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2b Coulomb collisions in plasmas

Published: 2015/09/15

Channel: Plasma Physics and Applications

Coulomb collision Meaning

Published: 2015/04/22

Channel: SDictionary

14A Coulomb Collisions | Introduction to Plasma Physics by J D Callen

Published: 2015/12/24

Channel: Lucius Fox

collision response with coulomb friction

Published: 2013/03/23

Channel: Glenn Fiedler

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

Published: 2010/08/17

Channel: Bengt Nyman

Collision Detection and Response - Interactive 3D Graphics

Published: 2015/02/23

Channel: Udacity

When Protons Collide

Published: 2016/05/04

Channel: Boston University

Robust Treatment of Simultaneous Collisions

Published: 2012/12/26

Channel: Walt Disney Animation Studios

Physics: How many electrons are in 1 coulomb?

Published: 2014/05/17

Channel: Smoleny1

Inelastic Collision Example # 1

Published: 2012/12/27

Channel: AK LECTURES

Physics 30: Lesson 4 - Elastic and Inelastic Collisions

Published: 2014/08/15

Channel: ms. Booth

Gravity & Coulomb repulsion

Published: 2009/07/09

Channel: Computer Physics Lab

angular collision response new

Published: 2013/03/23

Channel: Glenn Fiedler

Elastic Collisions

Published: 2016/01/04

Channel: Brad Homoelle

6.- Classical Electron Collision

Published: 2008/12/27

Channel: SpinningParticle

collision response linear

Published: 2013/03/23

Channel: Glenn Fiedler

collision response linear wrong

Published: 2013/03/23

Channel: Glenn Fiedler

angular collision response without friction

Published: 2013/03/23

Channel: Glenn Fiedler

Coulomb Focusing: Helping Electrons Hit the Bullseye

Published: 2013/10/02

Channel: Aaron Parsons

N-body Simulation of Counter-streaming ion beams.

Published: 2017/08/08

Channel: Andrew Chap

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

Published: 2015/08/06

Channel: Centre International de Rencontres Mathématiques

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's Law Overview

Published: 2013/04/14

Channel: Frank McCulley

Electric Charges: "Coulomb's Law" 1959 PSSC; Eric Rogers; Princeton University

Published: 2017/05/18

Channel: Jeff Quitney

Collision Meaning

Published: 2015/04/19

Channel: SDictionary

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

Published: 2012/02/17

Channel: DSFMvideo

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

Published: 2014/04/11

Channel: Guillaume Racicot

collision response rolling friction

Published: 2013/03/23

Channel: Glenn Fiedler

go stone spinning

Published: 2013/03/23

Channel: Glenn Fiedler

Coulomb attraction Meaning

Published: 2015/04/22

Channel: SDictionary

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?

Published: 2017/07/18

Channel: funny sparky

Electrostatics Starting Concepts, Conservation of Charge, Conductors, Coulomb's Law

Published: 2015/01/26

Channel: Greg Clements

Impulse based collision Response

Published: 2008/05/27

Channel: damien murtagh

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

Published: 2008/08/15

Channel: DSaitou

Coulomb-Friction-Based Needle Insertion/Withdrawal Model

Published: 2010/09/03

Channel: Ryo Kikuuwe

SPH4U 5.5 Collisions in two dimensions: Glancing collisions

Published: 2016/06/21

Channel: OnPhysics

Coulomb's Law

Published: 2014/02/03

Channel: SciencewithSwain

[Gazebo-DART] Coulomb friction test

Published: 2015/01/16

Channel: Jeongseok Lee

Purdue PHYS 342 L16.2: Nuclear Reactions: Fusion

Published: 2014/12/08

Channel: nanohubtechtalks

PHYSICS 8A COLLISION LAB part 1

Published: 2014/04/28

Channel: Gnaeus Pompeius

Coulomb barrier Meaning

Published: 2015/04/22

Channel: SDictionary

Coulomb-Friction-Based Needle Insertion/Withdrawal Model

Published: 2010/09/02

Channel: Ryo Kikuuwe

MHS CPI Physics (3B) Collisions

Published: 2016/12/12

Channel: Ryan Forcier

Charge Posturing, dipole formation and Coulomb attraction between 2 Hydrogen atoms

Published: 2010/08/17

Channel: Bengt Nyman

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.

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 *m*_{e} passing a stationary ion of charge +*Ze* and much larger mass at a distance *b* with a speed *v*. The perpendicular force is (1/4πε_{0})*Ze*^{2}/*b*^{2} 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*+d*b*) is *nv*(2π*b* d*b*), 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 πb_{0}^{2} 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*/(*m*_{e}*v*).

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:

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*.

- Effects of Ionization [ApJ paper] by Gordon Emslie
- [1] [NRL Plasma Formulary 2013 ed.]

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