Muon Catalyzed Fusion Research Articles

Effective Muon Losses in the Muon Catalyzed Fusion Cycle in a Double D/T Mixture at High Temperature and Density

The effective muon losses w measured in the last experiment of the JINR group with D/T mixture are analyzed. They are considered as a function of the tritium concentration C t taken for different temperatures. The obtained results indicate different muon transfer rates from deuterium and tritium to impurities with Z>1 (λ dZ and λ tZ ) and show that the ratio λ tZ /λ dZ increases with temperature.

Design of the Intense Neutron Source Based on Muon Catalyzed Fusion for Irradiation Materials of Fusion Reactors and Other Applications

CF-INS) is designed to test the structural materials of D–T fusion reactors by neutronirradiation [1, 2, 4–7, 13]. Recently a possibility of transmutation of radiotoxicisotopes using such a type of a neutron source was also considered in [3]. A com-parison of characteristics of different types of intense neutron sources is givenin [1, 23] and in the conclusion of this report. Here we recall only the main featuresof

Deuterium High-Pressure Target

The design of deuterium high-pressure target of 76 cm3 volume developed to study muon catalyzed fusion in diffusion-pure deuterium over an 80–800 K temperature range at up to 150 MPa pressure is presented.

Adiabatic Hyperspherical Approach to the Problems of Muon Catalyzed Fusion

The adiabatic hyperspherical approach (AHSA) is applied for the numerical investigation of the scattering processes and resonances in Coulomb three-body mesic atomic systems. The results of the calculations of elastic and inelastic cross sections in low-energy collisions aμ + b (a, b = p, d, t), energies, lifetimes and local characteristics of resonant states of mesic molecular ions nHeaμ+ (n = 3, 4) are presented.

Study of muon-catalyzed fusion in ortho-para controlled solid deuterium

We observed the dependence of the rate of the muon-catalyzed fusion (μCF) on the ortho–para state (the nuclear spin state) of deuterium in order to investigate the source of the surprising contradiction of the resonant formation rate of a ddμ molecule in solid between experiments and theories. The ortho–para dependence of the molecular formation rate and the dμ hyperfine transition rate was clearly observed for the first time. The rate of the hyperfine transition by scattering was determined and was smaller than that of the theoretical prediction. The back decay rate was experimentally determined for the first time. Also, new insight for phenomena of the dd–μCF in solid was presented by interpreting the observed ortho–para dependence.

Experimental Results on Muon Catalyzed dt Fusion in H/D/T Mixture

Experimental study on muon catalyzed dt fusion in a triple mixture of hydrogen isotopes (H/D/T) was carried out at the JINR phasotron. The measurements have been performed at various temperatures and densities with liquid and gaseous H/D/T mixtures. Results are presented for the main characteristics of the dtμ cycle. A reduction of the number of dt fusions is observed when hydrogen is added to the D/T mixture, This is mainly due to muon loss to the pt and pd cycles, which have a high sticking probability. We also observe an increase of the cycle rate when the temperature of the H/D/T mixture rises. This confirms the theoretical prediction.

Resonant formation of d&mgr;t molecules in deuterium: An atomic beam measurement of muon catalyzed dt fusion

Resonant formation of d&mgr;t molecules in collisions of muonic tritium ( &mgr;t) on D2 was investigated using a beam of &mgr;t atoms, demonstrating a new direct approach in muon catalyzed fusion studies. Strong epithermal resonances in d&mgr;t formation were directly revealed for the first time. From the time-of-flight analysis of 2036+/-116 dt fusion events, a formation rate consistent with 0.73+/-(0.16)(meas)+/-(0.09)(model) times the theoretical prediction was obtained. For the largest peak at a resonance energy of 0.423+/-0.037 eV, this corresponds to a rate of (7.1+/-1.8)x10(9) s(-1), more than an order of magnitude larger than those at low energies.

Treatment of thetμ+D2reaction by the methods of quantum reactive scattering

We have applied the methods of quantum reactive scattering to the key resonant reaction in the muon catalyzed fusion (MCF) cycle that leads to the formation of a $\mathrm{dt}\ensuremath{\mu}$ muonic molecular ion, in which fusion takes place very rapidly. We have calculated reaction probabilities for the resonances that occur in $t\ensuremath{\mu}+{\mathrm{D}}_{2}$ scattering for incident kinetic energies less than 0.6 eV and total angular momentum ${J}_{\mathrm{tot}}=0.$ To reduce the six-body problem to a three-body problem, the motions of the electrons were treated in the Born-Oppenheimer (BO) approximation while those of the muon were treated with a sophisticated adiabatic approximation. The resulting three-body potential energy surface (PES) was represented by a pairwise additive approximation. The $\mathrm{dt}\ensuremath{\mu}$ part of the PES was scaled to allow it to exhibit the correct binding energy of the crucial $(J,v)=(1,1)$ state. Scattering calculations were carried out using a hyperspherical formulation, and the positions of the resonances were found to occur at energies of a few meV greater than if $\mathrm{dt}\ensuremath{\mu}$ is assumed to be a point particle. A comparison of the resonances with the Breit-Wigner formula allowed us to calculate partial widths for back decay, ${\ensuremath{\Gamma}}_{e}^{{J}_{\mathrm{tot}}}.$ Once these are known for all significant ${J}_{\mathrm{tot}},$ the rate of formation of $\mathrm{dt}\ensuremath{\mu}$ can be determined. This rate, next to the sticking fraction, is the most important parameter in determining the rate of the entire MCF cycle. We have also carried out a calculation whereby the muon was treated in a BO formalism and have found significant differences in the final results, demonstrating the importance of treating the muon as accurately as possible. This work represents a successful ab initio calculation of this reaction.

Study of Nuclear Physics for Nuclear Fusion

Based on the concept of “damp matching” [1] and the famous d + t fusion data, a conventional quantum mechanics calculation shows that the plasma fusion, muon-catalyzed fusion, and the low-energy nuclear reaction are essentially same in the sense of resonant tunneling through the Coulomb barrier. The good agreement between theory and experimental data justifies the selectivity in resonant tunneling, which implies the possibility of having fusion energy with no strong neutron and gamma radiation.

Magnetic-field-stimulated transitions of excited states in fast muonic helium ions

It is shown that one can stimulate, by using the present-day laboratory magnetic fields, transitions between the $lm$ sub-levels of fast $\mu He^+$ ions formating in muon catalyzed fusion. Strong fields also cause the self-ionization from highly excited states of such muonic ions. Both effects are the consequence of the interaction of the bound muon with the oscillating field of the Stark term coupling the center-of-mass and muon motions of the $\mu He^+$ ion due to the non-separability of the collective and internal variables in this system. The performed calculations show a possibility to drive the population of the $lm$ sub-levels by applying a field of a few $Tesla$, which affects the reactivation rate and is especially important to the $K\alpha$ $x$-ray production in muon catalyzed fusion. It is also shown that the $2s-2p$ splitting in $\mu He^+$ due to the vacuum polarization slightly decreases the stimulated transition rates.

Experimental investigation of muon-catalyzed dt fusion at cryogenic temperatures

An experimental investigation of muon-catalyzed fusion ( μCF) in gaseous, liquid and solid mixtures of deuterium and tritium was performed. The target conditions included the range of densities of 0.03 ≲ φ ≲ 1.5, tritium concentrations of 2% ≲ c t ≲ 90% and temperatures of 13 ≲ T ≲ 40 K. The study was based on the analysis of observed cycling rates extracted from the measured time distributions of the fusion neutrons. For the first time, the density dependence of the rates λ ( dtμ) d 0 for the dtμ molecule formation in collisions of tμ atoms in the lower (F=0) hyperfine state with D 2 molecules was determined experimentally. Evidence for the proposed effects of below-threshold resonances on molecular formation was found. Measurements at low temperatures in mixtures of different molecular compositions revealed a clear predominance of the λ ( dtμ) d 0 formation rate. The probability q 1 s for dμ atoms to reach the ground state was determined as a function of density and tritium concentration.

Muon catalyzed fusion and muon to 3 He transfer in solid T 2 studied by X-ray and neutron detection

X-ray and neutron measurements were carried out for muon catalyzed fusion and related phenomena in solid T2. The X-ray originated from the μ- to α sticking in muon catalyzed fusion; t + t + μ-→ (μ-α) + 2n was measured for the first time, yielding Kα X-ray intensity of (μα) atom and the intensity ratio of Kβ to Kα. Utilizing the phenomena of 3He accumulation in solid T2, the X-ray in the μ- transfer process from (tμ) to 3He was detected, providing a formation rate and radiative decay branching-ratio of (t3Heμ) molecule. From fusion neutron measurements, estimated values were obtained for (ttμ) molecular formation rate as well as sticking probability ωt in ttμ fusion. A possible new insight in t + t fusion reaction process at a low energy limit is also obtained.

A TREATMENT OF THE TMU + D2 REACTION BY THE METHODS OF QUANTUM REACTIVE SCATTERING

In this article, we describe how we are applying the methods of chemically reactive scattering to the key resonant reaction in muon catalysed fusion. Preliminary results are presented for cross-sections.

Facility for preparation of gas mixture in muon catalyzed fusion experiments

A facility is described that allows safe handling of high tritium gas activity as dozens kilocuries in a regular laboratory environment. It is used to make and deliver into the target a mixture of specific isotopic composition with the contamination requirement of 10-7 v.f. for Z>1 elements, and recover it upon completion of operation. With this facility, efforts have been accomplished to investigate into the muon catalyzed fusion on two targets – liquid tritium and high-pressure tritium types. Also, the operation range was 0.1–120 MPa for pressure and 20–800 K for temperature and the amount of tritium used was about 100 kCi. The facility showed reliability in operation without indications of radiation beyond the safety level.

Magnetic field stimulated transitions of excited states in fast μHe+ ions

It is shown that one can stimulate, by using the present-day laboratory magnetic fields, transitions between the lm sub-levels of fast μHe+ ions formed in muon catalyzed fusion. This gives a possibility to drive the population of the lm sub-levels by applying a field of a few Tesla, which affects the reactivation rate and is especially important to the Kα X-ray production. Strong fields also cause the self-ionization from highly excited states of the muonic helium.

Hydrogen/deuterium-mixtures as a laboratory for the study of the muonic cascade and muon-catalyzed fusion

We have performed an experiment to investigate various processes induced by muons in hydrogen-deuterium mixtures. Preliminary results are given for cascade X-ray yields, q1s, relative yields of conversion muons and fusion γ-rays, molecular formation and hyperfine transition rates.

Muon catalyzed fusion in deuterium gas

We present the results of an experiment performed at PSI to investigate muon catalyzed fusion in pure deuterium gas of 5% density (LHD) at temperatures ranging from 28 K to 350 K. Using a new high pressure ionization chamber the reactions dd → n + 3He and dd → p+t were observed with 100% detection efficiency. The rates of dμd formation were measured with the absolute precision of 1% and the μd spin-flip rates with 0.5%. The temperature dependence of molecular formation and spin-flip rates display pronounced resonance structures. A preliminary fit based on the Vesman mechanism of resonant muonic molecule formation was carried out yielding a dd fusion rate of 3.5·108 s-1 and a hfs splitting energy \(\delta \varepsilon _{d\mu d} \) of 24.3 meV, both in good agreement with the theory.

A CRYOGENIC TARGET TO STUDY CHARGE NONSYMMETRIC MUONIC MOLECULES

An experimental setup, including a cryogenic gas target with temperature control and gas filling systems, has been developed to study muon catalyzed fusion in gas mixtures of hydrogen and helium isotopes.

Calculation of equilibrium composition and establishing time in a mixture of three hydrogen isotopes

A mathematical model describing the kinetics of establishing equilibrium is developed. Equilibrium concentrations of isotopic molecules for gas mixtures used in muon catalyzed fusion research are calculated.

Measurement of the fusion rate in μd 3 He

Many atomic and molecular processes may occur after a muon has been stopped in a mixture of hydrogen and helium isotopes. In particular, the muonic molecule μd3He can be formed. This molecule either decays or undergoes muon catalyzed fusion. Theory predicts a fusion rate much lower than the decay rate; moreover, the various theoretical predictions differ from each other by several orders of magnitude.