Threshold for emittance growth of A-G focused intense beams

The behavior of an intense beam propagating in a long alternate-gradient focusing channel is examined using computer simulations to determine, for phase advances between 60° and 90°, the emittance growth which might be expected to result from space charge nonlinearities and instabilities.

While strong evidence of space charge driven instabilities is found at a phase advance of 90°, for all beam distribution functions tested, these instabilities rapidly diminish as the phase advance is lowered. For an initial semi-Gaussian distribution at a phase advance of 80°, for example, no instability-caused emittance growth is observed down to the numerical limits of the simulations. This behavior appears to be relatively insenstive to lens fill and small initial mismatch, but the thresholds for emittance growth do appear to shift as the inital beam distribution is varied, so that a similar 80° K-V system does show evidence of instability-caused emittance growth.