Nonlinear Waves and Chaos in Space Plasmas Introduction(1.4)

 

The energy budget

Combine the energy equation
1/A d/dr(A3/2 pu) + 1/A p d/dr(Au) + 1/A d/dr(Aq) = 1/A d/dr(F+Fr)
with the particle conservation and force balance equations

Fm0+Fq0+M(-1/2u20+g/(g+1)p0/rho0)

=Fm+Fq+M(-GMS/r-1/2u2+g/(g+1)p/rho)+Fr