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As the second stage of the CEPC-SPPC project, SPPC (Super Proton-Proton Collider) aims at exploring new physics beyond the Standard Model. The key design goal for the SPPC accelerator complex is to reach 75 TeV in center of mass energy with a circumference of 100 km for the collider and an injector chain of four accelerators in cascade to support the collider. As an important part of the SPPC conceptual study, the longitudinal beam dynamics was studied systematically, which includes the dynamics in the collider and its complex injector chain. First, the bunch filling scheme of the SPPC complex was designed on the basis of various constraints such as the technical challenges of the kicker magnets, limited extraction energy per injection and so on. Next, the study on the longitudinal dynamics in the collider focused on the RF scheme to meet the requirements for luminosity and mitigate relevant instabilities. A higher harmonic RF system (800 MHz) together with the basic RF system (400 MHz) to form a dual-harmonic RF system was employed to mitigate collective instabilities and increase the luminosity by producing shorter bunches. In addition, the longitudinal matchings between the bunches in the different accelerator stages were studied, with special attention to the space charge effects and the beam loading effect in the two lower energy rings (p-RCS and MSS), which result in an optimization of the RF schemes. A set of self-consistent beam and RF parameters for the SPPC complex was obtained. The collider and the three proton synchrotrons of the injector chain have unprecedented features, thus this study demonstrates how a future proton-proton collider complex looks like., Comment: 24 pages, 13 figures

Using test particle simulations we study electron acceleration at collisionless shocks with a two-component model turbulent magnetic field with slab component including dissipation range. We investigate the importance of shock normal angle $\theta_{Bn}$, magnetic turbulence level $\left(b/B_0\right)^2$, and shock thickness on the acceleration efficiency of electrons. It is shown that at perpendicular shocks the electron acceleration efficiency is enhanced with the decreasing of $\left(b/B_0\right)^2$, and at $\left(b/B_0\right)^2=0.01$ the acceleration becomes significant due to strong drift electric field with long time particles staying near the shock front for shock drift acceleration (SDA). In addition, at parallel shocks the electron acceleration efficiency is increasing with the increasing of $\left(b/B_0\right)^2$, and at $\left(b/B_0\right)^2=10.0$ the acceleration is very strong due to sufficient pitch-angle scattering for first-order Fermi acceleration, as well as due to large local component of magnetic field perpendicular to shock normal angle for SDA. On the other hand, the high perpendicular shock acceleration with $\left(b/B_0\right)^2=0.01$ is stronger than the high parallel shock acceleration with ($\left(b/B_0\right)^2=10.0$), the reason might be the assumption that SDA is more efficient than first-order Fermi acceleration. Furthermore, for oblique shocks, the acceleration efficiency is small no matter the turbulence level is low or high. Moreover, for the effect of shock thickness on electron acceleration at perpendicular shocks, we show that there exists the bend-over thickness, $L_{\text{diff,b}}$. The acceleration efficiency does not change evidently if the shock thickness is much smaller than $L_{\text{diff,b}}$. However, if the shock thickness is much larger than $L_{\text{diff,b}}$, the acceleration efficiency starts to drop abruptly., Comment: 27 pages, 9 figures

Using test particle simulations we study particle acceleration at highly perpendicular ($\theta_{Bn}\geq 75^\circ$) shocks under conditions of modeling magnetic turbulence. We adopt a backward-in-time method to solve the Newton-Lorentz equation using the observed shock parameters for quasi-perpendicular interplanetary shocks, and compare the simulation results with $ACE$/EPAM observations to obtain the injection energy and timescale of particle acceleration. With our modeling and observations we find that a large upstream speed is responsible for efficient particle acceleration. Our results also show that the quasi-perpendicular shocks are capable of accelerating thermal particles to high energies of the order of MeV for both kappa and Maxwellian upstream distributions, which may originate from the fact that in our model the local background magnetic field has a component parallel to the shock normal., Comment: 23 pages, 7 figures

Shock acceleration is considered one of the most important mechanisms for the acceleration of astrophysical energetic particles. In this work, we calculate the trajectories of a large number of test charged particles accurately in a parallel shock with magnetic turbulence. We investigate the time evolution of the accelerated-particle energy spectrum in the downstream of the shock in order to understand the acceleration mechanism of energetic particles. From simulation results we obtain power-law energy spectra with a bend-over energy, $E_0$, increasing with time. With the particle mean acceleration time and mean momentum change during each cycle of the shock crossing from diffusive shock acceleration model (following Drury), a time-dependent differential equation for the maximum energy, $E_{acc}$, of particles accelerated at the shock, can be approximately obtained. We assume the theoretical bend-over energy as $E_{acc}$. It is found that the bend-over energy from simulations agrees well with the theoretical bend-over energy using the non-linear diffusion theory, NLGCE-F, in contrast to that using the classic quasi-linear theory (QLT)., Comment: 22 pages, 6 figures and 2 table

We modify the NonLinear Guiding Center (NLGC) theory (Matthaeus et al. 2003) for perpendicular diffusion by replacing the spectral amplitude of the two-component model magnetic turbulence with the 2D component one (following Shalchi 2006), and replacing the constant $a^2$, indicating the degree particles following magnetic field line, with a variable $a^{\prime 2}$ as a function of the magnetic turbulence. We combine the modified model with the NonLinear PArallel (NLPA) diffusion theory (Qin 2007) to solve perpendicular and parallel diffusion coefficients simultaneously. It is shown that the new model agrees better with simulations. Furthermore, we fit the numerical results of the new model with polynomials, so that parallel and perpendicular diffusion coefficients can be calculated directly without iteration of integrations, and many numerical calculations can be reduced., Comment: Accepted for publication in ApJ

The interface and electronic structure of thin (~20-74 nm) Co3O4(110) epitaxial films grown by oxygen-assisted molecular beam epitaxy on MgAl2O4(110) single crystal substrates have been investigated by means of real and reciprocal space techniques. As-grown film surfaces are found to be relatively disordered and exhibit an oblique low energy electron diffraction (LEED) pattern associated with the O-rich CoO2 bulk termination of the (110) surface. Interface and bulk film structure are found to improve significantly with post-growth annealing at 820 K in air and display sharp rectangular LEED patterns, suggesting a surface stoichiometry of the alternative Co2O2 bulk termination of the (110) surface. Non-contact atomic force microscopy demonstrates the presence of wide terraces separated by atomic steps in the annealed films that are not present in the as-grown structures; the step height of ~ 2.7 A corresponds to two atomic layers and confirms a single termination for the annealed films, consistent with the LEED results. A model of the (1 * 1) surfaces that allows for compensation of the polar surfaces is presented., Comment: 8 pages, 7 figures