MAGNETIC FIELD ANALYSIS OF PERMANENT MAGNET UNDULATOR

2 Dimensional magnetic field expression of permanent magnet undulator with gradually varied magnetization is derived. Conditions for minimizing high order harmonics are given. Three different types of permanent magnet undulator —— the "gradually varied" type, mixed type and simple type ——are compared. Upon these comparisions we conclude that "gradually varied" type is superior to mixed type except for Δh/λ0.1.     

INCREASE OF BEAM PROJECTIVE EMITTANCE IN SYSTEM WITH DISPERSION

In this paper, the increase of beam projective emittance caused by the momentum dispersion in the transport systems is discussed, and the incrementary ratio is derived. If the bending plane is (XOZ), the incrementary ratio of the transversal emittance is

and the longitudinal one is

Here ε_x0 and ε_z0 are original emittances in the x-direction and z-direction respectively, (Δp/p)_maxis beam momentum spread β_xf, α_xf, γ_xf being acceptance parameters of the system in x-direction for betatron oscillations, η and η' are dispersion function and its derivative.     

Chiral magnetic effect in isobar collisions from stochastic hydrodynamics

We studied the chiral magnetic effect in AuAu, RuRu, and ZrZr collisions at \begin{document}$\sqrt{s_{{NN}}}=200\;{\rm{GeV}}$\end{document}. The axial charge evolution was modeled with stochastic hydrodynamics, and geometrical quantities were calculated with the Monte Carlo Glauber model. By adjusting the relaxation time of the magnetic field, we found our results are in good agreement with background subtracted data for AuAu collisions at the same energy. We also made predictions for RuRu and ZrZr collisions. We found a weak centrality dependence on initial chiral imbalance, which implies that the centrality dependence of chiral magnetic effect signals results mainly from the effects of the magnetic field and volume factor. Furthermore, our results show an unexpected dependence on system size. While the AuAu system has larger chiral imbalance and magnetic field, it was observed to have a smaller signal for the chiral magnetic effect due to the larger volume suppression factor.     

方形载流线圈的空间磁场计算

利用教材中一个常见例题的结论，将方形载流线圈视为四段载流导线，采取分段计算然后叠加的方法，导出了方形载流线圈空间磁场分布的普遍表达式，并讨论了线圈平面上的磁场分布情况．     

Landau quantization and spin polarization of cold magnetized quark matter

The magnetic field and density behaviors of various thermodynamic quantities of strange quark matter under compact star conditions are investigated in the framework of the thermodynamically self-consistent quasiparticle model. For individual species, a larger number density \begin{document}$ n_i $\end{document} leads to a larger magnetic field strength threshold that aligns all particles parallel or antiparallel to the magnetic field. Accordingly, in contrast to the finite baryon density effect which reduces the spin polarization of magnetized strange quark matter, the magnetic field effect leads to an enhancement of it. We also compute the sound velocity as a function of the baryon density and find the sound velocity shows an obvious oscillation with increasing density. Except for the oscillation, the sound velocity grows with increasing density, similar to the zero-magnetic field case, and approaches the conformal limit \begin{document}$ V_s^2=1/3 $\end{document} at high densities from below.     

Magnetic moment predictions of odd-A nuclei with the Bayesian neural network approach

The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei. The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square (rms) deviations from data, i.e., 0.949 \begin{document}$ \mu_\mathrm{N} $\end{document} and 1.272 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-neutron nuclei and odd-proton nuclei, respectively. By including the dependence of the nuclear spin and Schmidt magnetic moment, the machine-learning approach precisely describes the magnetic moments of odd-A nuclei with rms deviations of 0.036 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-neutron nuclei and 0.061 \begin{document}$ \mu_\mathrm{N} $\end{document} for odd-proton nuclei. Furthermore, the evolution of magnetic moments along isotopic chains, including the staggering and sudden jump trend, which are difficult to describe using nuclear models, have been well reproduced by the Bayesian neural network (BNN) approach. The magnetic moments of doubly closed-shell \begin{document}$ \pm1 $\end{document} nuclei, for example, isoscalar and isovector magnetic moments, have been well studied and compared with the corresponding non-relativistic and relativistic calculations.     

HIGH ENERGY CLUSTER SCATTERING THEORY OF MANY PARTICLES SYSTEM

Within the framework of the Glauber theory, we divide the many particle systeminto two subsystems formed. by the "valence" particles and "sea" particles respective-ly. Then the multiple scattering amplitudes can be divided into "sea","sea","sea","valence", "valence","sea", and "valence","valence" multiple scattering amplitude.For the calculations of these different amplitudes different effective approximatemethods are proposed, Finally, for "sea"."sea". "sea""valence", "valence" "sea"and "valence"."valence" processes, we obatain the respective S-matrices which phy-sically clear and convenient in calculation.     

Mass spectra and decay of mesons under strong external magnetic field

We study the mass spectra and decay process of σ and \begin{document}$ \pi_0 $\end{document} mesons under a strong external magnetic field. To achieve this goal, we deduce the thermodynamic potential in a two-flavor, hot and magnetized Nambu–Jona-Lasinio model. We calculate the energy gap equation through the random phase approximation (RPA). Then we use the Ritus method to calculate the decay triangle diagram and self-energy in the presence of a constant magnetic field B. Our results indicate that the magnetic field has little influence on the mass of \begin{document}$ \pi_0 $\end{document} at low temperatures. However, for quarks and σ mesons, their mass clearly changes, which reflects the influence of magnetic catalysis (MC). The presence of a magnetic field accelerates the decay of the meson while the presence of a chemical potential will decrease the decay process.     

Electromagnetic field produced in high-energy small collision systems within charge density models of nucleons

Recent experiments show that \begin{document}$ \Delta\gamma $\end{document}, an observable designed to detect the chiral magnetic effect (CME), in small collision systems (\begin{document}$ p+A $\end{document}) is similar to that in heavy ion collisions (\begin{document}$ A+A $\end{document}). This introduces a challenge to the existence of the CME because it is believed that no azimuthal correlation exists between the orientation of the magnetic field (\begin{document}$ \Phi_B $\end{document}) and participant plane (\begin{document}$ \Phi_2 $\end{document}) in small collision systems. In this work, we introduce three charge density models to describe the inner charge distributions of protons and neutrons and calculate the electric and magnetic fields produced in small \begin{document}$ p+A $\end{document} collisions at both RHIC and LHC energies. Our results show that the contribution of the single projectile proton is the main contributor to the magnetic field after averaging over all participants. The azimuthal correlation between \begin{document}$ \Phi_B $\end{document} and \begin{document}$ \Phi_2 $\end{document} is small but not vanished. Additionally, owing to the large fluctuation in field strength, the magnetic-field contribution to \begin{document}$ \Delta\gamma $\end{document} may be large.     

η mesons in hot magnetized nuclear matter

\begin{document}$\eta N$\end{document} interactions are investigated in hot magnetized asymmetric nuclear matter using the chiral SU(3) model and chiral perturbation theory (ChPT). In the chiral model, the in-medium properties of η-mesons are calculated using medium modified scalar densities under the influence of an external magnetic field. Further, in a combined chiral model and ChPT approach, off-shell contributions of the \begin{document}$\eta N$\end{document} interactions are evaluated from the ChPT effective \begin{document}$\eta N$\end{document} Lagrangian, and the in-medium effect of scalar densities are incorporated from the chiral SU(3) model. We find that the magnetic field has a significant effect on the in-medium mass and optical potential of η mesons, and we observe a deeper mass-shift in the combined chiral model and ChPT approach than in the solo chiral SU(3) model. In both approaches, no additional mass-shift is observed due to the uncharged nature of η mesons in the presence of a magnetic field.     

The effect of single-particle space-momentum angle distribution on two-pion HBT correlation in relativistic heavy-ion collisions using a multiphase transport model

Using the string melting version of a multiphase transport (AMPT) model, we analyze the transverse momentum dependence of the HBT radius \begin{document}$R_{\rm s}$\end{document} and the single-pion angle distribution on the transverse plane in central Au+Au collisions at \begin{document}$\sqrt{S_{NN}}$\end{document}=19.6, 27, 39, 62.4, and 200 GeV. Additionally, a numerical connection between these two phenomena is established with a series of functions. We can estimate the single-pion angle distribution on the transverse plane from HBT analysis.     

Chiral phase structure of the sixteen meson states in the SU(3) Polyakov linear-sigma model for finite temperature and chemical potential in a strong magnetic field

In characterizing the chiral phase-structure of pseudoscalar(J~(pc) = 0~(-+)), scalar(J~(pc) = 0~(++)), vector(J~(pc) =1~(--)) and axial-vector(J~(pc) = 1~(++)t) meson states and their dependence on temperature, chemical potential, and magnetic field,we utilize the SU(3) Polyakov linear-sigma model(PLSM) in the mean-field approximation. We first determine the chiral(non)strange quark condensates,σ_l and σ_s, and the corresponding deconfinement order parameters, φ and φ~*, in thermal and dense(finite chemical potential) medium and finite magnetic field. The temperature and the chemical potential characteristics of nonet meson states normalized to the lowest bosonic Matsubara frequency are analyzed. We note that all normalized meson masses become temperature independent at different critical temperatures. We observe that the chiral and deconfinement phase transitions are shifted to lower quasicritical temperatures with increasing chemical potential and magnetic field. Thus, we conclude that the magnetic field seems to have almost the same effect as the chemical potential, especially on accelerating the phase transition, i.e. inverse magnetic catalysis. We also find that increasing the chemical potential enhances the mass degeneracy of the various meson masses, while increasing the magnetic field seems to reduce the critical chemical potential, at which the chiral phase transition takes place. Our mass spectrum calculations agree well with the recent PDG compilations and PNJL, lattice QCD calculations, and QMD/UrQMD simulations.     

THE CLASSIFICATION OF THE WAVE FUNCTIONS OF BOSONS AND FERMIONS

In this paper we have proved that the wave functions for bosons and fermionscan be classified by either of the following two Lie superalgebra chains U(2l+1/2j+1) SU(2l+1/2j+1) SU(2l+1)SU(2j+1) SO(2l+1)Sp(2j+1) SO(3)SO(3), U(2l+1/2j+1) SU(2l+1/2j+1) OSp(2l+1/2j+1) SO(2l+1)Sp(2j+1) SO(3)SO(3) The wave functions for bosons and fermions classified by the Lie superalgebra chain U(2l+1/2j+1) SU(2l+1/2j+1) SU(2l+1)SU(2j+1) SO(2l+1)Sp(2j+1) SO(3)SO(3), are calculated also.     

THREE LIMITS IN THE INTERACTIONS OF THE s,d, g,BOSONS

In the I. B. M., when s, d, g bosons are presented, the boson Hamiltonian has thestructure of group U(15). This paper deals with the various chains of subgroups ofgroap U(15). Especially, the following chains:SU(15)SU(3)SO(3), SU(15)SU(5)SO(5)SO(3), U(15)U(14)SO(5)SO(3).are studied in detail, The formulae of the energy spectra are also given.     

Bardeen black hole surrounded by perfect fluid dark matter

We derive an exact solution for a spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM). By treating the magnetic charge g and dark matter parameter \begin{document}$\alpha$\end{document} as thermodynamic variables, we find that the first law of thermodynamics and the corresponding Smarr formula are satisfied. The thermodynamic stability of the black hole is also studied. The results show that there exists a critical radius \begin{document}$r_{+}^{C}$\end{document} where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range \begin{document}$0<r_{+}<r_{+}^{C}$\end{document} . In addition, the critical radius \begin{document}$r_{+}^{C}$\end{document} increases with the magnetic charge g and decreases with the dark matter parameter \begin{document}$\alpha$\end{document} . Applying the Newman-Janis algorithm, we generalize the spherically symmetric solution to the corresponding rotating black hole. With the metric at hand, the horizons and ergospheres are studied. It turns out that for a fixed dark matter parameter \begin{document}$\alpha$\end{document} , in a certain range, with the increase of the rotation parameter a and magnetic charge g, the Cauchy horizon radius increases while the event horizon radius decreases. Finally, we investigate the energy extraction by the Penrose process in a rotating Bardeen black hole surrounded by PFDM.     

Searching for axion-like particles with the blazar observations of MAGIC and Fermi-LAT

In this study, we explore the axion-like particle (ALP)-photon oscillation effect in the γ-ray spectra of the blazars Markarian 421 (Mrk 421) and PG 1553+113, which are measured by the Major Atmospheric Gamma Imaging Cherenkov Telescopes (MAGIC) and Fermi Large Area Telescope (Fermi-LAT) with high precision. The Mrk 421 and PG 1553+113 observations of 15 and five phases are used in the analysis, respectively. We find that the combined analysis with all the 15 phases improves the limits of the Mrk 421 observations. For the selected blazar jet magnetic field and extragalactic background light models, the combined limit set by the Mrk 421 observations excludes the ALP parameter region with the ALP-photon coupling of \begin{document}$g_{a\gamma} \gtrsim 2 \times 10^{-11} \; {\rm GeV}^{-1}$\end{document} for the ALP mass of \begin{document}$ \sim 8\times 10^{-9} \lesssim m_a \lesssim 2\times 10^{-7}\rm \; eV $\end{document} at 95% confidence level. The main uncertainties of the analysis originate from the blazar jet magnetic field model. We also find that the ALP hypothesis can slightly improve the fit to the PG 1553+113 results in several parameter regions. We do not set the limit in this case.     

Chiral phase transition and equation of state in chiral imbalance

The chiral phase transition and equation of state are studied within a novel self-consistent mean-field approximation of the two-flavor Nambu-Jona-Lasinio model. In this newly developed model, modifications to the chemical μ and chiral chemical \begin{document}$\mu_5$\end{document} potentials are naturally included by introducing vector and axial-vector channels from Fierz-transformed Lagrangian to the standard Lagrangian. In the proper-time scheme, the chiral phase transition is a crossover in the \begin{document}$T-\mu$\end{document} plane. However, when \begin{document}$\mu_5$\end{document} is incorporated, our study demonstrates that a first order phase transition may emerge. Furthermore, the chiral imbalance will soften the equation of state of quark matter. The mass-radius relationship and tidal deformability of quark stars are calculated. The maximum mass and radius decrease as \begin{document}$\mu_5$\end{document} increases. Our study also indicates that the vector and axial-vector channels exhibit an opposite influence on the equation of state.     

THE PERTURBATION EXPANSION OF THE QUANTIZED COMPOSITE FIELD THEORY AND GAUGE INVARIANCE

In this paper we introduce the concept of "same order" in the perturbution expansion of the quatized composite field theory which is different from single particle theory. For example, in the case of Q. E. D., "same order" is defined by means of a coupling constant, but here it closely relates the operators occuring in the B. S. equations. Feymann graphs of the "same order" are defined for different kinds of transitions in the composite field theory. Finally, we prove that guage invariance is a natural result as long as all "same order" Feymann graphs are calculated for an electromagnetic transition between composite particles.