1. Beam characteristics UCLA What is a “perfect” beam? It comes from the Injector. It is affected by many factors A few highlights from contributed talks… Beam Environment Capillary discharge (S. Hooker); scaling matched w o ; wall ultimately comes into play at small radii or low n e. Hollow channel (N. Andreev); multimode not detrimental to wakefield; phase relation between Ez and Ey changes in a channel. Few-cycle driver (M. Geissler); very rapid evolution of wake; effects of density ramps; sharp edge needed for external injection, N bunch > N ion. “Non-linear” effects; Beam Loading Beam loading (A. Reitsma);   E/E tradeoff; f slippage to flatten  E/E; function of L bunch / p. Beam loading in PWFA (K. Lotov); minimize residual energy flux --> optimal witness pulse shape, linear to blowout regimes. Dark current (T. Katsouleas); Seen in SLAC PWFA experiment; E crit ~ SQRT(k’) = Dawson cold wavebreaking for blowout conditions.

2. Beam characteristics (cont.) UCLA What is a “perfect” beam? It comes from the Injector. It is affected by many factors A few highlights from contributed talks (cont.)… Beam Environment “Non-linear” effects; Beam Loading Transport and Staging Transport and focusing (Y. Saveliev); finite path length differences in divergent beam -> temporal stretch; curved photocathode. General issue for all transport optics. Head-tail coupling; (part of T. Katsouleas’ talk); for long bunchs in plasma, head defines a “structure” and head-tail coupling is similar to RF structures. For short bunch (blowout/bubble), equivalent “structure” is time-dependent -> head-tail coupling is damped. Transverse dynamics (A. Reitsma); strong beam loading transverse field modification -> damping of head-tail breakup; helps slice-dependent ‘beta matching’.

3. Related topics (Participant input)… UCLA Is it possible to marry the bubble/blowout structure with external injection? Questions are; Can a witness beam “load” enough to distort the bubble and prevent self-injection? How to precisely place the bunch initially or at the next stage? (see W. Leemans, session1; W. Lu & M. Tzoufras, session2; M. Geissler, session3, A. Pukov, session2) Beam breakup instability (BBI) in a linac -> betatron motion couples head-to-tail. Is this the same as hosing? Is there a damping mechanism (e.g., BNS)? Yes, similar. Yes, ideas for damping (see T. Katsouleas session3; P. Muggli, session1&2). Electromagnetic Magnus Effect -> non-ideal driver -> meandering of wake vector. Seen in self-sidescatter (RAL, LBNL). Due to asymmetries in transverse ponderomotive force. Related to laser hosing, but not an instability. Stabilized in plasma channel(?) (B. Bingham, session3; W. Leemans comment). Synchotron-damping is larger off axis -> halo reduction? Emittance damping?  Effective damping for E ~ TeV. Synchrotron radiation is getting into the codes. For positron emittance damping? (see P. Muggli, ibid).

4. Related topics (Participant input, cont.)… UCLA Axicon channel between acceleration stages -> minimize temporal dispersion. = temporal distortion -> minimize  (see Y. Saveliev session3; N. Lopes, slide 5). Laser shaping: Plasma mirror to setup a “matched beam” (pre-erode the head)  Works in simulation. (see W. Lu, session2) Need “FROG” measurements from experiments. Short length of plasma to increase a 0 via photon deceleration. Seen in simulations; responsible for the “Dream Beams” (L. Silva, slide 6). Diagnostics and feedback sub-micron BPM -> Thomson scattering off wake; collection of expelled e -  Technologies could be developed/tested in near-term experiments. coherent THz -> current profile Multi-shot autocorrelator (see W. Leemans, session1), single shot electrooptic (see D. Jaroszynski, session4).

5. Prevent e - bunch expansion…ion-channel guiding Maryland, Texas, Oxford, IST, UCLA etc. technologies Nelson Lopes

6. Nonlinear evolution of laser - a 0 amplifier UCLA Initially, no wave breaking Conservation of number of photons classical wave action Photon deceleration/frequency downshift Nonlinear evolution of laser pulse for long propagation distances leads to single cycle laser pulse with amplified a 0 F. Tsung et al, Proc. Natl. Acad. Sci. v. 99, 29 (2002) Higher a 0 leads to wave breaking   1/  |a|/a 0 a 0 = 3 c  L / p0 = 1/2