Transverse emittance equation with acceleration and compression

Summary form only given, as follows. The formula for emittance charge of a drifting beam in an inertial fusion driver (IFD) is generalized by the inclusion of acceleration and compression. Applications have been made to various acceleration schedules in a FODO transport channel. In particular, for the case of decompression in the head and tail of a bunch, the decrease of emittance has been predicted. As the tune depression becomes less (longer Debye length), the density profile becomes centrally peaked as opposed to uniform (minimum field energy state). Thus, a part of the transverse kinetic energy is converted to field energy and emittance decreases. With acceleration, the change of the normalized emittance is decreased due to a smaller radial size of the beam for a given undepressed tune, and with compression, the effect of the space charge on the emittance is amplified due to the larger available electrostatic energy. However, since the typical time scale of relaxation to a quasi-equilibrium state via random phase mixing is short compared with the time scale of the acceleration and compression in an ion IFD, these effects on the emittance change are not large.<>