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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
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
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 Detection and Response - Interactive 3D Graphics
Collision Detection and Response - Interactive 3D Graphics
Published: 2015/02/23
Channel: Udacity
When Protons Collide
When Protons Collide
Published: 2016/05/04
Channel: Boston University
Robust Treatment of Simultaneous Collisions
Robust Treatment of Simultaneous Collisions
Published: 2012/12/26
Channel: Walt Disney Animation Studios
Physics: How many electrons are in 1 coulomb?
Physics: How many electrons are in 1 coulomb?
Published: 2014/05/17
Channel: Smoleny1
Inelastic Collision Example # 1
Inelastic Collision Example # 1
Published: 2012/12/27
Channel: AK LECTURES
Physics 30: Lesson 4 - Elastic and Inelastic Collisions
Physics 30: Lesson 4 - Elastic and Inelastic Collisions
Published: 2014/08/15
Channel: ms. Booth
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
Elastic Collisions
Elastic Collisions
Published: 2016/01/04
Channel: Brad Homoelle
6.- Classical Electron Collision
6.- Classical Electron Collision
Published: 2008/12/27
Channel: SpinningParticle
collision response linear
collision response linear
Published: 2013/03/23
Channel: Glenn Fiedler
collision response linear wrong
collision response linear wrong
Published: 2013/03/23
Channel: Glenn Fiedler
angular collision response without friction
angular collision response without friction
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
N-body Simulation of Counter-streaming ion beams.
N-body Simulation of Counter-streaming ion beams.
Published: 2017/08/08
Channel: Andrew Chap
SAT collision detection/response
SAT collision detection/response
Published: 2013/09/09
Channel: Brutal Design
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
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
Coulomb
Coulomb's Law Overview
Published: 2013/04/14
Channel: Frank McCulley
Electric Charges: "Coulomb
Electric Charges: "Coulomb's Law" 1959 PSSC; Eric Rogers; Princeton University
Published: 2017/05/18
Channel: Jeff Quitney
Collision Meaning
Collision Meaning
Published: 2015/04/19
Channel: SDictionary
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
Physique 40S - collision à 2 dimensions.wmv
Physique 40S - collision à 2 dimensions.wmv
Published: 2012/02/17
Channel: DSFMvideo
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.
Accurate 2D collision responses
Accurate 2D collision responses
Published: 2014/04/11
Channel: Guillaume Racicot
collision response rolling friction
collision response rolling friction
Published: 2013/03/23
Channel: Glenn Fiedler
go stone spinning
go stone spinning
Published: 2013/03/23
Channel: Glenn Fiedler
Coulomb attraction Meaning
Coulomb attraction Meaning
Published: 2015/04/22
Channel: SDictionary
Deuterium nucleus formed by Coulomb forces between 1 proton and 1 neutron
Deuterium nucleus formed by Coulomb forces between 1 proton and 1 neutron
Published: 2010/10/07
Channel: Bengt Nyman
What Is The Definition Of Collision Insurance?
What Is The Definition Of Collision Insurance?
Published: 2017/07/18
Channel: funny sparky
Electrostatics Starting Concepts, Conservation of Charge, Conductors, Coulomb
Electrostatics Starting Concepts, Conservation of Charge, Conductors, Coulomb's Law
Published: 2015/01/26
Channel: Greg Clements
Impulse based collision Response
Impulse based collision Response
Published: 2008/05/27
Channel: damien murtagh
Net electric field from multiple charges in 2D | Physics | Khan Academy
Net electric field from multiple charges in 2D | Physics | Khan Academy
Published: 2016/07/29
Channel: Khan Academy Physics
Fokker-Planck Simulation (Collision term = 0) Cross-section
Fokker-Planck Simulation (Collision term = 0) Cross-section
Published: 2008/08/15
Channel: DSaitou
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Published: 2010/09/03
Channel: Ryo Kikuuwe
SPH4U 5.5 Collisions in two dimensions: Glancing collisions
SPH4U 5.5 Collisions in two dimensions: Glancing collisions
Published: 2016/06/21
Channel: OnPhysics
Coulomb
Coulomb's Law
Published: 2014/02/03
Channel: SciencewithSwain
[Gazebo-DART] Coulomb friction test
[Gazebo-DART] Coulomb friction test
Published: 2015/01/16
Channel: Jeongseok Lee
Purdue PHYS 342 L16.2: Nuclear Reactions: Fusion
Purdue PHYS 342 L16.2: Nuclear Reactions: Fusion
Published: 2014/12/08
Channel: nanohubtechtalks
PHYSICS 8A COLLISION LAB part 1
PHYSICS 8A COLLISION LAB part 1
Published: 2014/04/28
Channel: Gnaeus Pompeius
Coulomb barrier Meaning
Coulomb barrier Meaning
Published: 2015/04/22
Channel: SDictionary
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Coulomb-Friction-Based Needle Insertion/Withdrawal Model
Published: 2010/09/02
Channel: Ryo Kikuuwe
MHS CPI Physics (3B) Collisions
MHS CPI Physics (3B) Collisions
Published: 2016/12/12
Channel: Ryan Forcier
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
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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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