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The capability for three-dimensional RMS envelope simulation, including space charge, has been implemented in the SAD accelerator modeling environment used at KEK. The SAD (for Strategic Accelerator Design) modeling system consists of a compiled simulation engine, an in-house scripting language SADScript, and user interface support both in Tcl/tk script and SADScript. The RMS envelope simulator is implemented primarily in the SADScript language, which much resembles the Mathematica language. The dynamics within the model are similar to that used by TRACE3D, TRANSPORT, and XAL. Specifically, the symmetric matrix of all second-order beam moments is propagated using a linear beam optics model for the beamline. However, the current simulation engine employs an adaptive space-charge algorithm which actively adjusts the solution integration to maintain a specified accuracy, as well as imposing the symplectic condition. It is designed to keep the integration step size as large as possible while enforcing that the residual solution error remain below a given tolerance. The paper concentrates primarily on the adaptive nature of the RMS simulation, since this is the novel feature.
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