等离子体物理Chapter 3.pdfVIP

Chapter 3 Collisions in plasmas 3.1 Application of conservation laws to particle collisions Consider collision of α- and β- type particles. We assume that in collision the particles are not affected by any external forces. The energy and momentum of the system of interacting particles are known to remain unchanged. The system momentum is p p =+p m υ =+m υ (3-1) α β α α β β The momentum conservation law leads to the equality of the system’s pre-and post-collision momenta p p or m υ +m υ m υ =+m υ (3-2) α α β β α α β β The kinetic energy of the system is 1 2 1 2 K K =+K m υ =+ m υ (3-3) α β 2 α α 2 β β The energy conservation law makes it possible to determine the change in the kinetic energy of the system K K =+ΔK or 1 2 1 2 1 2 1 2 m υ + m υ m υ =+ m υ +ΔE (3-4) 2 α α 2 β β 2 α α 2 β β where ΔE is the net change in the internal particle energy as a result of collision. 1 In elastic collisions, ΔE is clearly equal to zero. Among the inelastic collisions, one distinguishes collision of the first kind with ΔE 0 from collisions of the second kind with ΔE 0. In the coordinates of the center of mass system, the coordinates of these particles is m r +m r α α β β r (3-5) o m