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Study of D-D Reaction at the Plasma Focus Device

Study of D-D Reaction at the Plasma Focus Device. P. Kubes, J. Kravarik, D. Klir, K. Rezac, E. Litseva, M. Scholz, M. Paduch, K. Tomaszewski, I. Ivanova-Stanik, B. Bienkowska, L. Karpinski , M. Sadowski , H. Schmidt CTU Prague, Technicka 2, 166 27 Prague, Czech Republ ic

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Study of D-D Reaction at the Plasma Focus Device

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  1. Study of D-D Reaction at the Plasma Focus Device P. Kubes, J. Kravarik, D. Klir, K. Rezac, E. Litseva, M. Scholz, M. Paduch, K. Tomaszewski, I. Ivanova-Stanik, B. Bienkowska, L. Karpinski, M. Sadowski, H. Schmidt CTU Prague, Technicka 2, 166 27 Prague, Czech Republic Institute of Plasma Physics and Laser Microfusion, 23 Hery, 00-908 Warsaw, Poland

  2. Outline Experimental and diagnostic set-up Distribution of neutron energies Distribution of ED producing neutrons Evaluation of the range of the ED producing neutrons Dimensions and densities of neutron sources Energy spectrum ofall fast deuterons Confinement of fast deuterons in magnetic field Heating and cooling of the neutron source by i-i and e-i Coulomb collisions Conclusions

  3. PF-1000 IPPLM Warsaw, Poland2 MA, 400 kJ, D-D reaction, D2 gas facility electrode system • 8 rods • Ø a = 230mm • Ø c = 400mm • L = 600mm • volume ~ 3.8 m3 • Ø = 1.4 m • L = 2.5 m

  4. Scheme of neutron diagnostics with temporal and energy distribution radial scheme - + axial scheme 10 HXR and neutron scintillation detectors 2 Cerenkov detectors for electrons and SXR

  5. Temporal evolution of neutron energies downstream shot No. 6573 with total neutron yield 5x1010 adapted time-of-flight and MC simulations ITOF(t0,E) temporal evolution of neutron energies adaptation: a) transformation of neutron energy down/up b) corrections for anisotropy down/up distribution of neutron energy per (100 keV*sterad)

  6. Determination of the axial component of deuteron energy producing observed neutrons adaptation: a) transformation of neutron energy down/up downstream upstream b) corrections for anisotropy down/up Shot 6573: axial componentof ED producing neutrons total No 5x1010 ND~ 1/ED-1

  7. Determination of the radial component of deuteron energy producing observed neutrons ? radial distribution of neutron energies ? We registered only in 7 m downstream, upstream and side-on; only partial energy distribution high anisotrophy for the shots with high neutron yield Shot 6573; NY 5x1010 : axial and side-on neutron signals in 7 m Shot 6552; NY 2x1011: axial and side-onneutron signals in 7 m Answers: a) isotropy distribution of deuteron velocities in the range below 100 keV in the shots with the lower neutron yield b) test of the chosen of the lower limit 10, 20 keV of D producing neutrons

  8. Determination of the deuteron energy producing observed neutrons downstream side-on upnstream Shot 6573: axial component of deuteron energy producing neutrons total energy distribution of deuterons producing neutrons; 5x1010 variants 10; 20; keV Shot 6573; NY 5x1010 : axial and side-on neutron signals in 7 m

  9. Distribution of the Ed componentin one direction (z) for monoenergy deuterons with isotropy distribution ofvelocities Ned… number of deuterons with energy of Ed NEd Ed Ned Ed(z) z z Ed 0 This dependence is constant along the range of 0- Ed Transformation of the axial energy component to the total energy – factor (Ed)1/2

  10. Probability of the D-D fusion reaction probability of D – D fusion collisions: pDD = l/DD= lni (Ed) ni…deuteron density of the neutron source… l … length of the neutron source dimensions of the source … experimental data Schmidt (2006), Sadowski (2006) … < 10 cm  density of the source .. >1025 m-3. dense structures in the PF surface density of the target nl.. >1024 m-2. • (ED)cross-section of D-D reaction Dependence of the length on the density of the target for neutron yield of 1010- 1011

  11. visual frames Dense structures in the PF first neutron peak (-10 – 50 ns) second neutron peak 100-200 ns supposition of the neutron source …length 2 cm, density 2x1025 m-3. Kubes P.et al: Correlation of Radiation with Electron and Neutron Signals Taken in a Plasma-Focus Device, IEEE TPS Vol. 34, Issue 5, Part 3, Oct. 2006, pp. 2349-2355.

  12. Evaluation of the deuteron energy distribution ni m-3 10 keV 20 keV 50 keV 100 keV 150 keV 200 keV Ed [keV] Number of deuterons E total [kJ] I total [kA] 1027 1x105 3.6x104 2.2x103 6.2x102 3.7x102 2.8x102 10 - 200 9x1018 17 170 1026 1x106 3,6x105 2.2x104 6.2x103 3.7x103 2.8x103 20 - 200 5x1017 3 140 1025 1x107 3.6x106 2.2x105 6.2x104 3.7x104 2.8x104 30 - 200 2.5x1017 1.7 70 1024 1x108 3.6x107 2.2x106 6.2x105 3.7x105 2.8x105 1 – (10-20) 1019 2 350 1023 1x109 3.6x108 2.2x107 6.2x106 3.7x106 2.8x106 Mean path of DD reaction; lDD = 1/n.s(E),[m] Supposition: isotropy distribution of d velocities target - l= 2 cm, density = 2x1025 m-3 TABLE I: TOTAL VALUES OF FAST DEUTERONS Shot 6573: distribution of energy of deuterons producing neutrons 100 keV … 1016 50 keV … 1017 Total number of deuterons with energy above 20 keV … 1018 10 keV ... 1019

  13. Confinement of the deuterons in magnetic field distribution of deuteron velocities: downstream 50 %, side-on 30-40%, upstream 10-20% • B = mI/2prp = mv/erL I = 2pmv/ em  v = I em/2pm; • The path of the fast deuterons can be partialy changed by internal magnetic field; Deuterons with energy a few tens of keV can be confined in the PF by magnetic field

  14. Relaxation time of Coulomb D-D collisions Te [ns] ii [ns] 0.1 keV 0.5 keV 0.3 keV 1 keV 1 keV 2 keV 3 keV 5 keV 10 keV 20 keV 1E27 m-3 0.05 0.14 0.39 1.6 4.4 13 1E27 m-3 0.27 1.5 8.5 44 1E26 m-3 0.5 1.4 3.9 15.6 44 130 1E26 m-3 2.7 15 85 440 1E25 m-3 5 14 39 156 440 1300 1E25 m-3 27 150 850 4400 1E24 m-3 50 140 390 1560 4400 13000 1E24 m-3 270 1500 8500 44000 Cooling of the deuterons and heating of electrons by Coulomb interaction with fast deuterons Relaxation time of Coulomb i-i collisions  Relaxation time of Coulomb e-i collisions independent on the Ed In the localities with the density 1025 m-3 effective heating of deuterons with i-i collisions up to 1-2 keV and effective cooling with e-i collisions at the temperature up to 0.1 keV. In the localities with the density 1026 m-3 – effective heating of deuteronswith i-i collisions up to 5 keV and effective cooling with e-i collisions up to 0.5 keV. In the localities with the density 1027 m-3 – effective heating of deuterons with i-i collisions up to 20 keV and effective cooling by e-i collisions up to 2 keV.

  15. Conclusions The energy distribution of fast deuterons can be determined knowing: axial and radial distribution of neutron energy, density and dimensions of the neutron sources. For the dimensions of the neutron source below 10 cm its deuteron density must be above 1025 m-3. The dense structures in the PF can be sources of observed neutrons. The lower limit of Ed for D-D reaction is about 10-20 keV and the upper limit of the total number of both – fast deuterons 1018 and deuterons in energy range 1-10 keV 1019. Magnetic fields in the pinched column at 1MA can partially confinethe deuterons with Ed up to 100 keV and increase the path of the fast deuterons in the dense plasma. It exists the range of Ed in which the relaxation time of Coulomb e-d ishigher than that of d-d collisions. These deuterons can heat the source of neutrons to the temperature a few keV. For the more exact estimation ofEdof fast deuterons we plan in this year installation of: neutron scintillation detectors side-on in distances 2 and 50 m and laser interferometry with 4-8 frames per shot.

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