Development of the self-modulation instability of a relativistic proton bunch in plasma

Verra, L. and Wyler, S. and Nechaeva, T. and Pucek, J. and Bencini, V. and Bergamaschi, M. and Ranc, L. and Zevi Della Porta, G. and Gschwendtner, E. and Muggli, P. and Agnello, R. and Ahdida, C. C. and Amoedo, C. and Andrebe, Y. and Apsimon, O. and Apsimon, R. and Arnesano, J. M. and Blanchard, P. and Burrows, P. N. and Buttenschön, B. and Caldwell, A. and Chung, M. and Cooke, D. A. and Davut, C. and Demeter, G. and Dexter, A. C. and Doebert, S. and Elverson, F. A. and Farmer, J. and Fasoli, A. and Fonseca, R. and Furno, I. and Gorn, A. and Granados, E. and Granetzny, M. and Graubner, T. and Grulke, O. and Guran, E. and Henderson, J. and Kedves, M. Á. and Kim, S.-Y. and Kraus, F. and Krupa, M. and Lefevre, T. and Liang, L. and Liu, S. and Lopes, N. and Lotov, K. and Calderon, M. Martinez and Mazzoni, S. and Moon, K. and Morales Guzmán, P. I. and Moreira, M. and Pakuza, C. and Pannell, F. and Pardons, A. and Pepitone, K. and Poimendidou, E. and Pukhov, A. and Ramjiawan, R. L. and Rey, S. and Rossel, R. and Saberi, H. and Schmitz, O. and Senes, E. and Silva, F. and Silva, L. and Spear, B. and Stollberg, C. and Sublet, A. and Swain, C. and Topaloudis, A. and Torrado, N. and Tuev, P. and Turner, M. and Velotti, F. and Verzilov, V. and Vieira, J. and Weidl, M. and Welsch, C. and Wendt, M. and Wing, M. and Wolfenden, J. and Woolley, B. and Xia, G. and Yarygova, V. and Zepp, M. (2023) Development of the self-modulation instability of a relativistic proton bunch in plasma. Physics of Plasmas, 30 (8): 083104. ISSN 1070-664X

Abstract

Self-modulation is a beam–plasma instability that is useful to drive large-amplitude wakefields with bunches much longer than the plasma skin depth. We present experimental results showing that, when increasing the ratio between the initial transverse size of the bunch and the plasma skin depth, the instability occurs later along the bunch, or not at all, over a fixed plasma length because the amplitude of the initial wakefields decreases. We show cases for which self-modulation does not develop, and we introduce a simple model discussing the conditions for which it would not occur after any plasma length. Changing bunch size and plasma electron density also changes the growth rate of the instability. We discuss the impact of these results on the design of a particle accelerator based on the self-modulation instability seeded by a relativistic ionization front, such as the future upgrade of the Advanced WAKefield Experiment.