The dual harmonic system has been widely used in high intensity proton synchrotrons to suppress the space charge effect, as well as reduce the beam loss. To investigate the longitudinal beam dynamics in the dual rf system, the potential well, the sub
-buckets in the bunch and the multi-solutions of the phase equation have been studied theoretically. Based on these theoretical studis, the optimization of bunching factor and rf voltage waveform are made for the dual harmonic rf system in the upgrade phase of the CSNS/RCS. In the optimization process, the simulation with space charge effect is done by using a newly developed code C-SCSIM.
We propose a valid scheme to measure the Hubble parameter $H(z)$ at high redshifts by detecting the Sandage-Loeb signal (SL signal) which can be realized by the next generation extremely large telescope. It will largely extend the current observation
al Hubble parameter data (OHD) towards the redshift region of $z in [2.0,5.0]$, the so-called redshift desert, where other dark energy probes are hard to provide useful information of the cosmic expansion. Quantifying the ability of this future measurement by simulating observational data for a CODEX (COsmic Dynamics and EXo-earth experiment)-like survey and constraining various cosmological models, we find that the SL signal scheme brings the redshift upper-limit of OHD from $z_mathrm{max}=2.3$ to $z_mathrm{max}simeq 5.0$, provides more accurate constraints on different dark energy models, and greatly changes the degeneracy direction of the parameters. For the $Lambda$CDM case, the accuracy of $Omega_m$ is improved by $58%$ and the degeneracy between $Omega_m$ and $Omega_ {Lambda}$ is rotated to the vertical direction of $Omega_k = 0$ line strongly; for the $w$CDM case, the accuracy of $w$ is improved by $15%$. The Fisher matrix forecast on different time-dependent $w(z)$ is also performed.
Many schemes have been proposed to perform a model-independent constraint on cosmological dynamics, such as nonparametric dark energy equation of state (EoS) omega(z) or the deceleration parameter q(z). These methods usually contain derivative proces
ses with respect to observational data with noise. However, it still remains remarkably uncertain when one estimates the numerical differentiation, especially the corresponding truncation errors. In this work, we introduce a global numerical differentiation method, first formulated by Reinsch(1967), which is smoothed by cubic spline functions. The optimal solution is obtained by minimizing the functional Phi(f). To investigate the potential of the algorithm further, we apply it to the estimation of the transition redshift z_{t} with simulated expansion rate E(z) based on observational Hubble parameter data(OHD). An effective method to determine the free parameter S appearing in Reinsch Splines is provided.
