THE INFLUENCE OF ELECTRON OSCILLATION ON PLASMA TRANSPORT THROUGH A MAGNETIC DUCT

A magnetic duct is inserted between the cathodic arc plasma source and the chamber to eliminate the macroparticles. In this paper, the plasma output of the magnetic duct is determined as a function of the magnetic field and the bias voltage under the Bilek biasing mode and entire duct biasing mode. The computer simulation and the experimental result indicate that the ${\vec E}\times{\vec B}$ drift results in an extra diffusion flux under the Bilek biasing mode. The test verifying the electron oscillation was conducted in the magnetic duct biased in the Bilek mode. The electron behaviour under Bilek biasing mode is different from that under entire duct biasing mode. The Bilek biasing mode has a lower plasma output than the entire duct biasing mode.     

A new method for calculating three-particle interaction in the theory of modulus elasticity

We propose a new method for calculating the potential of multiparticle interaction. Our method considers the energy symmetry for clusters that contain N identical particles with respect to permutation of the number of atoms and free rotation in three-dimensional space. As an example, we calculate moduli of third-order rigidity for copper considering only the three-particle interaction. We analyze nine models of energy dependence on the polynomials that form the integral rational basis of invariants (IRBI) for the group G ₃ = O(3) ? P ₃. In this work, we use only the simplest relation between energy and the invariants forming the IRBI: \(\varepsilon \left( {\left. {i,k,l} \right|j} \right) = \sum\nolimits_{i,k,l} {\left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } \right]}\), where I _j is the invariant number j (j = 1, 2,..., 9). The results are in good agreement with the experimental values. The best agreement is observed at n = 2, j = 4: \(I_4 = \left( {\vec r_{ik} \vec r_{kl} } \right)\left( {\vec r_{kl} \vec r_{li} } \right) + \left( {\vec r_{kl} \vec r_{li} } \right)\left( {\vec r_{li} \vec r_{ik} } \right) + \left( {\vec r_{li} \vec r_{ik} } \right)\left( {\vec r_{ik} \vec r_{kl} } \right)\).     

Toward a theory of the third-order elastic modulus of crystals with A2 structure: The case of α-Fe

The third-order elastic modulus of α-Fe were calculated based on the computation of lattice sums. The lattice sums were determined using an integer rational basis of invariants composed by vectors connecting equilibrium atomic positions in the crystal lattice. Irreducible interactions within clusters consisting of atomic pairs and triplets were taken into account in performing the calculations. Comparison with experimental data showed that the potential can be written in the form of e₉ = - ?_i,k A₁₉ r_ik ^{- 6} + ?_i,k A₂₉ r_ik ^{- 12} + ?_i,k,l Q₉ I₉ ^{- 1}\varepsilon _9 = - \sum\nolimits_{i,k} {A_{19} r_{ik}^{ - 6} } + \sum\nolimits_{i,k} {A_{29} r_{ik}^{ - 12} + \sum\nolimits_{i,k,l} {Q_9 I_9^{ - 1} } }, where I₉ = [(r)\vec]_ik² [ ( [(r)\vec]_ik [(r)\vec]_kl )² + ( [(r)\vec]_li [(r)\vec]_ik )² ] + [(r)\vec]_kl² [ ( [(r)\vec]_ik [(r)\vec]_kl )² + ( [(r)\vec]_kl [(r)\vec]_li )² ] + [(r)\vec]_li² [ ( [(r)\vec]_li [(r)\vec]_ik )² + ( [(r)\vec]_kl [(r)\vec]_li )² ]I_9 = \vec r_{ik}^2 \left[ {\left( {\vec r_{ik} \vec r_{kl} } \right)^2 + \left( {\vec r_{li} \vec r_{ik} } \right)^2 } \right] + \vec r_{kl}^2 \left[ {\left( {\vec r_{ik} \vec r_{kl} } \right)^2 + \left( {\vec r_{kl} \vec r_{li} } \right)^2 } \right] + \vec r_{li}^2 \left[ {\left( {\vec r_{li} \vec r_{ik} } \right)^2 + \left( {\vec r_{kl} \vec r_{li} } \right)^2 } \right]. If the values of [(r)\vec]_ik\vec r_{ik} are scaled in half-lattice constant units, then A₁₉ = 1.22 ë t⁹ û GPa, A₂₉ = 5.07 ×10² ë t¹⁵ û GPa, Q₉ = 5.31 ë t⁹ û GPaA_{19} = 1.22\left\lfloor {\tau ^9 } \right\rfloor GPa, A_{29} = 5.07 \times 10^2 \left\lfloor {\tau ^{15} } \right\rfloor GPa, Q_9 = 5.31\left\lfloor {\tau ^9 } \right\rfloor GPa, and τ = 1.26 ?. It is shown that the condition of thermodynamic stability of a crystal requires that we allow for irreducible interactions in atom triplets in at least four coordination spheres. The analytical expressions for the lattice sums determining the contributions from irreducible interactions in the atom triplets to the second- and third-order elastic moduli of cubic crystals in the case of interactions determined by I ₉ are presented in the appendix.     

Systematics of the nuclear spin polarization of12B in14N induced heavy ion reactions

Systematic study of polarization of projectile like fragment¹²B in¹⁴N induced reactions on light mass-number targets has been continued. A large positive polarization at small energy loss region was observed for an²⁷Al target at various reaction angles. Polarization is studied as a function of kinetic energy and reaction angle of¹²B in terms of a classical frictional force.Positive polarization is defined by where k_f and k_i are outgoing and incoming wave vectors, respectively.     

Dirac Equation in an Axial Coulomb Potential

We consider solutions to the Dirac equation in the presence of an external axial vector potential coupled to the spinor field psi through the interaction term . There turn out to be no bound-state energies in this system consistent with a normalizable wave function.     

e08-008: Exclusive study of deuteron electrodisintegration near threshold

The study of threshold electrodisintegration of and elastic scattering on the only stable two nucleon system, the deuteron, can reveal specific aspects of the N-N interaction. The simplicity of electrodisintegration along with the simplicity of the deuteron makes this study most appropriate for revealing these interactions. By using an incident beam of polarized electrons and by measuring the polarization of the recoiling proton, the ratio of the electric (G _E ) and magnetic (G _M ) form factors for $d\left( {\vec e,e'\vec p} \right)$ (and $p\left( {\vec e,e'\vec p} \right)$ ) reactions may be extracted. This experiment was conducted in Hall A at Jefferson Lab in Newport News, Virginia using a beam of polarized electrons provided by the CEBAF Accelerator incident on a liquid deuterium (and hydrogen) target. The scattered electron and the recoiling (polarized) proton were detected using the High Resolution Spectrometers of Hall A. To determine the polarization of the recoil proton, an analyzing material was placed perpendicular to the protons trajectory through the spectrometer, in front of a set of straw chambers. Due to the spin-orbit interactions involved in the scattering of the proton from the analyzer material, asymmetries seen in the distribution of events detected by these straw chambers reveal the polarization of the recoil proton. By tracking the spin procession of the polarized protons from the straw chambers back to the target, the transferred and induced polarization of the proton may be determined. The (double-spin) asymmetries observed in the straw chambers will first be studied for the well-known elastic $p\left( {\vec e,e'\vec p} \right)$ process and compared to the asymmetries for $d\left( {\vec e,e'\vec p} \right)n\left( {x_B = 1} \right)$ . The analysis will then be repeated to determine how these asymmetries change with increasing x _B (to the kinematic limit for deuteron electrodisintegration).     

Renormalized Electron Mass in Nonrelativistic QED

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, ${E_{\vec{P}}}Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, E_[(P)\vec]{E_{\vec{P}}}, of a dressed electron is twice differentiable in the momentum [(P)\vec]{\vec{P}} in a neighborhood of [(P)\vec]=0{\vec{P}=0}. Furthermore, \frac?²E_[(P)\vec](?|[(P)\vec]|)²{\frac{\partial^2E_{\vec{P}}}{(\partial |\vec{P}|)^2}} is bounded from below by a constant larger than zero. Our results are proven with the help of iterative analytic perturbation theory.     

Contribution of Electromagnetic Field to Atomic Spin

We examine the contribution of electromagnetic field to the atomic spin, by adopting two different, both gauge invariant definitions of the electromagnetic angular momentum: \vec{J}_I ≡ ∫d³ x ε₀ \vec{r} X (\vec{E} X \vec{B}) and \vec{J}_II ≡ ∫d³ x ( ε₀ \vec{E} X \vec{A}^\bot + ε₀ E_i \vec{r} X \vec{\nabla }A^{\bot}_i ). Notably, at the classical level, \vec{J}_II gives an exactly null result while \vec{J}_I gives a finite value. This suggests that \vec{J}_II leads to a simpler and more reasonable picture of the atomic spin, therefore qualifies as a more appropriate definition of the electromagnetic angular momentum. Our observation gives important hint on the delicate issue of gluon contribution to the nucleon spin.     

Spin interference in the spin density matrix of a compound nucleus in reactions of nuclear fission by cold polarized neutrons

Spin density matrices of neutron resonance states of a compound nucleus formed in the reaction of capture of a polarized neutron by a non-oriented target nucleus for different directions of neutron polarization vector are constructed within the quantum fission theory. The obtained spin matrices are used to calculate T-odd asymmetries in differential cross sections of ternary nuclear fission with the emission of different third particles. It is demonstrated that the expressions for T-odd asymmetries in the cases of neutron polarization direction [(p)\vec]_n\vec p_n along the x and y axes in the laboratory reference frame differ by the values of the unified correlator of the form ( [(p)\vec]_n ,[ [(k)\vec]_LF ,[(k)\vec]₃ ] )\left( {\vec p_n ,\left[ {\vec k_{LF} ,\vec k_3 } \right]} \right) (where [(k)\vec]_LF\vec k_{LF} and [(k)\vec]₃\vec k_3 are the wave vectors of a light fission fragment and the third particle, respectively), and are transformed into one another if the laboratory reference frame in which [(p)\vec]_n\vec p_n is directed along the x axis is rotated to a laboratory reference frame in which [(p)\vec]_n\vec p_n is directed along the y axis. It is shown that T-odd TRI and ROT asymmetries are associated, respectively, with the odd and even components of the amplitudes of the angular distribution of third particles perturbed by the collective rotation of a polarized fissile nucleus, and each of these amplitudes can be considerably amplified (or suppressed) relative to one another due to the interference from fission amplitudes of pairs of neutron resonances sJ _s and s′J _s′ .     

Thermal Entanglement for Interacting Spin-1/2 Systems and its Quantum Criticality

In this work, we investigate the thermal entanglement for interacting spin systems , by varying the parameters of temperature T, direction and magnetic field B. PACS numbers: 03.67.Mn, 03.65.Ud, 05.30.Cd, 73.43.Nq     

Computing lattice sums for calculating the elastic moduli of bcc metals via cluster decomposition

The complete potential energy of a crystal $E\left( {\vec r_{ik} } \right)$ is presented in the form of an expansion in irreducible interactions in clusters containing pairs, triplets, and quadruplets of atoms, situated on A2 lattice sites. The full set of invariants $\left\{ {I_j \left( {\vec r_{ik} } \right)} \right\}$ , on which $\left\{ {I_j \left( {\vec r_{ik} } \right)} \right\}$ can depend is found. Vectors $\vec r_{ik}$ are presented in the form of an expansion of the base of a Brave lattice. This allows us to present $I_j \left( {\vec r_{ik} } \right)$ in the form of integers (lattice sums) multiplied by τ ^m , where τ is half of an elementary cell rib, and m = const is determined by the model. The sum of the Lenard-Jones potential and the potentials of tri- and tetra-atomic interactions was chosen as the model potential. Within this model, elastic moduli of the second and third order were calculated for crystals with A2-type structure.     

Magnetic properties of high-T c superconductors from NQR and NMR measurements

NMR and NQR spectra and spin-lattice relaxation measurements carried out in LASCO and YBCO-type crystals are presented and analyzed in order to derive insights on the correlations and spin-dynamics of the Cu²⁺ ions and on the microscopic mechanisms of high-T _c superconductivity. As an illustrative example on how the magnetic correlation length and spin dynamics properties can be extracted from the relaxation rateW, the³⁵Cl NMR data in the two-dimensional Heisenberg system Sr₂CuCl₂O₂, around the paramagnetic-antiferromagnetic (PA-AF) transition are first considered. Then the¹³⁹La NQR relaxation measurements in La_2?xSr_xCuO₄ are briefly reviewed and it is shown how a simple picture of localized Cu²⁺ magnetic moments, whose spin fluctuation times are controlled by the charge defects induced by the doping, leads in a direct way to quantitative estimates for the progressive shift, on cooling, of the spectral density of the low-frequency spin excitations towards the high frequency range. This phenomenon can be described in terms of effective spin at the Cu²⁺ ions, and its similarities with the analogous effect of progressive delocalization in Heavy Fermions systems are pointed out. Thus, the superconducting transition appears to occur in an unconventional Fermi liquid with AF correlations among itinerant pseudoparticles, possibly involving a mechanism not directly related to the magnetic correlated dynamics. In fact, a universal behavior of the relaxation rates as a function of temperature is observed, regardless of the transition temperatureT _c. The independence ofT _c from the low frequency static and dynamical spin properties is also indicated by⁸⁹Y Knight shifts and from⁶³Cu relaxation rates in systems like YBa₂Cu₄O₈ (Y124), whereT _c can be changed by atomic substitutions and by controlling the oxygen stoichiometry. The effect of an external magnetic field on the correlated spin dynamics of the AF Fermi liquid is investigated and from a comparison of Cu NQR relaxation and NMR relaxation in oriented powder of YBCO and LASCO it is shown that the external field has the small but unambiguous effect of depressing the relaxation rates aboveT _c, besides strongly enhancing them in the superconducting phase. A maximum in the ratio \({{W\left( {NQR} \right)} \mathord{\left/ {\vphantom {{W\left( {NQR} \right)} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}} \right. \kern-0em} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}\) is thus observed around 80 K, either in LASCO or in YBCO, again indicating that the transition could be driven by a mechanism not directly involving the spin dynamic properties. To study the role of the fluxions belowT _c ⁸⁹Y NMR shifts and spectra in oriented powders of YBCO are analyzed. Information on the spin susceptibility and on the structure of the vortex lattice is obtained. In addition, from the temperature behavior of the linewidth a motional narrowing related to flux melting is evidenced. The effective correlation time for the vortex motion is derived and it is discussed why μ⁺SR cannot detect it in view of the different rigid-lattice line broadening.     

Generalized parton distributions in impact parameter space

The kinematical factor in the positivity bound (36) is incorrect. The bound correctly reads Our corrected result agrees with inequality (25) in [1], taking into account the different normalization conventions here and there.Published online: 9 October 2003Erratum published online: 10 October 2003     

Experiments on few-nucleon systems at MAMI

The experimental effort at the Mainz Microtron with respect to few-body physics is focused on a number of selected topics. The structure of ³He has been studied in the reactions $^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}n)$ and $^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}p)$ with large (transversal) missing momenta and in quasi-elastic electron scattering. Experiments to determine the neutron electric form factor G _en have been performed – a measurement at a four-momentum transfer Q ² ～ 1.5(GeV/c)² took place in July 2007. Electromagnetically induced two-nucleon knockout has been investigated in order to study the role of correlated nucleon-nucleon motion in the nucleus. Measurements of the (e,e′ pn) reaction on ³He and ¹⁶O were performed for the first time. A triple-polarization experiment of type $^3\vec{{\rm H}}{\rm e}(\vec{e},e{\prime}\vec{p})d$ has been performed in August 2007, where, in addition, the spin of the knocked-out proton is analyzed. This measurement provides information on the spin-dependent momentum distribution of proton-deuteron clusters in the ³He nucleus. By using this deuteron-tagging method spin-polarized ³He might also serve as an effective polarized proton target for electron scattering experiments.     

Strong magnetic fields,Dirichlet boundaries,and spectral gaps

We consider magnetic Schrödinger operators $$H(\lambda \vec a) = ( - i\nabla - \lambda \vec a(x))^2$$ inL ₂(R ⁿ ), where $\vec a \in C^1 (R^n ;R^n )$ and λεR. LettingM={x;B(x)=0}, whereB is the magnetic field associated with $\vec a$ , and $M_{\vec a} = \{ x;\vec a(x) = 0\}$ , we prove that $H(\lambda \vec a)$ converges to the (Dirichlet) Laplacian on the closed setM in the strong resolvent sense, as λ→∞,provided the set $M\backslash M_{\vec a}$ has measure zero. In various situations, which include the case of periodic fields, we even obtain norm resolvent convergence (again under the condition that $M\backslash M_{\vec a}$ has measure zero). As a consequence, if we are given a periodic fieldB where the regions withB=0 have non-empty interior and are enclosed by the region withB≠0, magnetic wells will be created when λ is large, opening up gaps in the spectrum of $H(\lambda \vec a)$ . We finally address the question of absolute continuity of $\vec a$ for periodic $H(\vec a)$ .     

What are spin currents in Heisenberg magnets?

We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive current operator in the plane spanned by the local order parameters and is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.Received: 1 September 2004, Published online: 5 November 2004PACS: 75.10.Jm Quantized spin models - 75.10.Pq Spin chain models - 75.30.Ds Spin waves - 73.23.Ra Persistent currents     

Runaway electrons as a diagnostic of plasma internal magnetic fluctuations

The transport of runaway electrons in a high-temperature plasma is relatively easy to measure in a steady state experiment and a perturbation experiment, which provides runaway electron diffusion coefficient D_r. This diffusion coefficient is determined by internal magnetic fluctuations, so it can be interpreted in terms of a magnetic fluctuation level. The internal magnetic fluctuation level ($\tilde {b}_r/B_T is estimated to be about (2--4)×^-4 in the HL-1M plasma. The results presented here demonstrate the effectiveness of using runaway electron transport techniques to determine internal magnetic fluctuations. A profile of magnetic fluctuation level in the HL-1M plasma can be estimated from D_r.     

Analysis of Dα（Hα） spectrum emitted in front of the limiter in HT-7^＊

In order to understand the recycling and emission processes of hydrogen atoms in HT 7, spectral profiles of the Dα（Hα） line emitted in front of the limiter have been observed with a high-resolution spectrometer and simulated by using the neutral particle transport code DEGAS 2. The results show that four processes are necessary to interpret the Dα（Hα） line shape： 1） atom desorption, 2） molecular dissociation, 3） particle reflection, and 4） charge-exchange. The products of the first two processes are cold atoms which emit photons near the peak of Dα（Hα） line shape, and those from the last two are warm atoms contributing to the blue side of the spectrum. For a typical ohmic discharge （shot 68520 ne（0） ≈ 3× 10^19 m^-3. these components contribute 32%, 15%, 32% and 21%, respectively. Dα（Hα） line shapes under different plasma parameters are also discussed in this paper.     

Overview of edge electrostatic turbulence experiments on TCV

Experiments on edge turbulence in the TCV tokamak have been performed for the first time at the beginning of 2003. This paper presents an overview of some of the results obtained, concentrating in particular on two areas: universality of density fluctuations and the dynamical coupling between radial turbulent-driven fluxes and parallel flows.Plasma fluctuations in the edge of the TCV tokamak have been found to exhibit statistical properties which are universal across a broad range of discharge conditions. Analysis of the time series of density fluctuations in the entire scrape-off layer (SOL) region from just inside the magnetic separatrix to the plasma-wall interface, yields a probability distribution function (PDF) of density which conforms closely to a Gamma distribution. In the wall vicinity, the density fluctuations exhibit clear evidence of self-similarity and are characterised by a PDF with universal shape and with a standard deviation proportional to the mean density. It is also found that radial particle-flux fluctuations scale solely with the mean density. Such findings indicate that it may be possible to improve the prediction of transport in the critical plasma-wall interaction region of future large-scale tokamaks.Recent experiments on JET [C. Hidalgo et al.: Phys. Rev. Lett. 91 (2003) 065001] have investigated a possible link between turbulent transport and the parallel flows. Similar experiments have been performed on TCV for a variety of plasma conditions and flow magnitudes. Although correlations have been found as seen on JET, especially in the wall vicinity, it appears that the magnitude of the coupling is insufficient to drive any significant flow.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Terahertz generation by nonlinear mixing of laser and its second harmonic in a rippled density plasma

Terahertz radiation generation by second-order nonlinear mixing of laser $ (\omega_{1} ,\,\vec{k}_{1} ) $ and its frequency shifted second harmonic $ \omega_{2} = 2\omega_{1} - \omega ,\,\,\vec{k}_{2} \, $ $ (\omega \ll \omega_{1} ) $ in a plasma, in the presence of an obliquely inclined density ripple of wave number $ \vec{q} $ , are investigated. The lasers exert ponderomotive force on electrons and drive density perturbations at $ (2\omega_{1} ,\,2\vec{k}_{1} - \vec{q}) $ and $ (\omega_{1} - \omega_{2} ,\,\vec{k}_{1} - \vec{k}_{2} - \vec{q}) $ . These perturbations beat with the electron oscillatory velocities due to the lasers to produce a nonlinear current at $ \omega ,\,\vec{k} = 2\vec{k}_{1} - \vec{k}_{2} - \vec{q} $ , resonantly driving the terahertz radiation when $ \vec{q} $ satisfies the phase matching condition. The radiated THz intensity depends on the relative polarization of the lasers and scales as the square of intensity of the fundamental laser and linearly with the square root of the intensity of the second harmonic. The THz emission is maximized when the polarization of the lasers is aligned. These results are consistent with the recent experimental results.