The particle shape function can be used to define the macroscopic plasma properties (e.g.,
density and flux),
sum_(k=1)^(N_(0)) S(x-x_(k))=n_(i)
sum_(k=1)^(N_(0)) v_(k)S(x-x_(k))=n_(i)u_(i)
By summing the equation of motion over all particles, derive a momentum conservation
relation for the particles contained in a volume, V. Hint: Use the two-fluid equations and
assume that the electrons are massless, i.e.,
E=-u_(e) imes B
Problem 1. (10 points) Consider the equation of motion for the kth particle in a colli- sionless plasma
(1) where
S(x-Xk)E(x)d3x
B(xk)
S(x-Xk)B(x)d3x
The particle shape function can be used to define the macroscopic plasma properties (e.g., density and flux), No ZS(x-xk)=ni k=1 No >VkS(x-Xk)=n;Ui k=1 By summing the equation of motion over all particles, derive a momentum conservation relation for the particles contained in a volume, V. Hint: Use the two-fluid equations and assume that the electrons are massless, i.e.,
E=-ue x B