Latest results on electron trapping and acceleration Konstantin Lotov, Alexey Petrenko, Alexander Sosedkin, Petr Tuev Budker Institute of Nuclear Physics SB RAS, Novosibirsk, Russia Novosibirsk State University, Novosibirsk, Russia AWAKE Collaboration

presented by K.Lotov at 11th AWAKE Physics Board Meeting, CERN Injection of realistic electron beams into realistic density plasma with a = 5 mm (orifice radius) Beam phase portrait taken from simulations of Ulrich Dorda Plasma density slope along 10 m Oblique electron injection

presented by K.Lotov at 11th AWAKE Physics Board Meeting, CERN Injection of realistic electron beams into realistic density plasma Beam parameters against acceptance at z=-40cm Electron energy distribution Trapping is good even for twice larger size and angular spread of the electron beam Injection parameters can be further optimized for more narrow energy spread The result is not very sensitive to injection parameters

presented by K.Lotov at 11th AWAKE Physics Board Meeting, CERN Effect of the small density slope on accelerating ability of the plasma A wide plateau centered at +1%, +0% is also good

presented by K.Lotov at 11th AWAKE Physics Board Meeting, CERN Characterization of the electron defocusing region at the entrance Typical map of the radial force acting on the electron beam in a low density plasma plasma boundary oscillating wakefield + repulsion by incompletely neutralized beam current focusing region outside the plasma As the beam current vanishes, the oscillating component of the wakefield is able to focus (trap) electrons) max. focusing force max. defocusing force

presented by K.Lotov at 11th AWAKE Physics Board Meeting, CERN Characterization of the electron defocusing region at the entrance Plasma density dependence of the forces at one glance: maximized (over xi) defocusing forcefocusing force stationary oscillating wakefield + repulsion by incompletely neutralized beam current, trapping and acceleration are possible varying-period oscillating wakefield + repulsion by the beam current, trapping not possible n~nb, repulsion dominates scattered plasma electrons make a focusing area n<<nb, repulsion dominates no force 0m6cm-14cm-40cm electron injection

Injected electrons marked by the black dots will be captured eventually: Red lines show the trajectories of plasma electrons. Dots show the 16 MeV electrons from the injected beam. Plasma electrons are ejected from plasma at the density ~0.1% of nominal ( ~ /cm 3 ). This results in strong focusing electric field extending for several mm outside plasma. Edge of plasma Prepared by A.Petrenko for PEB Meeting, CERN Action of radial forces on test electrons

The full injection and acceleration beam dynamics (10% density gradient) 10% density gradient over 10 m long plasma: Plasma edge Prepared by A.Petrenko for PEB Meeting, CERN

plasma p+p+ p+p+ ΔrbΔrb e-e- impact of plasma electrons impact of plasma ions perturbation of electrons e-e- r rbrb p+p+ F1F1 F2F2 F 3 =0 F 1 =F 2 - symmetry F 3 =0 Ampere's law, Gauss's law Conservation of the electron flux in the co-moving frame (through green circle) p + plasma Electron velocity, v e c c c The horizontal offset of the proton beam does not affect at the electrons, but the vertical offset can change electrons trajectory The influence of the offset of the proton beam Prepared by P. Tuev and K.Lotov for PEB Meeting, CERN No focusing force from the beam itself Net force only due to displacement of extra electrons, which by themselves make the force F 0 ~A r e -r  p /c F ~ F 0 (r+  r b ) – F 0 (r) ~ B b e -r  p /c  r b /r B b – magnetic force of the beam (equals the total focusing force in the plasma at small r)

presented by K.Lotov at 11th AWAKE Physics Board Meeting, CERN General comment We need to document our findings in papers! Entrance/injection story could result in several of them (my proposal): Flow simulations (Gennady) Acceleration in the ramped density plasma (Alexey) Wakefields in the narrow low-density plasma (Petr, Konstantin) Fast valve story, solutions to the problem, new baseline (many) General review of AWAKE refs.

presented by K.Lotov at 11th AWAKE Physics Board Meeting, CERN Summary The new baseline case that includes the oblique electron injection, a small plasma density gradient along 10 meters, a realistic electron beam, a realistic plasma density distributions at the entrance is simulated and shows a reasonably good results and no close tolerances. Wakefields excited by the proton beam in the low-density plasma are understood and present no danger for the oblique injection The case with the plasma density increase of ~10% along 10 meters is of interest as it provides a reasonably good result (~1 GeV electrons) at reduced requirements on the plasma density profile. Offset of the proton beam with respect to the laser beam produces a net force on test electrons in the direction of the offset and only in a low-density plasma. Do not forget to document the results in papers.

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