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In0000721 Redistribution of Thermal X-Ray Radiation In IN0000721 BARC/1999/E/043 CO > O CO to m o>»» REDISTRIBUTION OF THERMAL X-RAY RADIATION IN CAVITIES: VIEW-FACTOR METHOD AND COMPARISON WITH DSN CALCULATIONS by M.K. Srivastava Theoretical Physics Division and Vinod Kumar and S.V.G. Menon Solid State & Spectroscopy Group 31/30 1999 BARC/1999/E/043 GOVERNMENT OF INDIA ATOMIC ENERGY COMMISSION REDISTRIBUTION OF THERMAL X-RAY RADIATION IN CAVITIES: VIEW-FACTOR METHOD AND COMPARISON WITH DSN CALCULATIONS by M.K. Srivastava Theoretical Physics Division and Vinod Kumar and S.V.G. Menon Solid State & Spectroscopy Group BHABHA ATOMIC RESEARCH CENTRE MUMBAI, INDIA 1999 BARC/199S/E/043 BIBLIOGRAPHIC DESCRIPTION SHEET FOR TECHNICAL REPORT (as per IS : 9400 -1980) 01 Security classification: Unclassified 02 Distribution: External 03 Report status: New 04 Series : BARC External 05 Report type: Technical Report 06 Report No.: BARC/1999/E/043 07 Part No. or Volume No.: 08 Contract No.: 10 Title and subtitle: Redistribution of thermal x-ray radiation in cavities: view factor method and comparison with DSN calculations 11 Collation: 39 p., 9 figs. 13 Project No. : 20 Personal authors): 1) M.K. Srivastava 2) Vinod Kumar, S.V.G. Menon 21 Affiliation of authors): 1) Theoretical Physics Division, Bhabha Atomic Research Centre, Mumbai 2) Solid State and Spectroscopy Group, Bhabha Atomic Research Centre, Mumbai 22 Corporate authors): Bhabha Atomic Research Centre, Mumbai - 400 085 23 Originating unit: Theoretical Physics Division, BARC, Mumbai 24 Sponsors) Name: Department of Atomic Energy Type: Government Contd... (ii) -l- 30 Date of submission: December 1999 31 Publication/Issuedate: January 2000 40 Publisher/Distributor: Head, Library and Information Services Division, Bhabha Atomic Research Centre, Mumbai 42 Form of distribution: Hard copy 50 Language of text: English 51 Language ofsummary: English 52 No. of references: 24 reft. 53 Gives data on: Abstract :A view-factor method for studying distribution of tbermal x-ray radiation inside a hohlraum cavity is developed. This problem is of much relevance these days in an indirect-driven inertial confinement fusion (1CF) system where, one is supposed to optimize the irradiation pattern to derive maximum coupling with the fusion capsule. The x-ray reemission factor from the hohlraum wall is calculated by solving the instantaneous flux conservation equation, which is coupled with scaling laws derived from self-similar solutions of a one-dimensional planar radiation hydrodynamic equations. The method is applied to a gold capillary hohlraum with two typical primary sources for irradiation, viz., a disc source and a symmetric two-ring source. These two sources are of direct relevance to the actual implosion experiments. The relevant view factors are derived analytically in the present report. The earlier literatures used die same derived from a two-dimensional numerical integration in r-0 geometry. Our calculations show excellent agreement with those obtained from the exact numerical simulation. Apart from this, it also reproduces extremely well the actual experimental results obtained for a gold capillary hohlraum heated by a disc source. Further, to test our model against some standard technique, we also solve the same probtem using well known discrete ordinate (DSN) method. This method is applied to a steady-state radiation-transport problem in two-dimensional r-z geometry. The primary sources on the hohlraum surface are used as boundary conditions for the problem. Numerical results of this method (which can be generalized to solve even more complex radiation- transport problems) for the capillaries are compared with those of the view factor method. Excellent agreement is found between the two results. 70 Keywords/Descriptors : X RADIATION; ICF DEVICES; NUMERICAL SOLUTION; VALIDATION; IMPLOSIONS; SYMMETRY; ENERGY TRANSFER; IRRADIATION 71 INIS Subject Category: G5110;G3620 99 Supplementary elements: -n- Redistribution of Thermal X-ray Radiation in Cavities: View Factor Method and Comparison with DSN Calculations M. K. Srivastava1, Vinod Kumar2 and S. V. G. Menon2 1 Theoretical Physics Division 2 Solid State & Spectroscopy Group Bhabha Atomic Research Centre, Mumbai-400 085, INDIA Abstract A view-factor method for studying distribution of thermal X-ray radiation inside a hohlraum cavity is developed. This problem is of much relevance these days in an indirect-driven inertial confinement fusion (ICF) system where, one is supposed to optimize the irradiation pattern to derive maximum coupling with the fusion capsule. The X-ray reemission factor from the hohlraum wall is calculated by solving the instantaneous flux conservation equation, which is coupled with scaling laws derived from self-similar solutions of a one-dimensional planar radiation hydrodynamic equations. The method is applied to a gold capillary hohlraum with two typical primary sources for irradiation, viz., a disc source and a symmetric two-ring source. These two sources are of direct relevance to the actual implosion experiments. The relevant view factors are derived analytically in the present report. The earlier literatures used the same derived from a two-dimensional numerical integration in r-9 geometry. Our calculations show excellent agreement with those obtained from the exact numerical simulation. Apart from this, it also reproduces extremely well the actual experimental results obtained for a gold capillary hohlraum heated by a disc source. Further, to test our model against some standard technique, we also solve the same problem using well known discrete ordinate (DSN) method. This method is applied to a steady-state radiation-transport problem in two-dimensional r-z geometry. The primary sources on the hohlraum surface are used as boundary conditions for the problem. Numerical results of this method (which can be generalized to solve even more complex radiation-transport problems) for the capillaries are compared with those of the view factor method. Excellent agreement is found between the two results. 1. Introduction Study of thermal radiation distribution inside a closed cavity is of much interest these days, particularly, in connection with inertial confinement fusion (ICF)'. A very important issue in these ICF schemes is the symmetric implosion of the ICF target. In the usual direct-driven scheme this symmetry is achieved (with some acceptable degree of imperfection) by irradiating a large number of incident laser or ion beams on to the fusion target. However, it is seen that any deviation from the perfect symmetry (caused either by imperfection in the fuel surface itself or due to nonuniform illumination of the ICF target) is known to magnify in the due course (the so-called Rayleigh Taylor instability), resulting finally into hampering of the fusion process. Now, in order to achieve the perfect symmetric implosion, a novel scheme has been thought of, what is popularly known as indirect-driven fusion2'5. This scheme is based on the concept of a radiation cavity known as hohlraum6 .In this scheme, the driving laser or particle beams first generate thermal X-rays inside a high-Z (Z is charge number) cavity. These X-rays are then repeatedly absorbed and reemitted by the case walls till a desired equilibrium thermal radiation (known as Planckian radiation) is obtained. Finally, this thermal radiant energy is deposited on to the surface of a fusion capsule, placed at the center of the cavity (see Fig. 1), in a nearly perfectly symmetric manner. Another advantage of the indirect-driven scheme is that, unlike in the direct-driven system, it does not require the laser beams to be of very high optical quality and that they be arranged very symmetrically around the fusion capsule. Moreover, in the direct-driven system additional problem arises due to excitation of the collective plasma instabilities by the laser light. Much energy is lost in the form of hot electrons generated by the plasma instability. In the indirect-driven system what we get is just an energy- source in the form of intense and isotropic radiation and not the oscillating electric and magnetic fields of the laser light that might excite the plasma waves. However, the above advantages are not, without a cost. It is apparent that the indirect- driven scheme is energetically more demanding than the direct-driven one. Not only is a part of the laser energy converted into the X-rays, but also a certain amount of energy is required to maintain the radiating temperature of the cavity wall. Thus, less energy is left available for the actual implosion of the ICF target. Moreover, additional constraint comes from the geometric configuration. The coupling of the radiant energy to the fusion' capsule is characterized roughly by the ratio of the surface areas of the fusion capsule and the reemitting cavity wall. This ratio, obviously less than one, can not be fixed very large due to practical design limitation. Apart from application in the ICF, there are other wide range of interesting phenomena that can be studied by using a high-Z cavity. For example, using the currently available laser pulse of intensity ~ 1014 W/cm2 and duration ~ 10 nsec, one can expect to heat up the cavity wall (of diameter ~ a few mm) to a temperature of about 5xl06 °K. This temperature is close to what we observe in the interior of sun (~14xlOs degree K). Thus, the man made cavity can be used to investigate matter in a state of high density and temperature in the laboratory, which generally prevails only in stars. Another application of the high-temperature cavity could be in the field of material reprocessing where a suitably designed substance is treated by the focussed heating of a radiant energy flux. Hohlraum: a miniaturized sun A high-temperature cavity produced in the laboratory simulates in many respects the radiation environment prevailing in the sun6. In fact, the very concept of hohlraum to generate a very intense, isotropic and incoherent radiation originates from the sun itself. The sun is well known to sustain itself since billions of years by the fusion energy that it has been producing since its origin.
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