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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
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
Big Balls! Thermal Energy in Collisions
Big Balls! Thermal Energy in Collisions
Published: 2017/10/14
Channel: A Level Physics Online
Robust Treatment of Simultaneous Collisions
Robust Treatment of Simultaneous Collisions
Published: 2012/12/26
Channel: Walt Disney Animation Studios
Coulomb Focusing: Helping Electrons Hit the Bullseye
Coulomb Focusing: Helping Electrons Hit the Bullseye
Published: 2013/10/02
Channel: Aaron Parsons
Electric Charges: "Coulomb
Electric Charges: "Coulomb's Law" 1959 PSSC; Eric Rogers; Princeton University
Published: 2017/05/18
Channel: Jeff Quitney
Momentum and Collision Problemz | CCP10 |
Momentum and Collision Problemz | CCP10 | 'Sup Crash Course | Doc Physics
Published: 2016/06/03
Channel: Doc Schuster
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
collision response rolling friction
collision response rolling friction
Published: 2013/03/23
Channel: Glenn Fiedler
Collision Detection and Response - Interactive 3D Graphics
Collision Detection and Response - Interactive 3D Graphics
Published: 2015/02/23
Channel: Udacity
Gravity & Coulomb repulsion
Gravity & Coulomb repulsion
Published: 2009/07/09
Channel: Computer Physics Lab
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.
angular collision response new
angular collision response new
Published: 2013/03/23
Channel: Glenn Fiedler
2D Collision Response
2D Collision Response
Published: 2012/08/03
Channel: Jamie King
Physics: "Elastic Collision and Stored Energy" 1961 PSSC; James Strickland, Energy, Momentum...
Physics: "Elastic Collision and Stored Energy" 1961 PSSC; James Strickland, Energy, Momentum...
Published: 2017/06/23
Channel: Jeff Quitney
ATLAS 13 TeV Stable Beam Collisions
ATLAS 13 TeV Stable Beam Collisions
Published: 2015/06/08
Channel: ATLAS Experiment
N-body Simulation of Counter-streaming ion beams.
N-body Simulation of Counter-streaming ion beams.
Published: 2017/08/08
Channel: Andrew Chap
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
angular collision response without friction
angular collision response without friction
Published: 2013/03/23
Channel: Glenn Fiedler
Lecture 11 - Discharge physics, Gaseous electronics, mean free path, collision frequency
Lecture 11 - Discharge physics, Gaseous electronics, mean free path, collision frequency
Published: 2017/05/22
Channel: USYD - Senior Plasma Physics Lectures
collision response linear
collision response linear
Published: 2013/03/23
Channel: Glenn Fiedler
Episode 64 - Collision Response: Sliding
Episode 64 - Collision Response: Sliding
Published: 2013/04/06
Channel: TheChernoProject
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
Accurate 2D collision responses
Accurate 2D collision responses
Published: 2014/04/11
Channel: Guillaume Racicot
Elastic Collisions   Lewin at MIT
Elastic Collisions Lewin at MIT
Published: 2014/10/28
Channel: Peter Schwartz
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
go stone spinning
go stone spinning
Published: 2013/03/23
Channel: Glenn Fiedler
Coulomb
Coulomb's Law Overview
Published: 2013/04/14
Channel: Frank McCulley
1c Plasma definition: frequencies and parameters
1c Plasma definition: frequencies and parameters
Published: 2015/09/15
Channel: Plasma Physics and Applications
Coulomb barrier Meaning
Coulomb barrier Meaning
Published: 2015/04/22
Channel: SDictionary
6.- Classical Electron Collision
6.- Classical Electron Collision
Published: 2008/12/27
Channel: SpinningParticle
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Published: 2010/09/03
Channel: Ryo Kikuuwe
Inelastic Collision Analysis
Inelastic Collision Analysis
Published: 2009/12/14
Channel: Dan Fullerton
collision response no rotation
collision response no rotation
Published: 2016/05/15
Channel: RobotZer0
ELECTRO STATIC (COULOMB FORCE)
ELECTRO STATIC (COULOMB FORCE)
Published: 2017/11/13
Channel: Aakash krishna
Purdue PHYS 342 L16.2: Nuclear Reactions: Fusion
Purdue PHYS 342 L16.2: Nuclear Reactions: Fusion
Published: 2014/12/08
Channel: nanohubtechtalks
What is Radiation Measurements (Exposure in Air)
What is Radiation Measurements (Exposure in Air)
Published: 2017/06/01
Channel: RadTechBootCamp
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Published: 2010/09/02
Channel: Ryo Kikuuwe
Inelastic Collision Example # 1
Inelastic Collision Example # 1
Published: 2012/12/27
Channel: AK LECTURES
Linear Algebra- 2D Collision Response - Position
Linear Algebra- 2D Collision Response - Position
Published: 2012/08/06
Channel: Jamie King
Simulation of Coulomb crystal of 2685 Ca+
Simulation of Coulomb crystal of 2685 Ca+
Published: 2016/11/03
Channel: Thierry Matthey
Buggy Collision Lab Group 4
Buggy Collision Lab Group 4
Published: 2015/09/21
Channel: Mason Keys
What Is The Definition Of Collision Insurance?
What Is The Definition Of Collision Insurance?
Published: 2017/07/15
Channel: sparky STARS
proton collision jet
proton collision jet
Published: 2010/11/30
Channel: noxjumblebox
SiconosMechanics few cubes in an hopper
SiconosMechanics few cubes in an hopper
Published: 2016/03/24
Channel: Siconos
[Gazebo-DART] Coulomb friction test
[Gazebo-DART] Coulomb friction test
Published: 2015/01/16
Channel: Jeongseok Lee
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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[permanent dead link].) 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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