The discrete energy method in numerical relativity: Towards long-term stability

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test problems commonly used in numerical relativity and observe that while we obtain convergent schemes, fast growing modes, or ``artificial instabilities,'' contaminate the solution. We find that these growing modes can partially arise from the lack of a Leibnitz rule for discrete derivatives and discuss ways to limit this spurious growth.Comment: 18 pages, 22 figure

Experience with the ALPI linac resonators

Abstract The medium β section of the linac accelerator ALPI [G. Fortuna et al., Nucl. Instr. and Meth. A 328 (1993) 236] is now in operation: beams of 32 S, 37 Cl, 58 Ni, 76 Ge, 81 Br were accelerated for nuclear physics experiments in the first half of 1995. The medium β section of ALPI includes 12 cryostats containing four accelerating quarter-wave resonators each ( β = 0.11, f = 160 MHz). Two similar resonators are installed in a buncher cryostat and two in a rebuncher unit. Accelerating fields around 2.5 MV/m are available. The experience in cavity preparation, installation, conditioning and operation is described