Figure 3.6: (left) Initial energy dependence of seed electron bunch longitudinal centroid in the moving window at the speed of lightc and (right) its wakefield amplitude evaluated at r=200 µm. Plasma starts atz=0. Plasma density: n0=2×1014 cm−3. The low energy electron bunch has initially the lower velocity than the speed of light in the propagation axis. The relative phase between the low energy electron bunch and the long proton bunch must be changing in time. Additionally, the energy loss of the electron bunch particle accelerates the decrease of the wakefield amplitude.
exit. Among the pictures of (3×2) array, the columns indicate before and after the beam loss at the plasma exit and the rows indicate the charge of the electron bunch (Qe = 150 pC, 250 pC, and 800 pC), respectively. Since the rms lengths of electron bunches were not measured in the experiment, here we scanned the bunch duration fromσξ,e0/c=1−10 ps to see the overall aspect of the energy spectra.
The first column shows the energy spectra of electron bunch after 10 m propagation in plsma and before passing the plasma exit. Energy losses of electrons occur mostly at this stage. At this moment, there exist the electrons whose energies did not change from the initial value ∼18 MeV. During and after the transverse beam evolution, most of these electrons are transversely kicked out of the decelerating wakefield region by the transverse component of the wakefield at the defocusing phase. Some portion of electrons are dropped out of the drastically evolving wakefield even at the focusing phase. The second column shows the energy spectra of electron bunch after the plasma exit. After the elctron bunch passed the 5 mm radius aperture at the plasma exit, the particles outside of 5 mm radius are masked. In overall aspect, the electron bunch energy loss is seen larger with the larger charge and the shorter rms length as it was expected from the beginning. It indirectly implies how the wakefield driven by the low energy electron bunch would evolve in the 10 m-long plasma.
Figure 3.7: Evolution of electron bunch parameters and its driven radial wakefields forQe = 150 pC, 250 pC, and 800 pC with σξ,e0/c=2 ps in plasma. The bunch charges are from AWAKE Run 2(a) experiment. At the moment, the bunch length was unknown. (a) Bunch rms radius of (solid curves) total and (dashed curves) screen arriving particles. (b) Bunch rms length of (solid curves) total and (dashed curves) screen arriving particles. (c) Bunch maximum number density. (e) Averaged transverse wakefield behind the electron bunch weighted withr on Gaussian radial profile ofσr,p=200µm (no proton bunch in the simulation). Figure (a) shows that the significant portion of the seed bunch particles are radially outward and lost during the wakefield generation. The inset of Fig. (a) shows that the curves of the rms radial sizes near the plasma entrance follow the equilibrium radiusσr,eq=0.5σr,0.
bunch. The top of Fig. 3.9 shows the general geometry. The seed electron bunch is placed 4σz,p+away from the proton bunch longitudinal center atkpeξ≈ −638. We plot on the figures below the longitudinal wakefields to illustrate their phase in a−638≲kpeξ ≲−479 (−24 cm<ξ <−18 cm) range, near the proton bunch peak and after 10 m of plasma. In each case, the plot consists of five simulations for five values of the parameter that is varied. The first such figures shows that, as the seed electron bunch energy is lowered, the phase of the wakefields shifts backwards more. This is caused by the stronger evolution of the lower energy bunch along the plasma, as shown above. Over the 5-20 MeV energy range, the phase difference is almostπ. The amplitude of the wakefields also generally decreases with seed bunch energy. The "No seed" case, without electron bunch corresponds to the wakefields seeded
Figure 3.8: (top) Electron bunch energy spectra measured after passing through 10 m plasma in AWAKE Run 2(a) experiment. (bottom) PIC simulation results of energy spectra of electron bunch (left) before and (right) after the beam loss at the plasma exit for three bunch charges (Qe = 150 pC, 250 pC, and 800 pC) with bunch length scanning (σξ,e0/c=1−10 ps). Since the seed electron bunch lengths for the three charges were not measured, we scanned the bunch length in order to find the energy spectra comparable to the experimental results. Before the plasma exit, the long bunches still have the initial energy∼18 MeV, which means that a portion of bunch particles radially escaped from the wakefield region and were not decelerated . After the plasma exit, the radially outward bunch particles are masked by the aperture with the radial size∼5 mm. However, the matched energy peaks of the electron bunches after the plasma were not found at the reasonable bunch lengths (σz/c∼2−3ps). PIC simulation results showed the larger energy loss of the bunch particles than the experimental results.
in the simulation by the small proton bunch density step at its beginning. The middle figure shows that the phase of the wakefields is quite insensitive to the charge of the seed bunch (over this range). The
Figure 3.9: Phases of seeded self-modulation at the longitudinal centroid of long proton bunch by scan- ning seed beam initial energy (the second row), charge (the third row), and length (the fourth row). The reference seed bunch lengthσz,re f/c=2 ps. The seed electron beam is initially centered atkpeξ≈ −4.7.
Plasma density: n0=2×1014cm−3. Figures show the phase of the long proton bunch modulation is mostly affected by the seed bunch energy.
"No seed" case shows that electron bunch seeding does occur though, since its phase is different from those with electron bunch. The bottom figure shows that the phase is quite insensitive to the seed bunch length. Even though the length of seed bunch changes with propagation distance with different initial lengths, the evolution of the phase of the wakefields caused by the evolution of the bunch length is not significant. Here, we note that transition between the seeded self-modulation (SSM) and the self- modulation instability (SMI) was not observed in low energy (5 MeV) and charge (50 pC) seed beam cases, which could be different in the experiment because the noise levels are different (much lower in simulations).