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Prediction of the critical reduced electric field strength for carbon dioxide and its mixtures with copper vapor from Boltzmann analysis for a gas temperature range of 300 K to 4000 K at 0.4 MPa

The influence of copper vapor mixed in hot CO{sub 2} on dielectric breakdown properties of gas mixture at a fixed pressure of 0.4 MPa for a temperature range of 300 K–4000 K is numerically analyzed. First, the equilibrium composition of hot CO{sub 2} with different copper fractions is calculated using a method based on mass action law. The next stage is devoted to computing the electron energy distribution functions (EEDF) by solving the two-term Boltzmann equation. The reduced ionization coefficient, the reduced attachment coefficient, and the reduced effective ionization coefficient are then obtained based on the EEDF. Finally, the critical reduced electric field (E/N){sub cr} is obtained. The results indicate that an increasing mole fraction of copper markedly reduces (E/N){sub cr} of the CO{sub 2}–Cu gas mixtures because of copper's low ionization potential and large ionization cross section. Additionally, the generation of O{sub 2} from the thermal dissociation of CO{sub 2} contributes to the increase of (E/N){sub cr} of CO{sub 2}–Cu hot gas mixtures from about 2000 K to 3500 K.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The role of electron scattering with vibrationally excited nitrogen molecules on non-equilibrium plasma kinetics

Electron energy distribution functions have been calculated by a self-consistent model which couples the electron Boltzmann equation with vibrationally and electronically excited state kinetics and plasma chemistry. Moderate pressure nitrogen gas discharges in the E/N range from 30 to 60 Townsend are investigated comparing an electron-impact cross section set considering transitions starting from all the vibrational states, with reduced models, taking into account only collisions involving the ground vibrational level. The results, while confirming the important role of second kind collisions in affecting the eedf, show a large dependence of the eedf on the set of inelastic processes involving vibrationally and electronically excited molecules, pointing out the need of using a cross section database including processes linking excited states in non-equilibrium plasma discharge models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Polarization contributions to intermolecular interactions revisited with fragment electric-field response functions

The polarization energy in intermolecular interactions treated by self-consistent field electronic structure theory is often evaluated using a constraint that the atomic orbital (AO) to molecular orbital transformation is blocked by fragments. This approach is tied to AO basis sets, overestimates polarization energies in the overlapping regime, particularly in large AO basis sets, and lacks a useful complete basis set limit. These problems are addressed by the construction of polarization subspaces based on the responses of isolated fragments to weak electric fields. These subspaces are spanned by fragment electric-field response functions, which can capture effects up to the dipole (D), or quadrupole (DQ) level, or beyond. Schemes are presented for the creation of both non-orthogonal and orthogonal fragment subspaces, and the basis set convergence of the polarization energies computed using these spaces is assessed. Numerical calculations for the water dimer, water–Na{sup +}, water–Mg{sup 2+}, water–F{sup −}, and water–Cl{sup −} show that the non-orthogonal DQ model is very satisfactory, with small differences relative to the orthogonalized model. Additionally, we prove a fundamental difference between the polarization degrees of freedom in the fragment-blocked approaches and in constrained density schemes. Only the former are capable of properly prohibiting charge delocalization during polarization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Study of the dielectric breakdown properties of hot SF{sub 6}–CF{sub 4} mixtures at 0.01–1.6 MPa

The dielectric breakdown properties of SF{sub 6}–CF{sub 4} mixtures were investigated at different ratios of SF{sub 6}, 0.01–1.6 MPa, and gas temperatures up to 3000 K. Initially, the equilibrium compositions of SF{sub 6}–CF{sub 4} mixtures were calculated by minimizing the Gibbs free energy under the assumptions of local thermodynamic and chemical equilibrium. Then the electron energy distribution function was obtained based on those data by solving the Boltzmann equation under the zero-dimensional two-term spherical harmonic approximation. Finally, the critical reduced electric field strength (E/N){sub cr} of SF{sub 6}–CF{sub 4} mixtures, which is defined as the value for which total ionization reaction is equal to total attachment reaction, were determined and analyzed. The results confirm the superior breakdown properties of pure SF{sub 6} at relatively low gas temperatures. However, for higher gas temperatures (i.e., T > 2200 K at 0.4 MPa), the (E/N){sub cr} in SF{sub 6}–CF{sub 4} mixtures are obviously higher than that in pure SF{sub 6} and the values of (E/N){sub cr} increase with the reduction of the ratio of SF{sub 6}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anisotropic Thermal and Mechanical Characteristics of Graphene: A Molecular Dynamics Study

In the present work, molecular dynamics simulation has been performed to characterize the thermal and mechanical behavior of graphene sheet. For this purpose, graphene sheet is subjected to dynamic heating process and its melting point has been predicted. Structural and thermal properties have been analyzed using radial distribution function and energy per atom. To analyze factors affecting melting temperature, four graphene sheets with different dimensions have been chosen for the dynamic heating process. The melting temperature of graphene decreases with increase in the sheet dimension, hence graphene sheet having smaller dimensions show relatively better thermal stability. To analyze the mechanical behavior, graphene sheet has been subjected to uniaxial tensile loading along zigzag and armchair directions respectively. It is observed that zigzag-oriented graphene sheet shows high fracture strength and stability as compared to armchair direction. Multilayer graphene sheets have been selected to investigate the effect of multilayers on the mechanical strength. It can be revealed from results that fracture strength decreases with increase in layers, however, brittleness of the sample relatively decreases with increase in a number of graphene layers.

79 ASTRONOMY AND ASTROPHYSICS↗

Towards a better comprehension of plasma formation and heating in high performances electron cyclotron resonance ion sources (invited)

Further improvements of electron cyclotron resonance ion sources (ECRIS) output currents and average charge state require a deep understanding of electron and ion dynamics in the plasma. This paper will discuss the most recent advances about modeling of non-classical evidences like the sensitivity of electron energy distribution function to the magnetic field detuning, the influence of plasma turbulences on electron heating and ion confinement, the coupling between electron and ion dynamics. All these issues have in common the non-homogeneous distribution of the plasma inside the source: the abrupt density drop at the resonance layer regulates the heating regimes (from collective to turbulent), the beam formation mechanism and emittance. Possible means to boost the performances of future ECRIS will be proposed. In particular, the use of Bernstein waves, in preliminary experiments performed at Laboratori Nazionali del Sud (LNS) on MDIS (microwave discharge ion sources)-type sources, has permitted to sustain largely overdense plasmas enhancing the warm electron temperature, which will make possible in principle the construction of sources for high intensity multicharged ions beams with simplified magnetic structures.

43 PARTICLE ACCELERATORS↗

Effect of hydrogen ratio on plasma parameters of N{sub 2}-H{sub 2} gas mixture glow discharge

A dc plane glow discharge in a nitrogen-hydrogen (N{sub 2}-H{sub 2}) gas mixture has been operated at discharge currents of 10 and 20 mA. The electron energy distribution function (EEDF) at different hydrogen concentrations is measured. A Maxwellian EEDF is found in the positive column region, while in both cathode fall and negative glow regions, a non-Maxwellian one is observed. Langmuir electric probes are used at different axial positions, gas pressures, and hydrogen concentrations to measure the electron temperature and plasma density. The electron temperature is found to increase with increasing H{sub 2} concentration and decrease with increasing both the axial distance from the cathode and the mixture pressure. At first, with increasing distance from the cathode, the ion density decreases, while the electron density increases; then, as the anode is further approached, they remain nearly constant. At different H{sub 2} concentrations, the electron and ion densities decrease with increasing the mixture pressure. Both the electron and ion densities slightly decrease with increasing H{sub 2} concentration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Computational study of plasma sustainability in radio frequency micro-discharges

We apply an implicit particle-in-cell Monte-Carlo (PIC-MC) method to study a radio-frequency argon microdischarge at steady state in the glow discharge limit, in which the microdischarge is sustained by secondary electron emission from the electrodes. The plasma density, electron energy distribution function (EEDF), and electron temperature are calculated in a wide range of operating conditions, including driving voltage, microdischarge gap, and pressure. Also, the effect of gap size scaling (in the range of 50-1000 μm) on the plasma sustaining voltage and peak electron density at atmospheric pressure is examined, which has not been explored before. In our simulations, three different EEDFs, i.e., a so-called three temperature hybrid mode, a two temperature α mode, and a two temperature γ mode distribution, are identified at different gaps and voltages. The maximum sustaining voltage to avoid a transition from the glow mode to an arc is predicted, as well as the minimum sustaining voltage for a steady glow discharge. Our calculations elucidate that secondary electrons play an essential role in sustaining the discharge, and as a result the relationship between breakdown voltage and gap spacing is far away from the Paschen law at atmospheric pressure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

MONTE CARLO SIMULATION OF METASTABLE OXYGEN PHOTOCHEMISTRY IN COMETARY ATMOSPHERES

Cometary atmospheres are produced by the outgassing of material, mainly H{sub 2}O, CO, and CO{sub 2} from the nucleus of the comet under the energy input from the Sun. Subsequent photochemical processes lead to the production of other species generally absent from the nucleus, such as OH. Although all comets are different, they all have a highly rarefied atmosphere, which is an ideal environment for nonthermal photochemical processes to take place and influence the detailed state of the atmosphere. We develop a Monte Carlo model of the coma photochemistry. We compute the energy distribution functions (EDF) of the metastable O({sup 1}D) and O({sup 1}S) species and obtain the red (630 nm) and green (557.7 nm) spectral line shapes of the full coma, consistent with the computed EDFs and the expansion velocity. We show that both species have a severely non-Maxwellian EDF, that results in broad spectral lines and the suprathermal broadening dominates due to the expansion motion. We apply our model to the atmosphere of comet C/1996 B2 (Hyakutake) and 103P/Hartley 2. The computed width of the green line, expressed in terms of speed, is lower than that of the red line. This result is comparable to previous theoretical analyses, but in disagreement with observations. We explain that the spectral line shape does not only depend on the exothermicity of the photochemical production mechanisms, but also on thermalization, due to elastic collisions, reducing the width of the emission line coming from the O({sup 1}D) level, which has a longer lifetime.

79 ASTRONOMY AND ASTROPHYSICS↗

Production of neutron-rich heavy nuclei in deep-inelastic 208 Pb + 208 Pb collisions within the stochastic mean-field theory

In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Theory of extreme correlations using canonical Fermions and path integrals

The t–J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson–Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ{sub 0} that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum E{sub Q}{sup ∗}∼γQ−√(Γ{sub 0}{sup 2}+Q{sup 2}), where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ{sub 0} on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations. -- Highlights: •Spectral function of the Extremely Correlated Fermi Liquid theory at low energy. •Electronic origin of low energy kinks in energy dispersion. •Non Hermitian representation of Gutzwiller projected electrons. •Analogy with Dyson–Maleev representation of spins. •Path integral formulation of extremely correlated electrons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

First principles investigation of GaNbO{sub 4} as a photocatalytic material

We have performed first principles density functional total energy calculations on pure and doped GaNbO{sub 4} to investigate its applicability as a photo catalyst. Pure GaNbO{sub 4} is an indirect, wide band gap semiconductor similar to the widely investigated TiO{sub 2} which is known to be a photo catalyst in UV light [K. Yang et. al. Chem. Mater. 20, 6528 (2008)]. S atom doping of TiO{sub 2} reduces the band gap [F. Tian et. al. J. Phys. Chem. B 110, 17866 (2006)], and increases its efficiency in the visible light range. It has been experimentally reported that S doping of GaNbO{sub 4} at the O site, decreases its photo catalytic efficiency. Our band structure calculations show that both pure and doped GaNbO{sub 4} have indirect band gaps and S atom doping reduces the band gap in agreement with experiments. The decrease in the band gap is due to the lowering of the conduction band minimum towards the Fermi level. An unequal reduction in the band gap was observed at the four inequivalent O sites chosen for S doping. This suggests that the photo catalytic activity varies with the dopant site.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A New Method for Low Cost Production of Titanium Alloys for Reducing Energy Consumption of Mechanical Systems

This project investigated an innovative manufacturing process intended to minimize the cost of production of titanium materials and components, and increase the adoption of Ti components for energy consuming applications, such as automobiles. A key innovation of the proposed manufacturing approach is a novel Ti powder sintering technology for making titanium materials with ultrafine grain microstructure in the as-sintered state with minimum, or an absence, of post-sintering processes. The new sintering technology is termed Hydrogen Sintering and Phase Transformations (HSPT), and constitutes a promising manufacturing technology that can be used to produce titanium (Ti) materials and components in a near-net-shape form, thus also minimizing machining costs. Our objective was to meet, or possibly surpass, the mechanical property levels for ASTM B348 Grade 5 for wrought Ti-6Al-4V. Although specific applications call for varying mechanical property requirements, ASTM B348 was created for the demanding applications of the aerospace industry, and is the established standard for Ti-6Al-4V. While the primary goal was to meet, or exceed this standard, the team also had the goal of demonstrating this could be done at a significantly lower cost of production. Interim goals of the project were to fully develop this novel sintering process, and provide sufficient baseline testing to make the method practical and attractive to industry. By optimizing the process parameters for the sintering of titanium hydride (TiH 2 ) powders in a hydrogen atmosphere and controlling the phase transformations during and after sintering, the HSPT process was expected to reduce the energy consumption, and thus cost, of making Ti alloys and fabricating Ti components. The process was designed such that no high temperature melting is required for producing Ti alloys; little or no post-sintering processing is needed for producing desired microstructures (and therefore enhanced mechanical properties), and finally, minimum machining is needed to fabricate finished Ti components. An energy analysis within this report provides more detail, but calculated values indicate that the HSPT process is less than half as energy intensive as conventional wrought processing, while producing mechanical properties that are comparable. In addition to the energy savings anticipated from the industrial production of Ti components, a second prong of energy savings resides in the use phase of components produced, primarily from use in the transportation sector. Titanium has a number of material qualities appropriate for the auto industry, particularly low mass and corrosion resistance. By reducing the weight of automobiles and other vehicles, energy costs and CO 2 production will be reduced over the lifetime of the vehicles, and components in corrosive environments on vehicles, such as exhaust systems and other under carriage parts, may not have to be replaced during a vehicle’s lifetime. Our analysis indicates that by replacing only 5.6 kg of steel parts in an auto with Ti components across the entire US fleet would save approximately 486 million gallons of gasoline per year. This correlates to a reduction of 3.6 million metric tons of CO 2 per year. The potential for replacing many more of the steel parts in automobiles with lighter weight titanium components is clear. The project was very successful overall, meeting all milestones and surpassing project goals in terms of mechanical properties and microstructures produced. In addition to tensile properties, fatigue properties were emphasized in the project work. Powder metallurgy processes often have porosity to some degree in their final microstructure, and porosity is a well-known cause of crack initiation and low fatigue performance. Although many automobile applications do not undergo fatigue stress regimes, many others do encounter cyclic stress, and design criteria in the latter case require good fatigue properties. Production and testing of HSPT parts showed excellent tensile properties and fracture toughness, and fatigue properties that exceeded all previously reported powder metallurgy Ti methods, overlapping with wrought processed values. Fatigue limits exceeded 500 MPa and tensile strength exceeded 1,000 MPa while maintaining good ductility. Microstructures produced during the project period easily surpassed pre-project expectations. In addition to producing very fine grains in the as-sintered state (without post sintered thermo-mechanical work), porosity was reduced and industrially relevant microstructures previously undemonstrated in any other powder metallurgy titanium method were produced using HSPT materials. These microstructures, both bi-modal and globularized, were produced with simple post-sinter heat treatments, but without the need for energy intensive mechanical work. The employed heat treatments expanded the available mechanical property range (tensile strength vs. ductility) of the HSPT system in Ti-6Al-4V. The project has resulted in the publication, thus far, of five refereed journal articles and five conference proceedings papers, as well as a patent application, two dissertations and a master’s thesis. Two additional journal articles are currently under review, and at least three others are currently in preparation, with several additional students anticipated to graduate within the coming year. Presentations and papers were a particular focus of the second half of the project, once significant experimentation had been performed and analyzed. As part of our efforts to disseminate information of our results, the Ti research teams within Prof. Fang’s and Prof. Chandran’s research groups had a strong presence at the 13th World Conference on Ti, August 16-20, 2015, in San Diego. Several research groups in the US and in Europe are now performing experiments using the HSPT process. Accompanying efforts to bring HSPT to the Ti community at large, and industry in particular, work has continued with our partners and with other interested industrial Ti users and producers, including Boeing and GKN (a major powder metallurgy parts manufacturer). Commercialization has been a central focus of the final phase of the project, and Reading Alloys signed a provisional licensing agreement in summer of 2015. They are currently seeking an appropriate customer with which to pursue initial parts manufacturing efforts. Other licensing options and partners are continuing to be pursued. The promise of lightweight, strong and corrosion resistant Ti alloys with long fatigue lifetimes for automobile or transportation applications has been the vision of the metal industry since titanium came to the attention of scientists and engineers. The sole limitation of realizing these goals has been cost, which is primarily a function of energy used in production. The HSPT process was shown through this work to be capable of realizing this goal, and facilitating the practical use of titanium in US automotive and other industries.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Limitations of electron cyclotron resonance ion source performances set by kinetic plasma instabilities

Electron cyclotron resonance ion source (ECRIS) plasmas are prone to kinetic instabilities due to anisotropy of the electron energy distribution function stemming from the resonant nature of the electron heating process. Electron cyclotron plasma instabilities are related to non-linear interaction between plasma waves and energetic electrons resulting to strong microwave emission and a burst of energetic electrons escaping the plasma, and explain the periodic oscillations of the extracted beam currents observed in several laboratories. It is demonstrated with a minimum-B 14 GHz ECRIS operating on helium, oxygen, and argon plasmas that kinetic instabilities restrict the parameter space available for the optimization of high charge state ion currents. The most critical parameter in terms of plasma stability is the strength of the solenoid magnetic field. It is demonstrated that due to the instabilities the optimum B{sub min}-field in single frequency heating mode is often ≤0.8B{sub ECR}, which is the value suggested by the semiempirical scaling laws guiding the design of modern ECRISs. It is argued that the effect can be attributed not only to the absolute magnitude of the magnetic field but also to the variation of the average magnetic field gradient on the resonance surface.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

External control of electron energy distributions in a dual tandem inductively coupled plasma

The control of electron energy probability functions (EEPFs) in low pressure partially ionized plasmas is typically accomplished through the format of the applied power. For example, through the use of pulse power, the EEPF can be modulated to produce shapes not possible under continuous wave excitation. This technique uses internal control. In this paper, we discuss a method for external control of EEPFs by transport of electrons between separately powered inductively coupled plasmas (ICPs). The reactor incorporates dual ICP sources (main and auxiliary) in a tandem geometry whose plasma volumes are separated by a grid. The auxiliary ICP is continuously powered while the main ICP is pulsed. Langmuir probe measurements of the EEPFs during the afterglow of the main ICP suggests that transport of hot electrons from the auxiliary plasma provided what is effectively an external source of energetic electrons. The tail of the EEPF and bulk electron temperature were then elevated in the afterglow of the main ICP by this external source of power. Results from a computer simulation for the evolution of the EEPFs concur with measured trends.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

First Measurement of $\nu_{\mu}$ Induced Charged-Current $\pi^0$ Production Cross Sections on Polystyrene at $E_{\bar{\nu}_{\mu}}$ 2-10 GeV

Understanding of the $\pi^0$ production via anti-neutrino-nucleus charged current interaction in the neutrino energy region of 1-10 GeV is essential for neutrino oscillation experiments. In this thesis, we present a measurement of charged current $\pi^0$ production from anti-muon neutrinos scattering on a polystyrene scintillator (CH) target in the MINER$\nu$A experiment. A method for selecting and reconstructing $CC\pi^0$ events is presented. The $\pi^0$ and $\mu^+$ are fully reconstructed in the final state allowing for the measurement of the final state kinematics and the neutrino energy. We describe the two methods developed in this analysis for \p0 reconstruction in the MINERvA experiment: Hough Transform and Angle Scan. Interacting neutrinos have energy $\sim3.0 GeV$ and $\pi^0$ have energy $\sim0.3GeV$. The total $CC\pi^0$ cross-section is presented as a function of neutrino energy and $Q^2$. The total Exclusive $CC\pi^0$ cross-section is presented as a function of neutrino energy, $Q^2$ and the final state kinematics. Cross Section ratio between Exclusive $CC\pi^0$ and Inclusive $CC\pi^0$ for data and Monte Carlo are presented. Neutrino beam data corresponding to $1.019 \times 10^{20}$ protons on target have been analyzed. For inclusive $CC\pi^0$ sample we reconstructed 891 events, and for exclusive $CC\pi^0$ sample we reconstructed 514 events.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Critical point of gas-liquid type phase transition and phase equilibrium functions in developed two-component plasma model

A two-component plasma model, which we called a “shelf Coulomb” model has been developed in this work. A Monte Carlo study has been undertaken to calculate equations of state, pair distribution functions, internal energies, and other thermodynamics properties. A canonical NVT ensemble with periodic boundary conditions was used. The motivation behind the model is also discussed in this work. The “shelf Coulomb” model can be compared to classical two-component (electron-proton) model where charges with zero size interact via a classical Coulomb law. With important difference for interaction of opposite charges: electrons and protons interact via the Coulomb law for large distances between particles, while interaction potential is cut off on small distances. The cut off distance is defined by an arbitrary ε parameter, which depends on system temperature. All the thermodynamics properties of the model depend on dimensionless parameters ε and γ = βe{sup 2}n{sup 1/3} (where β = 1/k{sub B}T, n is the particle's density, k{sub B} is the Boltzmann constant, and T is the temperature) only. In addition, it has been shown that the virial theorem works in this model. All the calculations were carried over a wide range of dimensionless ε and γ parameters in order to find the phase transition region, critical point, spinodal, and binodal lines of a model system. The system is observed to undergo a first order gas-liquid type phase transition with the critical point being in the vicinity of ε{sub crit}≈13(T{sub crit}{sup *}≈0.076),γ{sub crit}≈1.8(v{sub crit}{sup *}≈0.17),P{sub crit}{sup *}≈0.39, where specific volume v* = 1/γ{sup 3} and reduced temperature T{sup *} = ε{sup −1}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ion acceleration in a helicon source due to the self-bias effect

Time-averaged plasma potential differences up to 165 V over several hundred Debye lengths are observed in low pressure (p{sub n} < 1 mTorr) expanding argon plasmas in the Madison Helicon eXperiment (MadHeX). The potential gradient leads to ion acceleration greater than that predicted by ambipolar expansion, exceeding E{sub i} Almost-Equal-To 7 kT{sub e} in some cases. RF power up to 500 W at 13.56 MHz is supplied to a half-turn, double-helix antenna in the presence of a nozzle magnetic field, adjustable up to 1 kG. A retarding potential analyzer (RPA) measures the ion energy distribution function (IEDF) and a swept emissive probe measures the plasma potential. Single and double probes measure the electron density and temperature. Two distinct mode hops, the capacitive-inductive (E-H) and inductive-helicon (H-W) transitions, are identified by jumps in density as RF power is increased. In the capacitive (E) mode, large fluctuations of the plasma potential (V{sub p-p} Greater-Than-Or-Equivalent-To 140V, V{sub p-p}/V{sub p} Almost-Equal-To 150%) exist at the RF frequency and its harmonics. The more mobile electrons can easily respond to RF-timescale gradients in the plasma potential whereas the inertially constrained ions cannot, leading to an initial flux imbalance and formation of a self-bias voltage between the source and expansion chambers. In the capacitive mode, the ion acceleration is not well described by an ambipolar relation, while in the inductive and helicon modes the ion acceleration more closely follows an ambipolar relation. The scaling of the potential gradient with the argon flow rate and RF power are investigated, with the largest potential gradients observed for the lowest flow rates in the capacitive mode. The magnitude of the self-bias voltage agrees with that predicted for RF self-bias at a wall. Rapid fluctuations in the plasma potential result in a time-dependent axial electron flux that acts to 'neutralize' the accelerated ion population, resulting in a zero net time-averaged current through the acceleration region when an insulating upstream boundary condition is enforced. Grounding the upstream endplate increases the self-bias voltage compared to a floating endplate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗