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2b Coulomb collisions in plasmas
2b Coulomb collisions in plasmas
Published: 2015/09/15
Channel: Plasma Physics and Applications
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
Coulomb collision Meaning
Coulomb collision Meaning
Published: 2015/04/22
Channel: SDictionary
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
collision response with coulomb friction
collision response with coulomb friction
Published: 2013/03/23
Channel: Glenn Fiedler
Physics - E & M: Coulomb
Physics - E & M: Coulomb's Law (8 of 8) Example 4 (Challenging Problems)
Published: 2016/09/07
Channel: Michel van Biezen
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
collision response linear
collision response linear
Published: 2013/03/23
Channel: Glenn Fiedler
Coulomb Focusing: Helping Electrons Hit the Bullseye
Coulomb Focusing: Helping Electrons Hit the Bullseye
Published: 2013/10/02
Channel: Aaron Parsons
Robust Treatment of Simultaneous Collisions
Robust Treatment of Simultaneous Collisions
Published: 2012/12/26
Channel: Walt Disney Animation Studios
Accurate 2D collision responses
Accurate 2D collision responses
Published: 2014/04/11
Channel: Guillaume Racicot
collision response linear wrong
collision response linear wrong
Published: 2013/03/23
Channel: Glenn Fiedler
coulomb
coulomb's law.mp4
Published: 2012/02/21
Channel: szygmunt
Electric Charges: "Coulomb
Electric Charges: "Coulomb's Law" 1959 PSSC; Eric Rogers; Princeton University
Published: 2017/05/18
Channel: Jeff Quitney
Coulomb
Coulomb's Law, Force of a Proton and an Electron in Hydrogen Atom
Published: 2014/01/26
Channel: Step-by-Step Science
angular collision response new
angular collision response new
Published: 2013/03/23
Channel: Glenn Fiedler
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Published: 2010/09/03
Channel: Ryo Kikuuwe
angular collision response without friction
angular collision response without friction
Published: 2013/03/23
Channel: Glenn Fiedler
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Published: 2010/09/02
Channel: Ryo Kikuuwe
collision response rolling friction
collision response rolling friction
Published: 2013/03/23
Channel: Glenn Fiedler
Inelastic Collision Example # 1
Inelastic Collision Example # 1
Published: 2012/12/27
Channel: AK LECTURES
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
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
N-body Simulation of Counter-streaming ion beams.
N-body Simulation of Counter-streaming ion beams.
Published: 2017/08/08
Channel: Andrew Chap
Collision response with rotation
Collision response with rotation
Published: 2016/05/01
Channel: RobotZer0
Purdue PHYS 342 L16.2: Nuclear Reactions: Fusion
Purdue PHYS 342 L16.2: Nuclear Reactions: Fusion
Published: 2014/12/08
Channel: nanohubtechtalks
Coulomb
Coulomb's Law Overview
Published: 2013/04/14
Channel: Frank McCulley
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
[Gazebo-DART] Coulomb friction test
[Gazebo-DART] Coulomb friction test
Published: 2015/01/16
Channel: Jeongseok Lee
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.
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
Collision Response
Collision Response
Published: 2015/02/22
Channel: Fan Li
go stone spinning
go stone spinning
Published: 2013/03/23
Channel: Glenn Fiedler
Episode 64 - Collision Response: Sliding
Episode 64 - Collision Response: Sliding
Published: 2013/04/06
Channel: TheChernoProject
Collision Detection and Response - Interactive 3D Graphics
Collision Detection and Response - Interactive 3D Graphics
Published: 2015/02/23
Channel: Udacity
collision response no rotation
collision response no rotation
Published: 2016/05/15
Channel: RobotZer0
Two Protons outside the range of strong Coulomb force produces Coulomb repulsion
Two Protons outside the range of strong Coulomb force produces Coulomb repulsion
Published: 2010/10/07
Channel: Bengt Nyman
Introduction to Friction
Introduction to Friction
Published: 2012/03/06
Channel: Darryl Morrell
freight car collision problem--momentum conservations
freight car collision problem--momentum conservations
Published: 2010/08/02
Channel: gbsphysics
Slow speed collision between 2 protons resulting in repulsion
Slow speed collision between 2 protons resulting in repulsion
Published: 2010/08/17
Channel: Bengt Nyman
Linear Algebra- 2D Collision Response - Position
Linear Algebra- 2D Collision Response - Position
Published: 2012/08/06
Channel: Jamie King
SAT collision detection/response
SAT collision detection/response
Published: 2013/09/09
Channel: Brutal Design
2D Collision Response Fail
2D Collision Response Fail
Published: 2013/03/04
Channel: Seigata
PHYSICS 8A COLLISION LAB part 1
PHYSICS 8A COLLISION LAB part 1
Published: 2014/04/28
Channel: Gnaeus Pompeius
Physique 40S - collision à 2 dimensions.wmv
Physique 40S - collision à 2 dimensions.wmv
Published: 2012/02/17
Channel: DSFMvideo
Charge Posturing, dipole formation and Coulomb attraction between 2 Hydrogen atoms
Charge Posturing, dipole formation and Coulomb attraction between 2 Hydrogen atoms
Published: 2010/08/17
Channel: Bengt Nyman
Quantité de Mouvement et Propulsion - Mathrix
Quantité de Mouvement et Propulsion - Mathrix
Published: 2017/02/18
Channel: Mathrix
Charge posturing and Coulomb attraction between 2 neutrons represented by 3 quarks
Charge posturing and Coulomb attraction between 2 neutrons represented by 3 quarks
Published: 2010/08/13
Channel: Bengt Nyman
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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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