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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 - PowerPoint PPT Presentation
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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
Outline
Experimental and diagnostic set-upDistribution of neutron energiesDistribution of ED producing neutronsEvaluation of the range of the ED producing neutronsDimensions and densities of neutron sourcesEnergy spectrum of all fast deuteronsConfinement of fast deuterons in magnetic fieldHeating and cooling of the neutron source by i-i and e-i Coulomb collisionsConclusions
PF-1000 IPPLM Warsaw, Poland 2 MA, 400 kJ, D-D reaction, D2 gas
• volume ~ 3.8 m3
• Ø = 1.4 m• L = 2.5 m
• 8 rods• Ø a = 230 mm• Ø c = 400 mm• L = 600 mm
facilityelectrode system
Scheme of neutron diagnostics with temporal and energy distribution
P IN
streak cam era
q uad ro cam era
M C P cam eracham b er
e lec ro d es
x -rayN e1 02 a
radial scheme
axial scheme
10 HXR and neutron scintillation detectors2 Cerenkov detectors for electrons and SXR
+ -
adapted time-of-flight and MC simulations ITOF (t0,E)
Temporal evolution of neutron energies downstream2 .0 M e V
3 .0 M e V
2 .5 M e V
0 10 0 2 00 30 0 ns
temporal evolution of neutron energies
distribution of neutron energy per (100 keV*sterad)
shot No. 6573 with total neutron yield 5x1010
adaptation:a) transformation of neutron energy down/upb) corrections for anisotropy down/up
Determination of the axial component of deuteron energy producing observed neutrons
1,0E+06
1,0E+07
1,0E+08
1,0E+09
1,0E+10
1 10 100 1000
axial component of Ed [keV]
nu
mb
er
of
deu
tero
ns p
er
1 k
eV
Shot 6573: axial component of ED producing neutronstotal No 5x1010
ND ~ 1/ED-1
adaptation:
a) transformation of neutron energy down/up
b) corrections for anisotropy down/up
downstream upstream
Shot 6552; NY 2x1011: 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 5x1010 : 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
1,0E+06
1,0E+07
1,0E+08
1,0E+09
1,0E+10
1 10 100 1000
axial component of Ed [keV]
nu
mb
er
of
deu
tero
ns p
er
1 k
eV
Shot 6573: axial component of deuteron energy producing
neutrons
Shot 6573; NY 5x1010 : 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 deuteronsproducing neutrons; 5x1010
Distribution of the Ed component in one direction (z)
for monoenergy deuterons with isotropy distribution of velocities
NEd
Ed
Ned … number of deuterons with energy of Ed
]1[)sin
1(sin
4sin
444]1[
2
0
22
0
2 keVzE
N
Edz
dz
dz
ddE
NdE
NNS
NkeVN
d
Ed
dd
Edd
EdEdEdEd
This dependence is constant along the range of 0- Ed
zz
Ed(z)
Transformation of the axial energy component to the total energy – factor (Ed)1/2
Ned
Ed0
Probability of the D-D fusion reaction
(ED) cross-section of D-D 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 dataSchmidt (2006), Sadowski (2006) … < 10 cm
density of the source .. > 1025 m-3. dense structures in the PFsurface density of the target nl.. > 1024 m-2.
length 50 cm 5 cm 5 mm 0,5 mm
density 1024 m-3 1025 m-3 1026 m-3 1027 m-3
Dependence of the length on the density of the target for neutron yield of 1010- 1011
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.
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. 2349-2355.
Shot 6573: distribution of energy of deuterons producing neutrons
Evaluation of the deuteron energy distribution
Supposition:isotropy distribution of d velocitiestarget - l= 2 cm, density = 2x1025 m-3
TABLE I: TOTAL VALUES OF FAST DEUTERONS
Ed [keV] Number of deuterons
E total [kJ] I total [kA]
10 - 200 9x1018 17 170
20 - 200 5x1017 3 140
30 - 200 2.5x1017 1.7 70
1 – (10-20) 1019 2 350 100 keV … 1016
50 keV … 1017
Total number of deuterons with energy above 20 keV … 1018
10 keV ... 1019
ni m-3 10 keV 20 keV 50 keV 100 keV 150 keV 200 keV
1027 1x105 3.6x104 2.2x103 6.2x102 3.7x102 2.8x102
1026 1x106 3,6x105 2.2x104 6.2x103 3.7x103 2.8x103
1025 1x107 3.6x106 2.2x105 6.2x104 3.7x104 2.8x104
1024 1x108 3.6x107 2.2x106 6.2x105 3.7x105 2.8x105
1023 1x109 3.6x108 2.2x107 6.2x106 3.7x106 2.8x106
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/2rp = mv/erL I = 2mve v = I e/2m;
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
Ed 10 keV 30 keV 100 keV 300 keV
v 106 m/s 1.7x106 m/s 3x106 m/s 5x106 m/s
path 30ns 3 cm 5 cm 10 cm 30 cm
I 4x105 A 7x105 A 1.2x106 A 4x106 A
Cooling of the deuterons and heating of electrons by Coulomb interaction with fast deuterons
Relaxation time of Coulomb e-i collisions
Relaxation time of Coulomb i-i collisions
ii [ns] 0.5 keV 1 keV 2 keV 5 keV 10 keV 20 keV
1E27 m-3 0.05 0.14 0.39 1.6 4.4 13
1E26 m-3 0.5 1.4 3.9 15.6 44 130
1E25 m-3 5 14 39 156 440 1300
1E24 m-3 50 140 390 1560 4400 13000
Te [ns] 0.1 keV 0.3 keV 1 keV 3 keV
1E27 m-3 0.27 1.5 8.5 44
1E26 m-3 2.7 15 85 440
1E25 m-3 27 150 850 4400
1E24 m-3 270 1500 8500 44000
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 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 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.
21
5
2317
ln109.5
105.4
m
M
n
T
vi
iiii
2/3
i
Eiiie E
T
m
M
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 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 confine the 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 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 Ed of fast deuterons we plan in this year installation of: neutron scintillation detectors side-on in distances 2 and 50 m andlaser interferometry with 4-8 frames per shot.