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The capability for simulating the envelopes of three-dimensional
(bunched) beams has been implemented in the SAD accelerator modeling
environment. The simulation technique itself is similar to that of
other common envelope codes, such as Trace3D, TRANSPORT, and the XAL
online model. Specifically, we follow the second-order statistics of
the beam distribution rather than tracking individual particles. If
we assume that the beam maintains ellipsoidal symmetry in phase space,
we can include the first order effects due to space charge using a
semi-analytic model. This is the attractive characteristic of
envelope codes, since it greatly reduces computational time. This new
feature of SAD is implemented primarily in the SADScript interpreted
language, with only a small portion appearing as compiled code. As
such, the simulation does run slower than other compiled envelope
codes such as TRACE3D or XAL, however, as interpreted code it does
have the benefit of being easily modified. We demonstrate use of the
new feature and present example simulations of the J-PARC linear
accelerator section.
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