Photon coupling theory for plasmas with strong Compton scattering: Four temperature theory

Molvig, Kim; Alme, Marv; Webster, Robert; Galloway, Conner
February 2009
Physics of Plasmas;Feb2009, Vol. 16 Issue 2, pN.PAG
Academic Journal
When an equimolar mixture of deuterium (D) and tritium (T) at high density undergoes fusion burn, the system becomes extremely nonequilibrium. The ion temperature rises much higher than the electron temperature which, in turn, is much higher than the radiation temperature. Accurately simulating this nonequilibrium burn process has previously required a multigroup representation of the radiation field. Although simulating this D–T burn with a simple three temperature model (3T) also results in significant departures from thermal equilibrium, the ion and electron temperature histories from the 3T simulations are much lower than from the multigroup simulations. In this paper, a theory that overcomes the deficiencies of the 3T model in simulating burn of high density D–T is developed. The primary deficiency of the 3T model for this physical system is with the treatment of the Compton scattering energy exchange. The theory here developed culminates in a four temperature model (4T) which describes the radiation field with two temperatures. These are TR, which is the standard radiation temperature of the 3T model (proportional to the fourth root of the radiation energy density), and Tp, which is the true thermodynamic temperature of the photon distribution. This 4T theory gives excellent agreement with the multigroup model for the nonequilibrium burn of D–T. Further, the 4T model transitions smoothly to the 3T model when this is appropriate. Thus the kinetic theory derivation of the 4T model also provides a solid theoretical foundation for the 3T model. Extensions of the theory to inhomogeneous systems are under development to allow treatment of geometries where the computational efficiency of the 4T approach can convey a sizable advantage. There appear to be at least two important applications where the model can be applied. One is for inertial confinement fusion capsules that are optically thick and utilize volume ignition. The second application involves astrophysical accretion disks in the high temperature regime that also exhibit matter heating radiation, albeit without a fusion energy source. A reduced complexity radiation model with the associated reduced computer resource requirements has the potential to facilitate high resolution two dimensional and three dimensional simulations of these astrophysical objects.


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