Abstract
This paper develops an approximate steady state Fokker Planck theory for energetic electron transport in a spherical laser fusion target. First, we apply the theory to only a small population of electrons, which is specified at the outset. Then, one determines the nonlocal electron energy flux of these electrons at a particular position. These energetic electrons may either come from the tail of the thermal distribution function or be generated by an instability. This paper develops two approximate methods of solution, which we call the “characteristic method” and “sparse eigenfunction.” The former works only in planar geometry and the latter in both planar and spherical geometry. Comparison of the two methods in planar geometry shows that even though the approximations are very different, they give about the same result, increasing their credibility. For the example we have chosen, spherical effects are not important for electrons from the tail of the distribution function but may well be for instability generated electrons, which have much higher energy. Comparing planar to spherical, one finds an additional spherical barrier protecting the fuel. It turns out that the associated fuel preheat a Fokker Planck model predicts is considerably less than that predicted by the Krook models as developed at both NRL and other places.
Highlights
This paper develops an approximate steady state Fokker Planck theory for energetic electron transport in a spherical laser fusion target
In our earlier papers with like sounding titles,1,2 we developed preliminary theories for the nonlocal transport of energetic electrons in a laser fusion target plasma, using a steady state Fokker Planck (FP)2 and Krook1 model, both for planar geometry
The most basic three approximations were first to consider only the relatively small population of energetic electrons and to calculate their interaction with the larger number of ions and thermal electrons, second to neglect their energy diffusion, which is small by the electron temperature over the energetic electron energy, and third to use a two term Legendre polynomial expansion for the distribution function
Summary
In our earlier papers with like sounding titles, we developed preliminary theories for the nonlocal transport of energetic electrons in a laser fusion target plasma, using a steady state Fokker Planck (FP) and Krook model, both for planar geometry. The two possibilities we consider are as follows: first, they may arise from an instability and second from the tail of the thermal electron distribution function.1,2 In the latter case, we estimate the energetic electron energy flux near the point of maximum flux with a Krook model but follow their deposition with a Fokker Planck model neglecting energy diffusion. For the case where the energetic electrons arise from the tail of the Maxwellian, we get the initial nonlocal flux at the position of maximum nonlocal flux as given by the Krook model, which can be solved relatively
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
