Phys. Rev. ST Accel. Beams 6, 014205 (2003) [12 pages]

Longitudinal collective echoes in coasting particle beams

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Ahmed Al-Khateeb *, Oliver Boine-Frankenheim , Rainer W. Hasse, and Ingo Hofmann
Gesellschaft für Schwerionenforschung mbH (GSI), Planckstraße 1, D-64291 Darmstadt, Germany

Received 12 November 2002; published 23 January 2003

Longitudinal ballistic and collective beam echoes with diffusion effects are investigated theoretically. In the presence of the space-charge impedance, the collective echo amplitude is obtained as a closed form expression. In contrast to the ballistic case, the collective echo amplitude consists of one maximum at time techo. The echo amplitude grows up and damps down with a rate proportional to the Landau damping rate of space-charge waves. The effect of weak diffusion is found to modify the ballistic and the collective echo amplitudes in the same manner. This effect of diffusion was confirmed using a “noiseless,” grid-based simulation code. As a first application the amount of numerical diffusion in our simulation code was determined using the echo effect.


©2003 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevSTAB.6.014205
DOI: 10.1103/PhysRevSTAB.6.014205
PACS: 29.27.Bd, 29.20.–c, 52.59.Sa, 52.65.Ff

* Permanent address: Department of Physics, Faculty of Science, Yarmouk University, Irbid, Jordan.
Corresponding author. Email address: O.Boine-Frankenheim@gsi.de

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