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To reveal the mysterious and still controversial mechanism of high ionization efficiency during helicon discharges, this work focuses particularly on the role of second-order derivative in radial density profile, both analytical and numerically. It is found that: (i) the radially localized potential well that plays a critical role in resonance power absorption from antenna to plasma is localized where the second-order derivative vanishes, (ii) the power absorption increases for positive second-order derivative, decreases for negative second-order derivative, and maximizes where second-order derivative becomes zero, (iii) the power absorption decreases near plasma core and increases near plasma edge when the radial location of vanishing second-order derivative moves outwards, which is also a process of Trivelpiece-Gould mode overwhelming helicon mode. These findings can be very interesting for helicon plasma applications that require certain power distribution or heat flux configuration, e. g. material processing, which can be controlled by adjusting the profile and zero-crossing location of second-order radial density gradient.

We construct the quark-antiquark scattering kernels of Bethe-Salpeter equation from the quark self-energy directly under two specific forms of quark-gluon vertices. The quark dressed tensor vertex is then calculated within this consistent framework and rainbow-ladder(RL) approximation. After employing a simplified nucleon model, the nucleon tensor charge can be defined with the tensor vertex. We then compute the tensor charge with the bare tensor vertex and the dressed vertices obtained in this framework and in RL approximation. The obtained results are consistent with the lattice QCD calculations. We also find that typically the gluon dressing effects suppress the nucleon tensor charge compared to the bare tensor vertex, by about $23\%$ for RL approximation, and turn to be about $13\%$ in this framework., Comment: 9 pages, 6 figures, 3 tables

A symmetry-preserving approach to the continuum bound-state problem in quantum field theory is used to calculate the masses, leptonic decay constants and light-front distribution amplitudes of empirically accessible heavy-light mesons. The inverse moment of the $B$-meson distribution is particularly important in treatments of exclusive $B$-decays using effective field theory and the factorisation formalism; and its value is therefore computed: $\lambda_B(\zeta = 2\,{\rm GeV}) = 0.54(3)\,$GeV. As an example and in anticipation of precision measurements at new-generation $B$-factories, the branching fraction for the rare $B\to \gamma(E_\gamma) \ell \nu_\ell$ radiative decay is also calculated, retaining $1/m_B^2$ and $1/E_\gamma^2$ corrections to the differential decay width, with the result $\Gamma_{B\to \gamma \ell \nu_\ell}/\Gamma_B = 0.47(15)$ on $E_\gamma > 1.5\,$GeV., Comment: 6 pages, 6 figure, 5 tables

A novel radio-frequency antenna consisting of isolated solenoids is reported to generate plasma for pressure up to thousands of pascals. The underlying mechanism involves capacitive coupling, inductive coupling and axial confinement from magnetic mirrors. It can ionize the air reliably with pressure up to $2500$~Pa for the $1$~kW-$13.56$~MHz power supply employed, and maintain the discharge steadily from tens of minutes to hours. This ionization method is particularly useful for plasma propulsion in near space and other low-temperature plasma applications where sub-atmospheric pressure is required.

A two-fluid flowing plasma model is applied to describe the plasma rotation and resulted instability evolution in magnetically enhanced vacuum arc thruster (MEVAT). Typical experimental parameters are employed, including plasma density, equilibrium magnetic field, ion and electron temperatures, cathode materials, axial streaming velocity, and azimuthal rotation frequency. It is found that the growth rate of plasma instability increases with growing rotation frequency and field strength, and with descending electron temperature and atomic weight, for which the underlying physics are explained. The radial structure of density fluctuation is compared with that of equilibrium density gradient, and the radial locations of their peak magnitudes are very close, showing an evidence of resistive drift mode driven by density gradient. Temporal evolution of perturbed mass flow in the cross section of plasma column is also presented, which behaves in form of clockwise rotation (direction of electron diamagnetic drift) at edge and anti-clockwise rotation (direction of ion diamagnetic drift) in the core, separated by a mode transition layer from $n=0$ to $n=1$. This work, to our best knowledge, is the first treatment of plasma instability caused by rotation and axial flow in MEVAT, and is also of great practical interest for other electric thrusters where rotating plasma is concerned for long-time stable operation and propulsion efficiency optimization.

Although it is well recognized that waves propagating in periodic media have forbidden gaps in the continuous spectrum, it is still yet unknown about the minimum number and depth of periodic modulations for clear spectral formation. This limit is explored by investigating shear Alfv\'{e}n waves propagating through magnetic mirror array in a low temperature plasma cylinder, referring to an existing experiment [Zhang et al., Phys. Plasmas 15, 012103 (2008)]. It is found that the bottom-edge ratio, a defined parameter characterizing how "noisy" the formed spectral gap is, scales inversely with the square of the number and depth of magnetic mirrors, and they should be bigger than $7$ and $0.4$ respectively to form a clear spectral gap for the plasma conditions employed. This scaling is consistent with a pervious analysis [Kryuchkyan and Hatsagortsyan, Phys. Rev. Lett. 107, 053604 (2011)], and also applicable to other fields such as optics and semiconductors. Moreover, it shows that the center of spectral gap experiences a parabolic shape of descending frequency shift when the modulation depth is increased, which is believed to be a new discovery.

Characterizing the gap eigenmode of shear Alfv\'{e}n waves (SAW) and its interaction with energetic ions is important to the success of magnetically confined fusion. Previous studies have reported an experimental observation of the spectral gap of SAW on LAPD (Zhang et al 2008 Phys. Plasmas 15 012103), a linear large plasma device (Gekelman et al 1991 Rev. Sci. Instrum. 62 2875) possessing easier diagnostic access and lower cost compared with traditional fusion devices, and analytical theory and numerical gap eigenmode using ideal conditions (Chang 2014 PhD Thesis at Australian National University). To guide experimental implementation, the present work models the gap eigenmode of SAW using exact LAPD parameters. A full picture of the wave field for previous experiment reveals that the previously observed spectral gap is not global but an axially local result. To form a global spectral gap, the number of magnetic mirrors has to be increased and stronger static magnetic field makes it more clear. Such a spectral gap is obtained for the magnetic field of $B_0(z)=1.2+0.6\cos[2\pi (z-33.68)/3.63]$ with $7.74$~m magnetic beach. By introducing two types of local defects (corresponding to $E_\theta(z_0)=0$ and $E_\theta'(z_0)=0$ respectively), odd-parity and even-parity discrete eigenmodes are formed clearly inside the gap. The strength of these gap eigenmodes decreases significantly with collision frequency, which is consistent with previous studies. Parameter scans show that these gap eigenmodes can be even formed successfully for the field strength of $B_0(z)=0.2+0.1\cos[2\pi (z-33.68)/3.63]$ and with only $4$ magnetic mirrors, which are achievable by LAPD at its present status. This work can serve as a strong motivation and direct reference for the experimental implementation of the gap eigenmode of SAW on LAPD and other linear plasma devices.

Large volume helicon plasma sources are of particular interest for large scale semiconductor processing, high power plasma propulsion and recently plasma-material interaction under fusion conditions. This work is devoted to studying the coupling of four typical RF antennas to helicon plasma with infinite length and diameter of $0.5$~m, and exploring its frequency dependence in the range of $13.56-70$~MHz for coupling optimization. It is found that loop antenna is more efficient than half helix, Boswell and Nagoya III antennas for power absorption; radially parabolic density profile overwhelms Gaussian density profile in terms of antenna coupling for low-density plasma, but the superiority reverses for high-density plasma. Increasing the driving frequency results in power absorption more near plasma edge, but the overall power absorption increases with frequency. Perpendicular stream plots of wave magnetic field, wave electric field and perturbed current are also presented. This work can serve as an important reference for the experimental design of large volume helicon plasma source with high RF power.

To guide the experimental design of a linear plasma device for studying the interaction between energetic ions and Alfv\'{e}nic gap eigenmode (AGE), this work computes AGE referring to fusion conditions in a ultra-long large plasma cylinder ended with strong magnetic throats for axial confinement of charged particles. It is shown that: (i) for uniform equilibrium field between the ending throats, the dispersion relation of computed wave field agrees well with a simple analytical model for shear Alfv\'{e}nic mode; (ii) for periodic equilibrium field with local defect, clear AGE is formed inside spectral gap for both low and high depths of magnetic throats, although lower depth yields easier observation. The strongest AGE can be in order of $3.1\times10^{-4}$ to equilibrium field, making it conveniently measurable in experiment. The AGE is a standing wave localized around the defect which is introduced to break the system's periodicity, and its wavelength is twice the system's period, consistent with Bragg's law. Parameter scan reveals that the AGE remains nearly the same when the number of magnetic ripples is reduced from $18$ to $8$, however, there occurs an upward frequency shift when the depth of magnetic ripples drops from $0.5$ to $0.1$, possibly due to a flute-like effect: shrinking resonant cavity of spectral gap.

We report progress on the development of Perturbative Integral Representation Ans\"atze to compute the nucleon Faddeev Wave function, using an explicit quark-diquark picture. Our formalism is able to handle non-pointlike diquark and to mimic the strong, dynamical correlations observed when solving the Faddeev Equation. We then project the wave function in order to compute the leading-twist Parton Distribution Amplitude., Comment: 6 pages, 2 figures, contribution to the proceedings of the XXII International Conference on Few-Body Problems in Physics (FB22) 2018, July 9-13, Caen, France

Using a continuum approach to the hadron bound-state problem, we calculate $\gamma^\ast \gamma \to \eta, \eta^\prime$ transition form factors on the entire domain of spacelike momenta, for comparison with existing experiments and in anticipation of new precision data from next-generation $e^+ e^-$ colliders. One novel feature is a model for the contribution to the Bethe-Salpeter kernel deriving from the non-Abelian anomaly, an element which is crucial for any computation of $\eta, \eta^\prime$ properties. The study also delivers predictions for the amplitudes that describe the light- and strange-quark distributions within the $\eta, \eta^\prime$. Our results compare favourably with available data. Important to this at large-$Q^2$ is a sound understanding of QCD evolution, which has a visible impact on the $\eta^\prime$ in particular. Our analysis also provides some insights into the properties of $\eta, \eta^\prime$ mesons and associated observable manifestations of the non-Abelian anomaly., Comment: 16 pages, 7 figures, 3 tables

A continuum approach to quark-antiquark bound-states is used to determine the electromagnetic form factors of pion-like mesons with masses $m_{0^-}/{\rm GeV}=0.14$, $0.47$, $0.69$, $0.83$ on a spacelike domain that extends to $Q^2 \lesssim 10\,$GeV$^2$. The results enable direct comparisons with contemporary lattice-QCD calculations of heavy-pion form factors at large values of momentum transfer and aid in understanding them. They also reveal, inter alia, that the form factor of the physical pion provides the best opportunity for verification of the factorised hard-scattering formula relevant to this class of exclusive processes and that this capacity diminishes steadily as the meson mass increases., Comment: 6 pages, 2 figures, 1 table

It is thought that strong interactions within the Standard Model can generate bound-states in which non-Abelian gauge-bosons play a dual role, serving both as force and matter fields. In this context we introduce a novel approach to the hybrid-meson (valence-gluon+quark+antiquark) bound-state problem in relativistic quantum field theory. Exploiting the existence of strong two-body correlations in the gluon-quark, $q_g=[gq]$, and gluon-antiquark, $\bar q_g=[g\bar q]$ channels, we argue that a sound description of hybrid properties can be obtained by solving a coupled-pair of effectively two-body equations; and, consequently, that hybrids may be viewed as highly-correlated $q_g \bar q \leftrightarrow q \bar q_g$ bound-states. Analogies may be drawn between this picture of hybrid structure and that of baryons, in which quark+quark (diquark) correlations play a key role. The potential of this formulation is illustrated by calculating the spectrum of light-quark isovector hybrid mesons., Comment: 5 pages, 2 figures, 1 table

Algebraic Ansaetze for the Poincar\'e-covariant Bethe-Salpeter wave functions of the pion and kaon are used to calculate their light-front wave functions (LFWFs), parton distribution amplitudes (PDAs), quasi-PDAs (qPDAs), valence parton distribution functions (PDFs), and quasi-PDFs (qPDFs). The LFWFs are broad, concave functions; and the scale of flavour-symmetry violation in the kaon is roughly 15%, being set by the ratio of emergent masses in the $s$-and $u$-quark sectors. qPDAs computed with longitudinal momentum $P_z =1.75\,$GeV provide a semiquantitatively accurate representation of the objective PDA; but even with $P_z=3\,$GeV, they cannot provide information about this amplitude's endpoint behaviour. On the valence-quark domain, similar outcomes characterise qPDFs. In this connection, however, the ratio of kaon-to-pion $u$-quark qPDFs is found to provide a good approximation to the true PDF ratio on $0.3\lesssim x \lesssim 0.8$, suggesting that with existing resources computations of ratios of quasi-parton-distributions can yield results that support empirical comparison., Comment: 10 pages, 8 figures

We explain how the emergent phenomenon of dynamical chiral symmetry breaking ensures that Poincar\'e covariant analyses of the three valence-quark scattering problem in continuum quantum field theory yield a picture of the nucleon as a Borromean bound-state, in which binding arises primarily through the sum of two separate contributions. One involves aspects of the non-Abelian character of Quantum Chromodynamics that are expressed in the strong running coupling and generate tight, dynamical color-antitriplet quark-quark correlations in the scalar-isoscalar and pseudovector-isotriplet channels. This attraction is magnified by quark exchange associated with diquark breakup and reformation, which is required in order to ensure that each valence-quark participates in all diquark correlations to the complete extent allowed by its quantum numbers. Combining these effects, we arrive at a properly antisymmetrised Faddeev wave function for the nucleon and calculate, e.g. the flavor-separated versions of the Dirac and Pauli form factors and the proton's leading-twist parton distribution amplitude. We conclude that available data and planned experiments are capable of validating the proposed picture., Comment: Contribution to the proceedings of the Workshop: Critical Stability of Quantum Few-Body Systems (Crit17). Oct. 16-20, 2017. Dresden, Germany