PMT ISEET
Published: 2012/10/10
Channel: ConquerIITJEE
Coulomb Focusing: Helping Electrons Hit the Bullseye
Coulomb Focusing: Helping Electrons Hit the Bullseye
Published: 2013/10/02
Channel: Aaron Parsons
collision response linear
collision response linear
Published: 2013/03/23
Channel: Glenn Fiedler
Gravity & Coulomb repulsion
Gravity & Coulomb repulsion
Published: 2009/07/09
Channel: Computer Physics Lab
angular collision response new
angular collision response new
Published: 2013/03/23
Channel: Glenn Fiedler
angular collision response without friction
angular collision response without friction
Published: 2013/03/23
Channel: Glenn Fiedler
collision response linear wrong
collision response linear wrong
Published: 2013/03/23
Channel: Glenn Fiedler
James D. Callen: Fluid and transport modeling of plasmas 1: collisional plasma kinetics, solutions
James D. Callen: Fluid and transport modeling of plasmas 1: collisional plasma kinetics, solutions
Published: 2015/08/06
Channel: Centre International de Rencontres Mathématiques
collision response rolling friction
collision response rolling friction
Published: 2013/03/23
Channel: Glenn Fiedler
Lec 15: Momentum and Its Conservation | 8.01 Classical Mechanics, Fall 1999 (Walter Lewin)
Lec 15: Momentum and Its Conservation | 8.01 Classical Mechanics, Fall 1999 (Walter Lewin)
Published: 2014/12/10
Channel: For the Allure of Physics
8.01x - Module 18 01   Elastic collision of sliders with unequal masses, one at rest
8.01x - Module 18 01 Elastic collision of sliders with unequal masses, one at rest
Published: 2015/02/16
Channel: Lectures by Walter Lewin. They will make you ♥ Physics.
Farade
Farade's Experiment
Published: 2017/04/02
Channel: Knight King
go stone spinning
go stone spinning
Published: 2013/03/23
Channel: Glenn Fiedler
Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly el
Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly el
Published: 2015/12/19
Channel: WNY Tutor
Particle Physics: "Electrons in a Uniform Magnetic Field" 1959 Educational Services
Particle Physics: "Electrons in a Uniform Magnetic Field" 1959 Educational Services
Published: 2013/03/24
Channel: Jeff Quitney
Particle Dynamics Screencast 4.1 - Coulomb Friction
Particle Dynamics Screencast 4.1 - Coulomb Friction
Published: 2015/03/30
Channel: DrDynamics
Collision response with rotation
Collision response with rotation
Published: 2016/05/01
Channel: Pentagrid
Visualization of Interactions with Matter - Alpha Radiation
Visualization of Interactions with Matter - Alpha Radiation
Published: 2015/04/07
Channel: Nuclear Power for Everybody
dynamic simulation of human hand grasping (proof of concept)
dynamic simulation of human hand grasping (proof of concept)
Published: 2012/03/09
Channel: Qiushi Fu
Keshe reactor simulation animation. - YouTube2.flv
Keshe reactor simulation animation. - YouTube2.flv
Published: 2012/12/15
Channel: kevin chambers
James D. Callen: Fluid and transport modeling of plasmas 2: kinetic and fluid solutions of PKE
James D. Callen: Fluid and transport modeling of plasmas 2: kinetic and fluid solutions of PKE
Published: 2015/08/06
Channel: Centre International de Rencontres Mathématiques
SiconosMechanics 3000 apericube falling on ground
SiconosMechanics 3000 apericube falling on ground
Published: 2016/03/22
Channel: Siconos
SiconosMechanics. apericubes shake by a vibrating ground
SiconosMechanics. apericubes shake by a vibrating ground
Published: 2016/11/08
Channel: Siconos
Electron
Electron
Published: 2016/03/01
Channel: Century Old
Java 2D physics from scratch - Rigid Body Test #2: linear impulse resolution (no rotation)
Java 2D physics from scratch - Rigid Body Test #2: linear impulse resolution (no rotation)
Published: 2017/03/24
Channel: Leo Ono
[量子力學]第10-1講、Collision Theory
[量子力學]第10-1講、Collision Theory
Published: 2012/11/14
Channel: 臺大科學教育發展中心 .NTU CASE
SiconosMechanics few cubes in an hopper
SiconosMechanics few cubes in an hopper
Published: 2016/03/24
Channel: Siconos
Physics simulation: Claus Fuhrer
Physics simulation: Claus Fuhrer's truck, suspension, articulated bed
Published: 2009/03/27
Channel: Sequoia
Linear Algebra- 2D Collision Response - Position
Linear Algebra- 2D Collision Response - Position
Published: 2012/08/06
Channel: Jamie King
Line 23a20  Anisotropic Kepler Mass Tensor Coulomb Poincaré Trajectories  WOW SETI
Line 23a20 Anisotropic Kepler Mass Tensor Coulomb Poincaré Trajectories WOW SETI
Published: 2014/04/27
Channel: theideagirlsays
Introduction to Momentum (Collisions, Conservation of Momentum and Variable mass Systems)
Introduction to Momentum (Collisions, Conservation of Momentum and Variable mass Systems)
Published: 2017/03/02
Channel: A Journey Into Physics
Disk Toy
Disk Toy
Published: 2012/06/28
Channel: Benedek Vartok
Animated Digital Fabric Collisions | Columbia Computer Graphics Group
Animated Digital Fabric Collisions | Columbia Computer Graphics Group
Published: 2011/01/04
Channel: DigitalDesignTherapy
Line 18 a3z5b3a Nuclear Fusion Collision Spin Polarized Plasmas Electron 5g WOW SETI
Line 18 a3z5b3a Nuclear Fusion Collision Spin Polarized Plasmas Electron 5g WOW SETI
Published: 2012/04/13
Channel: theideagirlsays
Line 18 a3z5b5 Coulomb Barrier Nuclear Bi-sphere Fiber Laser Light Resonators 5g WOW SETI
Line 18 a3z5b5 Coulomb Barrier Nuclear Bi-sphere Fiber Laser Light Resonators 5g WOW SETI
Published: 2012/04/17
Channel: theideagirlsays
Physics-based Assistive Grasping for Robust Object Manipulation in Virtual Reality
Physics-based Assistive Grasping for Robust Object Manipulation in Virtual Reality
Published: 2016/08/15
Channel: Kiran Nasim
La théorie des collisions Partie 2
La théorie des collisions Partie 2
Published: 2016/02/24
Channel: Mme Chimie
Line 18 a3z5b4 Stern-Gerlach Spin Nuclear FUSE Polarized Fuels Coulomb Barrier 5g WOW SETI
Line 18 a3z5b4 Stern-Gerlach Spin Nuclear FUSE Polarized Fuels Coulomb Barrier 5g WOW SETI
Published: 2012/04/17
Channel: theideagirlsays
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WIKIPEDIA ARTICLE

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A Coulomb collision is a binary elastic collision between two charged particles interacting through their own electric field. As with any inverse-square law, the resulting trajectories of the colliding particles is a hyperbolic Keplerian orbit. This type of collision is common in plasmas where the typical kinetic energy of the particles is too large to produce a significant deviation from the initial trajectories of the colliding particles, and the cumulative effect of many collisions is considered instead.

Mathematical treatment for plasmas[edit]

In a plasma a Coulomb collision rarely results in a large deflection. The cumulative effect of the many small angle collisions, however, is often larger than the effect of the few large angle collisions that occur, so it is instructive to consider the collision dynamics in the limit of small deflections.

We can consider an electron of charge -e and mass me passing a stationary ion of charge +Ze and much larger mass at a distance b with a speed v. The perpendicular force is (1/4πε0)Ze2/b2 at the closest approach and the duration of the encounter is about b/v. The product of these expressions divided by the mass is the change in perpendicular velocity:

Note that the deflection angle is proportional to . Fast particles are "slippery" and thus dominate many transport processes. The efficiency of velocity-matched interactions is also the reason that fusion products tend to heat the electrons rather than (as would be desirable) the ions. If an electric field is present, the faster electrons feel less drag and become even faster in a "run-away" process.

In passing through a field of ions with density n, an electron will have many such encounters simultaneously, with various impact parameters (distance to the ion) and directions. The cumulative effect can be described as a diffusion of the perpendicular momentum. The corresponding diffusion constant is found by integrating the squares of the individual changes in momentum. The rate of collisions with impact parameter between b and (b+db) is nv(2πb db), so the diffusion constant is given by

Obviously the integral diverges toward both small and large impact parameters. At small impact parameters, the momentum transfer also diverges. This is clearly unphysical since under the assumptions used here, the final perpendicular momentum cannot take on a value higher than the initial momentum. Setting the above estimate for equal to mv, we find the lower cut-off to the impact parameter to be about

We can also use πb02 as an estimate of the cross section for large-angle collisions. Under some conditions there is a more stringent lower limit due to quantum mechanics, namely the de Broglie wavelength of the electron, h/(mev).

At large impact parameters, the charge of the ion is shielded by the tendency of electrons to cluster in the neighborhood of the ion and other ions to avoid it. The upper cut-off to the impact parameter should thus be approximately equal to the Debye length:

Coulomb logarithm[edit]

The integral of 1/b thus yields the logarithm of the ratio of the upper and lower cut-offs. This number is known as the Coulomb logarithm and is designated by either lnΛ or λ. It is the factor by which small-angle collisions are more effective than large-angle collisions. For many plasmas of interest it takes on values between 5 and 15. (For convenient formulas, see pages 34 and 35 of the NRL Plasma formulary.) The limits of the impact parameter integral are not sharp, but are uncertain by factors on the order of unity, leading to theoretical uncertainties on the order of 1/λ. For this reason it is often justified to simply take the convenient choice λ = 10.

The analysis here yields the scalings and orders of magnitude. For formulas derived from careful calculations, see page 31 ff. in the NRL Plasma formulary.

See also[edit]

External links[edit]

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