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.