Barrier RF Stacking

A novel wideband RF system, nicknamed the barrier RF, has been designed, fabricated and installed in the Fermilab Main Injector. The cavity is made of seven Finemet cores, and the modulator made of two bipolar high-voltage fast solid-state switches. The system can deliver ±7 kV square pulses at 90 kHz. The main application is to stack two proton batches injected from the Booster and squeeze them into the size of one so that the bunch intensity can be doubled. High intensity beams have been successfully stacked and accelerated to 120 GeV with small losses. The problem of large longitudinal emittance growth is the focus of the present study. An upgraded system with two barrier RF cavities for continuous stacking is under construction. This work is part of the US-Japan collaborative agreement

High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows

The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10^-5 along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D = 24, corresponding to 4624-dimensional renormalization-group flows.Comment: 6 pages, 5 figure