Muon Cycling Research Articles

Studies on the Kinetics of Muon Catalyzed Fusion in the HT Mixture with Very Low Tritium Concentration

A method for determination of optimum muon cycling coefficient and energy gain in the HT mixture with very low tritium concentration is proposed. The kinetics of the mu-atomic and mu-molecular processes preceding the pt reaction in the ptµ molecule is described. The time variations of γ quanta and conversion muons and the other particles formation in nuclear fusion reactions in ptµ molecules are studied. Our calculations show that, the optimum value of muon cycling coefficient at Ct=0.01 is equal to 106. In this paper our obtained results from theoretical calculations and experimental results are compared with together and we can receive that the obtained results are in good agreement with measured values. the rate of muon transfer from pµ atom to triton, the rate of transition between hyperfine levels of tµ atoms, the rate of formation of the ptµ molecule, the rate of nuclear synthesis in it and muon sticking) to interpret correctly the results of experiments in the triple mixture of hydrogen isotopes H-D-T and to describe the kinetics of all processes occurring in the mixture. From the theoretical point of view, the experiments investigating µCF processes in hydrogen -tritium mixture will allow one to test an algorithm describing a three-body system of particles interacting according to coulomb rule. It is necessary to emphasize the importance of the µCF study in HT mixture in order to obtain the information about characteristics of pt-reaction at ultra law energy range (≈KeV). The investigation of the reaction between light nuclei at ultra law energies (≈KeV) is very important for verification of fundamental symmetries in string interactions (3)-(5) the contribution of muon exchange currents and to solve some astrophysical problems. At present, there are few experiments that investigate characteristics of µCF in a H-T mixture. Only one was performed with a HT mixture and the references with triple mixture H-D-T. In this paper the authors survey the major areas of research: Section I describes the details of the kinetics of the µCF in HT mixture, while Sec. II describes the nonlinear point dynamics equations in HT mixture. Sec.III discusses on the numerical solution of these equations versus time in muon life time range. Sec.IV describes the optimum cycling coefficient and energy gain. The final section presents an overview of what is known, and outline some directions for future research.

Muon catalyzed fusion in the target H-T/D2/H-D by taking fast muon conversion

In past years, two/three-layer hydrogen targets with a composition of H/D/T at temperature ~3K have been studied for muon catalyzed fusion. Several theoretical and experimental studies have evaluated that the conversion efficiency of fast muons in such targets is very low. Here, the muon cycling coefficient has been determined for the heterogeneous target of by taking the conversion efficiency of incident muons of momentum 26.25 . This parameter extremely affects the muon cycling coefficient by the reason of slow muon cycles in the third layer of . The optimal muon cycling coefficient equals 87.5. Key words: Three-layer target, condensed hydrogen-deuterium layer, muon cycling coefficient, fast muon.

Muon Dynamics in the Multilayered Target H–T/D2/H2–D2 at Low Temperature

Recently, muon catalyzed fusion in the multilayered targets H/D/T at temperature 3 K has been investigated. The latest theoretical and experimental works have confirmed that muon conversion efficiency in such multilayered systems is low. This strongly affects the muon cycling coefficient in the structure H–T/D2/H2–D2. The first layer emits tμ(1s) atoms. They are moderated in the pure deuterium layer. In the third layer, the muonic deuterium atoms rapidly cascade and reach the ground state. The probability that a μp atom reaches the 1s state depends on deuterium concentration. In low concentration of deuterium, the hyperfine transition of dμ(1s) atom is of particular interest. A kinetic model for such processes is given. Our work clearly shows Wolfenstein–Gerstein (W.G.) effect.

An optimized hydrogen target for muon catalyzed fusion

This paper deals with the optimization of the processes involved in muon catalyzed fusion. Muon catalyzed fusion ( μ CF ) is studied in all layers of the solid hydrogen structure H / 0.1 % T ⊕ D 2 ⊕ HD . The layer H/ T acts as an emitter source of energetic t μ atoms, due to the so-called Ramsauer–Townsend effect. These t μ atoms are slowed down in the second layer (degrader) and are forced to take place nuclear fusion in HD. The degrader affects time evolution of t μ atomic beam. This effect has not been considered until now in μ CF -multilayered targets. Due to muon cycling and this effect, considerable reactions occur in the degrader. In our calculations, it is shown that the fusion yield equals 180 ± 1.5 . It is possible to separate events that overlap in time.

MUONIC PROCESSES DYNAMIC IN SOLID HETEROGENEOUS H/D/T MIXTURE

The Ramsauer–Townsend effect in hydrogen is used in a heterogeneous solid hydrogen-deuterium-tritium (H/D/T) multi-layer system to provide forced resonance muonic deuterium-tritium molecule formation. The effects of hyperfine splitting in the μd atom on the final state of nuclear spins are studied in the μpd molecule at low temperature. As deuterium concentration increases, so does the spin-flip rate, thus reducing the initial population of the quartet (s=3/2) nuclear spin of the μpd molecule and enhancing the doublet (s=1/2) state. The doublet rate is dominant, and total fusion yield increases with deuterium concentration until the lack of protium atoms significantly reduces the rate of μpd molecule formation and μdd fusion dominates completely. The Wolfenstein–Gerstein effect and the no-quartet theorem in the solid H/D layer are considered by solving the muon dynamical equations for various deuterium concentrations. It is shown that the no-quartet theorem is not valid at low temperature and deuterium concentration, but is valid only if one neglects the mixed-symmetry components. The written coupled linear point dynamical equations for the suggested system are solved using the "Lsode" computer code. The results obtained for the optimum layer thicknesses and deuterium concentration are compared with the results of a solid homogeneous deuterium-tritium system in the same physical condition (temperature, density and deuterium concentration). It is shown that for the same physical conditions, the muon cycling coefficient of two isotopes of deuterium-tritium (D/T) has only 2.7% of the muon cycling coefficient of the suggested forced solid heterogeneous H/D/T fusion system. It is shown that with very little deuterium concentration (cd=0.005), the obtained muon cycling rate and coefficient are ~147 μ s -1 and 178, respectively.

FORCED MUON CATALYZED FUSION IN HETEROGENEOUS LAYERS OF HYDROGEN ISOTOPES

Muon cycling dynamics for muon catalyzed fusion in heterogeneous solid layers are considered through decay of complex molecule [Formula: see text]. The suggested fusion system consists of three layers which are alternatively repeated. The first layer is D/T (deuterium, tritium) which provides [Formula: see text] molecules. The second layer is T2 molecules which are used to slow down the muonic atoms and the third layer is D2 molecules. The design is in a way in which dtμ, muonic deuterium and tritium molecules, are produced in resonance. It is shown, by considering muonic dynamics theoretically in a suggested heterogeneous system and determining its cycling rate by using a more advanced calculational method, that for equal deuterium, tritium concentration (Cd=Ct=0.5) in D/T layer and ϕ'=ϕ0=ϕ=1 (relative density for each layer respectively and given in liquid hydrogen density LHD=4.25×1022 cm -3), the muon cycling rate is optimum for the suggested heterogeneous system and has 15% enhancement with respect to the conventional D/T system. It is also shown that for ϕ0<0.0003 the muon cycling rate in D2 is almost stopped, and for ϕ0≥1 muon cycling rate increases, but this is not recommended due to low and costly tritium availability.

Anomalous Temperature-Dependent Phenomena of Muon Catalyzed Fusion in Solid Deuterium and Tritium Mixtures

A systematic experimental study was conducted on muon-catalyzed fusion in solid deuterium and tritium mixtures. Various conditions were investigated, i.e. tritium concentrations from 20% to 70%, and temperatures from 5 K to 16 K. With decreasing temperature, unexpected increase in the muon cycling rate and decrease in the muon loss probability were observed. The former change is interpreted to be caused by the temperature dependence in the dtp formation process. The most probable origin of the latter change is the temperature dependence in the muon reactivation process after muon-to-a sticking.

MUON CATALYZED FUSION DYNAMICS IN SOLID HETEROGENEOUS H/D/T MIXTURE AND ITS COMPARISON WITH SOLID HOMOGENEOUS D/T SYSTEM

The Ramsauer–Townsend effect in hydrogen is used to force the muonic tritium in suggested heterogeneous solid hydrogen–deuterium–tritium (H/D/T) multilayer system to provide resonance muonic deuterium–tritium molecule formation. The written coupled linear point dynamical equations for the suggested system are solved by Monte-Carlo method using "Lsode" computer code. The obtained results for the optimum layer thicknesses and tritium concentration are compared with the results of solid homogeneous deuterium–tritium system in the same physical condition (temperature, density and tritium concentration). It is shown that for the same physical conditions, the muon cycling coefficient of two isotopes of deuterium–tritium (D/T) has only 3% muon cycling coefficient of suggested heterogeneous solid forced H/D/T fusion system. It is shown that with very little tritium concentration (ct = 0.005) the obtained muon cycling rate and coefficient are ~ 120 μs-1 and 165 respectively.

Discovery of temperature-dependent phenomena of muon-catalyzed fusion in solid deuterium and tritium mixtures.

A systematic experimental study on muon-catalyzed fusion was conducted using a series of solid deuterium and tritium mixtures. A variety of conditions were investigated, i.e., tritium concentrations from 20% to 70%, and temperatures from 5 to 16 K. With decreasing temperature, we observed an unexpected decrease in the muon cycling rate (lambda(c)) and an increase in the muon loss probability (W). The origins of these observed changes were interpreted by the temperature-dependence in the dt mu formation process for lambda(c) and that in the muon reactivation process after muon-to-alpha sticking for W.

EFFECTS OF THE SIDE-PATH MODEL ON THE MUON TOTAL STICKING COEFFICIENT AND CYCLING RATE IN D/T μCF

In this paper we explore the effects of the meta-stable states of dtμ* molecules on crucial parameters in μCF such as total sticking coefficient and muon cycling rate. For this purpose we establish a new approach in the study of the determination of the q1s parameter and the relative population of muonic atoms by solving the kinetics of μCF. We have answered the basic questions about the muon total sticking including the side-path effects.

Impact of the side-path model on the muon cycling rate density dependence in D-T mixtures

The side-path model previously suggested by us allows for muon transferfrom tritiumto deuterium via intermediate dtµ* resonances formed in tµ(2s)-D2 collisions. Taking this effect into account, the density dependence of the muon cycling rate in D-T mixtures at low temperatures is analysed. Compared with cascade models where only one-sided transfer is present, the predicted density dependence of λc is in better agreement with measurements.

Resonance sidepath in muon catalyzed fusion.

We have investigated a previously unconsidered sidepath in muon catalyzed fusion. We have found that high formation rates of metastable $\mathrm{dt}{\ensuremath{\mu}}^{*}$ molecules in $t\ensuremath{\mu}(2s)$-${\mathrm{D}}_{2}$ collisions and their subsequent decay into $t\ensuremath{\mu}(1s)$ or $d\ensuremath{\mu}(1s)$ atoms open a return path for the muon from tritium to deuterium. This process can be considered as muon transfer from $t\ensuremath{\mu}(2s)$ to $d\ensuremath{\mu}(1s)$ via three-body resonances of $\mathrm{dt}{\ensuremath{\mu}}^{*}$. This enlarges the $d\ensuremath{\mu}(1s)$ population and quenches the muon cycling rate, in agreement with experimental findings.

Muon-catalysed fusion as a finite Markov process

By regarding muon catalysis of nuclear fusion in a mixture of hydrogen isotopes as a series of stochastic processes. Markov chain theory is used to derive several exact analytic equations relating the rates of the various reactions and the sticking coefficients for the fusion channels. These include expressions for the mean number of pd, dd, dt, tt and pt fusion per muon, the mean total number of fusions per muon and the muon cycling rate lambda c, which reduce to the corresponding well known expressions for catalysis in a deuterium-tritium mixture. Inclusion of the fusion reaction dd mu to p mu +t provides a particularly interesting complication, as this process gives rise to a catalysis cycle that may not return a free muon to the system. The application of Markov chain theory to more complex catalysis schemes, such as those including hyperfine states of the mesic atoms and mesic molecules, is considered briefly.

Resonant Mesonic-Molecule Formation in Muon-Catalyzed D-T Fusion

In the resonant formation of $\mathrm{dt}\ensuremath{\mu}$ mesonic molecules, the incoming orbital and molecular angular momenta contribute in an essential way. The earlier calculation of Vinitsky et al. for the resonant molecular formation rate is generalized to incorporate these effects, and the resultant contributions of hundreds of resonances are included. The muon cycling rate is calculated and compared with recent experimental results.