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Coherent synchrotron radiations (CSR) emitted by a high-brightness electron beam during transport in a bending magnet is a double-edged sword in electron accelerators. While CSR contributes to a stronger radiation field than the incoherent radiation, it simultaneously leads to degradation of the electron beam quality. Specifically, CSR effects manifest in increases of the beam energy spread and the projected emittance, and amplification of the microbunching instability. This paper presents analytical formulas for the CSR-induced microbunching instability gain and for the induced emittance growth in an arbitrary achromatic four-bend chicane with inclusion of both the steady-state and transient CSR effects. The analytical formulas are compared and show good agreement with Vlasov calculations and particle tracking simulations. The obtained analytical formulas are then applied to evaluate the CSR effects in the design of a general achromatic four-bend bunch compressor chicane, providing a quick estimate on the microbunching gain and the induced emittance growth. From the widely adopted symmetric C-shape chicane to a non-symmetric S-shape chicane, our analytical formulas offer insight into the evolution of the microbunching gain and the emittance growth with the variations of design parameters. In comparison to particle tracking simulations currently employed for CSR effect analyses, the analytical formulas presented in this paper significantly reduce the evaluation time, enabling systematic study of parametric dependencies with inclusion of CSR effects within specified design parameter ranges., Comment: 31 pages, 7 figures

High peak current electron beams are essential for x-ray free-electron lasers (FELs), and generally realized through multi-stage compression with symmetric C-shape four-bend chicanes. However, the coherent synchrotron radiations (CSR), emitted for wavelengths longer than or comparable to the length of the electron bunch during the compression, may degrade the beam quality and finally affect the FEL performance. In this Letter, we show that zero net CSR kick cannot be achieved in a symmetric C-chicane by using an explicit point-kick analysis of the CSR effects, which is responsible for significant emittance growth when pursuing a peak current of $\gtrsim$ 10 kiloamperes. A four-bend chicane with non-symmetric S-shape geometry that can self-cancel the CSR kicks is proposed to effectively suppress the emittance growth. Compared to the symmetric C-chicane, beams with three times higher peak current and similar emittance growth can be achieved with the S-chicane for typical FEL operation parameters. We believe that this study provides a viable way of producing high quality and short intense electron beams, benefiting future development of FELs and other types of accelerator-based scientific facilities.

The most significant advances in the accelerator-based light sources (i.e., x-ray free electron lasers) are driven by the production of the high final peak current in the last several decades. As a prerequisite to attain the proposed high brightness, the symmetric C-chicane bunch compressor is typically exploited due to its simplicity, efficiency, and natural dispersion-free feature at all orders. However, during bunch compression for a high peak current requirement, a main contributing factor to the transverse emittance degradation is the emission of the coherent synchrotron radiation (CSR). Suppressing this effect is necessary to preserve the beam phase-space quality. To this end, this paper presents an analysis of one-dimensional CSR point-kick and derives the cancellation conditions in terms of compression factor. The CSR cancelation conditions indicate an asymmetric geometric design. We demonstrate concrete schemes for asymmetric C- and S-chicanes, and verify the CSR cancelation conditions using integration methods and ELEGANT simulations. Furthermore, the proposed asymmetric C- and S-chicanes can drastically suppress the emittance growth compared with the symmetric ones with identical bunch compression goals.

We embark on a systematical analysis of the quark and gluon gravitational form factors (GFFs) of the proton, by connecting energy-momentum tensor (EMT) and the near-threshold vector meson photoproduction (NTVMP). Concretely, the quark contributions of GFFs are determined by global fitting the cross section of the lightest vector meson $\rho^0$ photoproduction. Combined with the gluon GFFs achieved from heavy quarkonium $J/\psi$ photoproduction data, the complete GFFs are obtained and compared with the experimental results and Lattice QCD determinations. In addition, we use the Resonances Via Pad\'{e} (RVP) method based on the Schlessinger Point Method (SPM) to obtain a model-independent quark $D$-term distribution by direct analytical continuation of Deep Virtual Compton Scattering (DVCS) experimental data. If errors are considered, the results obtained by RVP are basically consistent with those obtained by NTVMP. Moreover, the comprehensive information on GFFs helps us to uncover the mass distribution and mechanical properties inside the proton. This work is not only an important basis for delving the proton enigmatic properties, unraveling the secrets of the proton internal nature but also have significance theoretical guiding for future JLab and EICs experimental measurements., Comment: 9 pages,8 figures

Inspired by the recent Hall C and GlueX measurements of $J/\psi$ photoproduction, a systematic analysis of the contribution of quantum anomalous energy (QAE) to the proton mass is carried out under the framework of the vector meson dominance model. The results show that the effective Pomeron model and the parametrized two gluon exchange model can explain the cross section of $J/\psi$ photoproduction well. Based on the predicted cross section values given by the two models, the distribution of the QAE contribution with the energy is extracted for the first time. Finally, the average value of the QAE contribution is estimated to be (3.50$\pm$0.70)$\%$, which suggests that the QAE contribution to the proton mass is small. Accordingly, we compared this result with those of other groups and explored the causes for the differences., Comment: 8 pages, 9 figures

Inspired by the recent near-threshold $J/\psi$ photoproduction measurements, we discuss gluon gravitational form factors (GFFs) and internal properties of the proton. This work presents a complete analysis of the proton gluon GFFs connecting the gluon part of the energy-momentum tensor and the heavy quarkonium photoproduction. In particular, a global fitting of the $J/\psi$ differential and total cross section experimental data is used to determine the gluon GFFs as functions of the squared momentum transfer $t$. Combined with the quark contributions to the $D$-term form factor extracted from the deeply virtual Compton scattering experiment, the total $D$-term is obtained to investigate their applications in describing the proton mechanical properties. These studies provide a unique perspective on investigating the proton gluon GFFs and important information for enhancing QCD constraints on the gluon GFFs., Comment: 8 pages, 4 figures

As it involves the lightest physical states excited from the vacuum by the vector quark current, near-threshold $\rho^0$ photoproduction is considered a possible way to research the proton radius and the absolute value of the scattering lengths of the $\rho^0$--proton interaction. In this work, under the assumption of a scalar form factor of dipole form, the value of the proton mass radius is calculated as $0.85\pm 0.06 \text{ fm }$ by fitting the differential cross section of the $\gamma p \rightarrow \rho^0 p$ reaction at near-threshold energy. For light vector meson photoproduction, because the exchange of a scalar quark--antiquark pair is not suppressed and should dominate the scalar gluon exchange, the radius we extract from $\rho^0$ photoproduction is likely to represent the quark radius of the proton. This fact may explain why the value obtained in this work is very near the proton charge radius. Moreover, the absolute value of the $\rho^0$--proton scattering length $|\alpha_{\rho^0 p}|= 0.31 \pm 0.06 \text{ fm}$ is obtained for the first time within the vector meson dominance model. This result disobeys the rule that the absolute value of the vector meson and proton scattering length $|\alpha_{V p}|$ increases with the meson's mass, which can be attributed to treating the $\rho^0$ meson as a point in the analysis. These results provide useful theoretical information for an in-depth understanding of proton structure and the proton--vector meson interaction., Comment: 6pages, 6 figures. To be published in Science China Physics, Mechanics & Astronomy

Under the framework of Vector Meson Dominance model, the value of scattering length can be expressed as a function of the ratio between total cross section $\sigma (W)$ and $R (W)$, where $R(W)$ is the ratio between final momentum $|{\bf p}_3 |$ and initial momentum $|{\bf p}_1|$ and positively correlated with the center-of-mass energy. Based on the theoretical study of charmoniums photoproduction within two gluon exchange model and effective pomeron model, we research the scattering lengths of vector mesons and proton interaction in this work. Results show that the scattering length $\left|\alpha_{J/\psi p}\right|$ obtained from the two models are close and basically in agreement with the theoretical prediction of Strakovsky and co-workers. Additionally, we first calculate the scattering length of $\psi(2S) $-proton interaction in two gluon exchange model and effective pomeron model as $ 1.31\pm 0.92$ am (1 am = $10^{-3}$ fm) and $ 3.24 \pm 0.63$ am, respectively. This is a little bit different from the two models and requires precise measurements from subsequent experiments. In short, our results will provide a theoretical reference for future studies on characterizing the vector meson-proton scattering length., Comment: 7 pages, 7 figures

In this work, the cross-section of the reaction $\gamma p \rightarrow V(J/\psi,\psi(2S)) p$ from the production threshold to medium energy is studied and systematically analyzed within two gluon exchange model. The obtained numerical results are in agreement with experimental data and other theoretical predictions. Under the assumption of the scalar form factor of dipole form, the value of proton mass radius is calculated as $0.55\pm 0.09$ fm and $ 0.77\pm 0.12$ fm from the fit to the predicted $J/\psi $ and $\psi(2S)$ differential cross-section, respectively. Finally the average value of proton mass radius is estimated to be $\sqrt{\left}=0.67\pm 0.11$ fm. Moreover, one find that extracting mass radius from the near-threshold differential cross-section of heavy quarkoniums is always affected by large $|t|_{min}$. These obtained results may provide important theoretical reference for understanding of nucleon structure and future relevant experiments., Comment: 7pages, 10figures

The near-threshold photoproduction of $J/\psi$ is regarded as one golden process to unveil the nucleon mass structure, pentaquark state involving the charm quarks, and the poorly constrained gluon distribution of the nucleon at large $x$ ($>0.1$). In this paper, we present an analysis of the current experimental data under a two-gluon exchange model, which shows a good consistency. Using a parameterized function form with three free parameters, we have determined the nucleonic gluon distribution at the $J/\psi$ mass scale. Moreover, we predict the differential cross section of the electroproduction of $J/\psi$ as a function of the invariant mass of the final hadrons $W$, at EicC, as a practical application of the model and the obtained gluon distribution. According to our estimation, thousands of $J/\psi$ events can be detected per year on EicC near the threshold. Therefore, the relevant experimental measurements are suggested to be carried out on EicC., Comment: 6 pages, 7 figures

In this paper we discuss epicycloid approximation of the trajectories of charged particles in axisymmetric magnetic fields. Epicycloid trajectories are natural in the Guiding Center approximation and we study in detail the errors arising in this approach. We also discuss how using exact results for particle motion in the equatorial plane of a magnetic dipole the accuracy of this approximation can be significantly extended. We also show that the epicycloids approximate the trajectory of a charged particle more accurately than the position of the particle along the trajectory., Comment: 8 pages, 10 figures