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, Prague, Czech Republic Institute of Plasma Physics and Laser Microfusion, 23 Hery, Warsaw, Poland

Outline Experimental and diagnostic set-up Distribution of neutron energies Distribution of E D producing neutrons Evaluation of the range of the E D producing neutrons Dimensions and densities of neutron sources Energy spectrum of all 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

PF-1000 IPPLM Warsaw, Poland 2 MA, 400 kJ, D-D reaction, D 2 gas volume ~ 3.8 m 3 Ø = 1.4 m L = 2.5 m 8 rods Ø a = 230 mm Ø c = 400 mm L = 600 mm facility electrode system

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 + -

adapted time-of-flight and MC simulations I TOF (t 0,E) Temporal evolution of neutron energies downstream temporal evolution of neutron energies distribution of neutron energy per (100 keV*sterad) shot No with total neutron yield 5x10 10 adaptation: a) transformation of neutron energy down/up b) corrections for anisotropy down/up

Determination of the axial component of deuteron energy producing observed neutrons Shot 6573: axial component of E D producing neutrons total No 5x10 10 N D ~ 1/E D -1 adaptation: a) transformation of neutron energy down/up b) corrections for anisotropy down/up downstream upstream

Shot 6552; NY 2x10 11 : axial and side-on neutron 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 Shot 6573; NY 5x10 10 : axial and side-on neutron signals in 7 m ? 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 Determination of the radial component of deuteron energy producing observed neutrons

Shot 6573: axial component of deuteron energy producing neutrons Shot 6573; NY 5x10 10 : axial and side-on neutron signals in 7 m Determination of the deuteron energy producing observed neutrons variants 10; 20; keV downstream side-on upnstream total energy distribution of deuterons producing neutrons; 5x10 10

Distribution of the E d component in one direction (z) for monoenergy deuterons with isotropy distribution of velocities N Ed EdEd N ed … number of deuterons with energy of E d This dependence is constant along the range of 0- E d z z E d (z) Transformation of the axial energy component to the total energy – factor (E d ) 1/2 N ed EdEd 0

Probability of the D-D fusion reaction  (E D ) cross-section of D-D reaction probability of D – D fusion collisions: p DD = l/ DD = ln i  (E d ) n i …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.. > m -3. dense structures in the PF  surface density of the target nl.. > m -2. length50 cm5 cm5 mm0,5 mm density10 24 m m m m -3 Dependence of the length on the density of the target for neutron yield of

Dense structures in the PF first neutron peak (-10 – 50 ns) second neutron peak ns supposition of the neutron source … length 2 cm, density 2x10 25 m -3. visual frames 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

Shot 6573: distribution of energy of deuterons producing neutrons Evaluation of the deuteron energy distribution Supposition: isotropy distribution of d velocities target - l= 2 cm, density = 2x10 25 m -3 TABLE I: TOTAL VALUES OF FAST DEUTERONS Ed [keV] Number of deuterons E total [kJ]I total [kA] x x x – (10-20) keV … keV … Total number of deuterons with energy above 20 keV … keV ni m keV20 keV50 keV100 keV150 keV200 keV x x x x x x x10 6 3,6x x x x x x x x x x x x x x x x x x x x x x x10 6 Mean path of DD reaction; DD = 1/n.  (E), [m]

Confinement of the deuterons in magnetic field distribution of deuteron velocities: downstream 50 %, side-on 30-40%, upstream 10-20% B =  I/2  r p = mv/er L  I = 2  mv  e   v = I e  /2  m;  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 EdEd 10 keV30 keV100 keV300 keV v10 6 m/s1.7x10 6 m/s3x10 6 m/s5x10 6 m/s path 30ns3 cm5 cm10 cm30 cm I4x10 5 A7x10 5 A1.2x10 6 A4x10 6 A

Cooling of the deuterons and heating of electrons by Coulomb interaction with fast deuterons Relaxation time of Coulomb D-D collisions Relaxation time of Coulomb e-i collisions Relaxation time of Coulomb i-i collisions  ii [ns] 0.5 keV1 keV2 keV5 keV10 keV20 keV 1E27 m E26 m E25 m E24 m Te [ns]0.1 keV0.3 keV1 keV3 keV 1E27 m E26 m E25 m E24 m In the localities with the density 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 m -3 – effective heating of deuterons with 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 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. independent on the Ed

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 m -3. The dense structures in the PF can be sources of observed neutrons. The lower limit of E d for D-D reaction is about keV and the upper limit of the total number of both – fast deuterons and deuterons in energy range 1-10 keV Magnetic fields in the pinched column at 1MA can partially confine the deuterons with E d up to 100 keV and increase the path of the fast deuterons in the dense plasma. It exists the range of E d in which the relaxation time of Coulomb e-d is higher 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 of E d of 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.