A plasma is made up of a mixture of various particle species, the type species having

A plasma is made up of a mixture of various particle species, the type α species having mass m_α, number density n_α, average macroscopic velocity u_α, random velocity C_α = v – u_α, scalar pressure P_α = n_αkT_α, temperature

and heat flow vector q_α = (n_αm_α/2) < c_α²c_α >. Similar quantities can be defined for the plasma as a whole, for example, we can define the total number density by

the average mass by

and the average flow velocity by

We can also define an alternative random velocity for the type a species, with reference to u₀, as C_α0 = v – u₀, as well as an alternative absolute temperature by

a corresponding pressure dyad by

and heat flow vector by

(a) Show that, for the plasma as a whole, the total pressure dyad is given by

and the total scalar pressure by

where w_α = u_α – u₀ is the macroscopic diffusion velocity.

(b) If C_α is isotropic, that is,

show that the total heat flow vector is given by

(c) If an average temperature T₀, for the plasma as a whole, is defined by requiring that P₀= n₀kT₀, show that

(d) Verify that

so that there is an average thermal energy of kT₀/2 per degree of freedom.

Transcribed Image Text:

Ta = (ma/3k) < c>, pressure dyad Pa = nama Caca >,