Measurement of the Astrophysical S-factor and Cross Sections of Reactions Between Light Nuclei at Infralow Energies Using Z-pinch Plasma Flow Collaboration: JINR(Joint Institute for Nuclear Research, Dubna, Russia) IEP RAS(Institute of Electrophysics, Yekaterinburg, Russia) HCEI RAS(High Current Electronics Institute, Tomsk, Russia) LLNL(Lawrence Livermore National Laboratory, Livermore, USA) UCI(University of California, Irvine, USA) FNPT(Faculty of Physics and Nuclear Techniques, UMM, Cracow, Poland) RINP TPU(Research Institute of Nuclear Physics at Tomsk Polytechnic University, Tomsk, Russia) UF(University of Florida, Gainesville, USA) Spokesman:V.M. Bystritsky (JINR)

Interest: 1)verification of the fundamental symmetries such as charge symmetry, iso-invariance – at present, only data on np, nd and nHe scattering lengths exist; 2)study of some dynamic mysteries, e.g. existence of weakly bound states or resonances in few-hadron system; 3)study of structure of exchange meson current which make a substantial contribution at the energies (for example, the radiative capture p + d → 3 He + γ); 4)for solving some astrophysics problems (for example, in stars and in the Galaxy one finds the deficiency of light nuclei, expect for 4 He) as compared with the predictions based on the theory of thermonuclear reactions and generally adapted models.

Reactions 3 He(0.8 MeV) + n(2.5 MeV) p(3.0 MeV) + t(1.03 MeV) p+d → 3 He + γ(5.5 MeV) E col = 2 ÷ 6 keV p(14.7 MeV) + α(3.7 MeV) 5 Li + γ(16.4 MeV) E col = 3 ÷ 10 keV

dd: S (E) = 5·10 -2 MeV·b pd: S (E) = 1.2·10 -7 MeV·b dHe: S (E) = 6.3 MeV·b

Present status experimental direct data for S-factors and cross sections of nuclear reaction in the energy range ÷10 keV practically are absent Idea using dense Z-pinch technology for studying reactions between light nuclei in the ~keV energy region classical accelerators – quite low intensity of beams of accelerated particles (p, d, He …) It’s possible very high intensity – ÷10 21 particles/pulse low energy radially converging ion flow (10 -1 ÷10 keV)

M(g/cm) = 2·10 10 × I 2 (MA) × ln(R/r) × V -2 (cm/s)

Accelerators of HCEI RAS (Tomsk, Russia) SGM: I = 950 kA; U = 1 MV; τ = 80 ns; W = 200 kJ MIG: I = 2.5 MA; U = 1.5 MG; τ = 80 ns; W = 450 kJ

First step dd – reaction Accelerator SGM HCEI RAS (Tomsk) (950 kA, τ = 80 ns) Finish – 2002

Shortcomming limited current amplitude (< 1 MA) small distance of deuterium liner acceleration to the axis limited the maximum attainable energy of the ion flows Invers e Z-pinch plasma is electrodynamically accelerated radially away from the axis of liner (inverse setup) Advantages to decrease the liner plasma density on the target surface to discriminate in time the processes of electrodynamic acceleration of plasma and its interaction with the target longer period of liner Correct information on the nuclear reaction characteristics demands: knowledge of the accelerated ion energy distribuion using the adequate models for the low energy ion interaction with the target

Sketch of the load used to form an inverse Z-pinch and the positions of the optical detectors dB/dt – dot probes; r 1 = 23 cm; r 2 = 34 mm Intercepting squirrel cage armature – metal roads d r = 1mm; HV electrode: wires d w = 120 μm target: copper sheet covered by CD 2 r = 370 mm; l = 40 mm

Schematic of the experimental device 1 – high-current generator, 2 – accelerator load module, 3 – measuring chamber, 4 – grid cathode, 5 – return conductor, 6 – supersonic Laval nozzle, 7 – liner, 8 – current-intercepting structure, 9, 10 – scintillator detector, 11 – thermal-neutron detector, 12 – Pb shielding, 13 – light-protecting cone, 14 – collimators, 15 – light guides, 16 – magnetic dB/dt probes, 17 – CD 2 -target

Experiment Experiments were performed in the Institute of High Electronics (Tomsk, Russia) at high current generator SGM (I ~ 1 MA, τ ≈ 80 ns) (unit load) Measurement of the ions energy distribution Registration of H α -lines (656.5 nm) generated in: ion charge exchange on the following de-excitation of the fast neutrals D + + N 2 → D * + N 2 → D + N hν collision – radiative recombination of slow D + ions e - + D + → D + hν e - + D + + e - → D + e - + hν – Bremst Liner ion energy distribution is related to the time distribution Δt ≈ · L · (1/E) 1/2 · (ΔE/E) Δt (ns) – FWHM of the light signal time distribution from LD at distance L (cm) from CIR; E, ΔE (keV) – most probable liner ion energy and full width energy distribution at the distance L

Signals from optical detectors LD1, LD2 and LD3 obtained in shot no. 3

Light pulses measurement results Two phases responsible for the main input in the light pulse formation at different radial distance. First phase At distance ≤ 10 cm – charge exchange processes: D + + N 2 → D * + N 2 → D + N hν (τ ≈ 10 ns) (LD2-LD1) Later: e - + D + → e - + D * → e - + D + hν, e - + D → e - + (D + ) * + e - → e - + D + + e - + hν, σ < cm 2 Second phase (L ~ 15÷20 cm) Main light yield: e - + D + → D + hν, e - + D + + e - → e - + D + hν (energy distrib. two positions of optic. detect.)

Bolometer signals: (1) Reference signal at the output of the bolometer and (2) bolometer signal when high-current generator is switched on

Energy distributions of the liner deuterons in shot no. 7. The solid line corresponds to interval between LD1 and LD2, and the dashed line – LD2 and LD3

Signal from neutron detector obtained in shot no. 7

Astrophysical S-factor for dd reactions as a function of the deuteron collision energy: the circle and solid circles the results of our research; solid triangles and solid squares are the data from A. Krauss (Nucl. Phys. A465 (1987) 150) and R.E. Brown (Phys. Rev. C41 (1990) 1391)

Dependence of the dd reaction cross section on the deuteron collision energy. The solid circle and circle are the results of our research; solid square is the result of A. Krauss (Nucl. Phys. A465 (1987) 150)

Second step pd reaction MIG (2.5 MA, τ ≈ 80 ns) HCEI RAS (Tomsk, Russia) Start 2003

Experimental lay-out: 1 – generator body; 2 – load module; 3 – diagnostic chamber; 4 – Laval nozzle; 5 – liner; 6 – scintillation detector 3; 7 and 9 – scintillation detectors 1 and 2; 8 – suspended lead shielding; 10 – lead shielding of detectors; 11 – light cone; 12 – collimators; 13 – light guides; 14 – magnetic dB/dt probes; 15 – CD 2 target; 16 – ion collectors

Scheme of ion collector

Oscillograms of the ion current measured with three ion collectors IK1–IK3 in shot 10. The synchronizing pulse is the high-voltage pulse at the load module of the MIG accelerator

Energy distributions of liner protons in shot 10 obtained by transformation of the IK2 and IK3 ion current oscillograms

Oscillograms of signals form optical detectors LD1–LD3 in shot 10

Energy distributions of liner protons P(E pd ) measured by LD- and IK-detectors

Oscillograms of signals from the γ-quantum plastic detectors Dγ1–Dγ3 in shot 10. The solid line is the calculations. The time origin is the time when the HV pulse appears at the load module

Test pd-experiment. Preliminary results (10.2 keV) ≤ 2.5·10 -7 MeV·b (2.7 < E col < 16.7 keV) ≤ 3.9· cm 2 (2.7 < E col < 16.7 keV) = 1.7· cm 2 (at S pd = 1.2·10 -7 MeV·b) S pd (E col ≈ 20 keV) = 1.09·10 -7 MeV·b (G.M. Griffiths et al., Can. J. Phys. 41 (1963) 734) S pd (17 < E col < 27 keV) = 1.2·10 -7 MeV·b (G.J. Schmid et al., Phys. Rev. Lett. 76 (1996) 3088)

A, C – anode, cathode; H – magnetic field; TD – calorimeter; DH – Hall sensor of magnetic field; 1-4 – plates for measuring of induced potential difference; Z1-Z4 – probes for measuring of Hall potential ; C1, C2 – collimators of optical detectors; IC – current of flux depolarization ceramic chamber (l = 150 cm; d = 18 cm) inside of magnetic field H = 2 T; electrodes: 2 pair, I d = 25kA: l = 24 cm, d = 4 cm, h = 2 cm, E flux ≈ 1 kJ; γ-detectors (plastic; S1, S2: 100×100×750 mm; S3: ø160 mm, H=200 mm); dimension of plasma fluxes: in the colliding region: l H = 6 ÷ 10 cm

Q ≈ 10 8 erg; S t = 1 cm 2 ; N 0 ≈ 4·10 16 cm -3 ; t p ≈ 10 μs; V 0 N 0 S 0 = V i N i S i S t – input cross-section of the thermoprobe; t p – duration of the HV pulse on the electrodes Measurement of the induced voltage U between 1 and 2 (3 and 4) Cu electrodes (d = 0.8 cm, S = 1×1 cm 2 ): – Larmor radius L – length of plasma flux depolarization ω i – ion cyclotron frequency

The characteristics of discharge. 1 – voltage on the disharge electrodes; 2 – current of discharge; 3 - power of discharge

Oscillograms: 1, 2 are signals from light detectors C1 and C2; 3 is the Hall potential between probes Z3 and Z4

Power of the discharge in the shots 16-31

Integral distribution of energy density of the one plasma flow Dependence of the energy density of plasma flow from neutral gas pressure in the chamber

Oscillograms of signal from the scintillation γ-detectors in shots 1dd-16dd, 2003 y. Detectors S1 and S3 are used.

Main Results dd-reaction The characteristics of the deuterium liner accelerated in the configuration of inverse Z-pinch at the SGM (I = 950 kA,  = 80 ns) and MIG (I = 1.7 MA,  = 80 ns) accelerators were measured At the MIG accelerator two various methods for studying the inverse Z-pinch formation process and for measuring the energy distribution of ions in the liner (techniques based on registration by light detectors of optical radiation of plasma (H α -line) and ions fluxes by collectors of ions) were desiged and developed It was done the test experiments at the MIG for estimation of background level at study of pd-reaction. The upper bound estimates are obtained for astrophysical S-factor and effective cross section of pd- reaction in the proton-deutron collision energy range 2.7 ÷ 16.7 keV: (10.2 keV) ≤ 2.5·10 -7 MeV·b (2.7 < E col < 16.7 keV) ≤ 3.9· cm 2

The test experiments on the generation of colliding deutron fluxes arising from a discharge current flow in the external magnetic field H = 2T shown that the efficiency of converting the energy introduced in the discharges into the directed motion of deutrons is 0.3– 0.6 (the total power-consuming per one deutron flux is 300 J) and the total number of deutrons in the fluxes is particles/pulse at energy collision 3-6 keV. Simple analytical expressions for estimation of product yields from reaction between light nuclei in the ultralow collision energy range taking in account the thickness and spread of incident particles have been obtained. The values of astrophysical S-factor and dd-reaction effective cross section were obtained: E col, keVS, b·keV, cm (68)4.3 (2.6) (30)9.8 (4.6) (16)21 (6) (18.1)133 (41)

Conclusion All the results obtained indicate that the methods proposed by us for generation of intense plasma fluxes by using the direct and “inverse” Z-pinch as well as colliding plasma fluxes hold much promise for studies of nuclear reactions between light nuclei in the energy range ~keV inaccessibly for classical accelerators

List of last publications (2002 – 2004) 3 He-Detectors in Experiments at the Powerful Pulsed Accelerators, NIM, A490 (2002) 344. Deuterium Liner and Multiparameter Study of the Inverse Z-Pinch Formation Process, JTP, 72 (2002) 29. Generation and Interaction of Intense Opposing Plasma Fluxes, Plasma Physics, 29 (2003) 714. Analytical Estimates of the Product Yields for Nuclear Reaction in the Ultralow Energy Range, Phys. At. Nuclei 66 (2003) 1. Measurement of the Astrophysical S Factor for the dd Reaction at Ultralow Deutron Collision Energies Using Inverse Z-Pinch, Phys. At. Nuclei, 33 (2003) Dynamic of Hydrogen Liner Formation in the Inverse Z-Pinch Configuration at the MIG Accelerator. First Results of Studying the pd Reaction (prepared to the publication). Study of the possibility to use the colliding deutron bems for measure dd-reaction (preparation to the publication in the progress).

Plans 2004 study of the acceleration dynamics of the axial hydrogen plasma bunch with energy content of 300 J and average ion velocity of (4–9)·10 7 cm/s test measurements of the γ quantum yield from the pd reaction in the proton velocity range (4–9)· cm/s investigation of the dd reaction by using colliding deuterium plasma fluxes in the deuteron collision energy range 3-6 keV 2005 measure the S-factor and pd-reaction effective cross sections in the collision energy range of protons with deutrons keV measure the S-factor and dd-reaction cross sections by using opposing deuterium plasma fluxes in the collision energy range 3-6 keV to make the load units for study of the d 3 He-reaction 2006 test study of d 3 He-reaction in the collision energy range of deutrons with nuclei of 3 He 3-10 keV to prepare and publish the results of dd and pd- experiments

Grants Present financial support Russian Foundation for Basic Research – 8 k$/year Grant of Plenipotentiary of Poland at JINR – 8 k$/year Submitted proposal US CRDF (Civilian Research and Development Foundation) (JINR – UCI(USA) – RFNC (Arzamas)) Financial requirements 40 k$/year