Properties of High-Energy-Density Plasmas

  • R. Paul Drake
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)


The discussion of energy in Sect. 2.1 was entirely based on the notion of a polytropic gas. The speed of sound waves, which we found by examining fluctuations in density and velocity, was found to depend upon the variation of pressure with density. These observations reveal the tip of an iceberg, and the iceberg is known as the closure problem. The fluid equations can be derived by taking moments of the velocity distribution of the particles, as is done for example in graduate courses in plasma physics. Here we designate particle velocities by v and fluid velocities by u. Thus the continuity equation is the moment taken with v0, the momentum equation is the moment with v, the energy equation is the moment with v2, the heat transport equation is the moment with v3, and one can keep going. The closure problem arises because every moment equation contains terms involving the next higher moment. Equation (2.1) involves the momentum (ρu), (2.2) involves the energy density (as p), and (2.3) would involve the heat flux had we not assumed it to be zero. Because we assumed the heat flux to be zero, (2.1) to (2.3) form a closed system of equations. In general, one obtains a closed system of fluid equations by assuming that some moment of the velocity distribution is either zero or a known function of lower moments. As another example, sometimes the energy equation is expressed as an equation for temperature and the heat flux is written as —κthT, which also produces a closed system of three equations.


Internal Energy Ionization Energy Electron Temperature Pressure Ionization Fermi Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer 2006

Authors and Affiliations

  • R. Paul Drake
    • 1
  1. 1.Atmospheric, Oceanic, and Space SciencesUniversity of MichiganAnn ArborUSA

Personalised recommendations