Yield of D-D and D-3He fusion reactions produced by the interaction of intense ultrafast laser pulses with molecular clusters

NN2012, May 31th 2012, San Antonio, TXM. Barbui

Basic idea

100-180 J150-200 fs

CD4 can be used in place of D23He can be added in different concentrations

1. Most of the laser energy is absorbed by the molecular clusters

2. The electrons escape first and the clusters coulomb explode

3. Some of the ions have enough energy to drive nuclear reactions

Expected fusion reactions:D + D T (1.01 MeV) + p (3.02 MeV) (50%)D + D 3He (0.82 MeV) + n (2.45 MeV) (50%)

cryogenic

D + 3He 4He (3.6 MeV) + p (14.69 MeV) (100%)D + T 4He (3.5 MeV) + n (14.1 MeV) (100%)

D + 3He 4He (3.6 MeV) + p (14.69 MeV) (100%)

Use the yield of 14.7 MeV protons from the D-3He reaction to extract the astrophysical S factor at very low energies.

Final goal

Since our medium is highly ionized and the electrons move away much faster than the ions we might be able to have a direct measurement of the bare nucleus S factor.

We used the D-D reaction as reference to extract the density of the medium. This reaction has been extensively studied in the last decades. R-matrix calculations of the cross-section of the 4He system are very stable and are supposed to be correct within a 5% for energies up to 1 MeV [Nucl. Fusion 32(1992)611]

Phase 1 D2 clusters D2 clusters + 4He

Phase 2 D2 clusters + 3He CD4 clusters + 3He

Experiment outlineD ions Temperature KT Yield of 2.45MeV n from D+D->n+3HeYield of 3.02MeV p from D+D->p+T

Relative concentration of D and 4HeCheck that adding 4He does not affect the cluster formation

D ions Temperature KTYield of 2.45MeV n from D+D->n+3HeYield of 14.7MeV p from D+3He->p+4HeRelative concentration of D and 3HeThe experimental yields of 14.7 MeV protons are normalized to the same atomic density of D and 3He

Experimental setup

Proton A Proton B

Neutron 4

Neutron 2Neutron 3

Neutron 1

Laser beam direction

Proton C

Faraday cup

3 plastic scintillators from UT

Cryo-cooled nozzle

3 plastic scintillators from UT

Measured observablesTemperature and the number of the energetic ions

3 MeV 14.7 MeV

Faraday cup

4 liquid scintillators NE213 placed at different angles and 6 plastic scintillators placed at 90 degreesThin (254 um) plastic scintillators BC400.

Yield of 3.02 MeV protons

Yield of 14.7 MeV protons

Yield of 2.45 MeV neutrons

Experimental data D-D

No evidence of angular distribution for 2.45 MeV n or 3 MeV p

Same yield for 2.45MeV n and3 MeV p

A different density of D atoms in different shots produce those different lines.

Decreasing density

Experimental data D-3He

Detection limit for the Faraday cup

Temperature estimated from the ratio

The ratio of the two yields is independent of the atomic density and shows a smooth behavior

Same density effect noticed for the D-D reaction

Can we explain what we measured using the available cross-section evaluations for the D-D and D-3He reactions?

D-D reactions may happen inside the plasma plume between two energetic D ions coming from the Maxwellian distribution of measured KT or between an energetic D ion and a D at rest outside the plasma plume.

D-D

2*R=5 mm

2*r=0.5-0.8 mm

<σ >¿𝑇=∫0

∞

2√ 𝐸𝜋 ( 1𝐾𝑇 )

3 /2

𝑒− 𝐸𝐾𝑇 σ (E )dE ¿

<σ v>¿𝑇=∫0

∞

√ 2𝜋 ( 𝑚𝑟

𝐾𝑇 )3 /2

v2𝑒−𝑚𝑟 v

2

2 𝐾𝑇 σ (v )dv ¿

𝜎 (𝐸)= 𝑆(𝐸)𝐸 𝑒−√𝐸𝐺/𝐸

Parameterizations exist for S(E) leading to values of that agree with R-matrix calculations within 1%

𝑆 (𝐸)=𝑎1+𝐸 (𝑎 2+𝐸 (𝑎 3+𝐸 (𝑎4+𝐸𝑎 5 ) ))

Can we explain what we measured using the available cross-section evaluations for the D-D and D-3He reactions?

D-3He reactions happen between energetic D ions coming from the measured Maxwellian distribution and 3He atoms at rest.

D-3He

<σ >¿𝑇=∫0

∞

2√ 𝐸𝜋 ( 1𝐾𝑇 )

3 /2

𝑒− 𝐸𝐾𝑇 σ (E )dE ¿

𝜎 (𝐸)=𝑆(𝐸)𝐸 𝑒− √𝐸𝐺/𝐸

𝑆 (𝐸)= 𝑎 1+𝐸(𝑎2+𝑎 3𝐸)1+𝐸 (𝑏1+𝐸 (𝑏2+𝐸𝑏3 ))

D-D reactivity <sv> and <s> Numerical integral with

parameterization S(E) from [1]- NACRE database

Numerical integral with parameterization S(E) from [1]

- NACRE database <sv>/v

[1]Nucl. Fusion 32(1992)611

D-3He reactivity <sv> and <s>

Numerical integral with parameterization S(E) from [1]

- NACRE database <sv>/v

Numerical integral with parameterization S(E) from [1]

- NACRE database

[1]Nucl. Fusion 32(1992)611

Yield ratio to calculate the ion temperature

Temperature estimated from the ratio

Calculated ratio

1) The yield ratio is independent of the atomic density 2) The temperatures estimated from the yield ratios agree with the temperatures measured from the time of flight 3) Therefore for each point there is an atomic density that reproduces both the yield of 2.45MeV neutrons and 14.7 protons.

We calculated the density needed to reproduce the yield of 2.45 MeV neutrons from the D-D reaction.

The yield of protons is calculated using :

Our data can be described by the bare nucleus S(E) parameterization from ref [1].

CD4

The calculated yield agrees with the measured one within the experimental errors.

Experimental <s> for the D-3He reaction as a function of the temperature in the center of mass

<σ >¿𝑇=∫0

∞

2√ 𝐸𝜋 ( 1𝐾𝑇 )3 /2

𝑒− 𝐸𝐾𝑇 𝑆(𝐸)

𝐸 𝑒−√𝐸𝐺 /𝐸dE ¿

Fitting function:

𝑆 (𝐸)=𝑎 1+𝐸(𝑎2+𝑎 3𝐸)

1+𝐸 (𝑏1+𝐸 (𝑏2+𝐸𝑏3 ))

The parameters b1,b2,b3 define the resonance at E=210 MeV and are fixed to the values of [1]

The parameters a1, a2, a3 are free

S(E) compared with other experimental data

• Aliotta 01 direct data• Krauss 87 direct data

La Cognata 05 THM “bare nucleus”

─ This work

─ La Cognata 05 fit line

We measured the yield of D(D,T)p, D(D,3He)n and D(3He,a)p and the ion temperature.

The temperature can also be calculated using the ratio of the yield of D-D and D-3He reactions This temperature agrees with the measured one within the experimental errors.

If we use the D-D reaction to estimate the atomic density of D. We can use the experimental values of <s>D-3He to fit the parameterization of S(E)D-3He

Our values are agreement with what used so far.

Summary

Improvements of the measurement

Measure of the cluster size and the electron density using Ryleigh scattering and short pulse interferometry as described in [Rev. Sci. Inst. 69(1998)3798]

Repetition of many shots without changing the nozzle conditions.

Larger dimensions of the detectors used for the 14.7MeV protons in order to decrease the statistical error.

Other reactions of can be studied with the same method

What is next?

Texas A&M: M. Barbui, K. Hagel, J.B. Natowitz, K. Schmidt, G. Giuliani.

INFN Italy: A. Bonasera (LNS), S. Kimura (LNS), M. Mazzocco (PD).

University of Texas: W. Bang, G. Dyer, H. Quevedo, E. Gaul, T. Borger, A. Bernstein, M. Martinez, M. Donovan, T. Ditmire.

ENEA Italy: F. Consoli, R. De Angelis, P. Andreoli.

Thank you for your attention!