Self-stabilizing positron acceleration in a plasma column

Plasma accelerators sustain extreme field gradients and potentially enable future compact linear colliders. Although tremendous progress has been achieved in accelerating electron beams in a plasma accelerator, positron acceleration with collider-relevant parameters is challenging. A recently proposed positron acceleration scheme relying on the wake generated by an electron drive beam in a plasma column has been shown to be able to accelerate positron witness beams with low emittance and low energy spread. However, since this scheme relies on cylindrical symmetry, it is possibly prone to transverse instabilities that could lead, ultimately, to beam breakup. In this article, we show that the witness beam itself is subject to various damping mechanisms and, therefore, this positron acceleration scheme is inherently stable toward the misalignment of the drive and witness beams. This enables stable, high-quality plasma-based positron acceleration.

Figure 1

Wakefield generated in a plasma column by an aligned (left column) and misaligned (right column) drive beam. The normalized plasma charge density, the accelerating field, and the focusing field in the $x\text{−}\zeta$-plane are shown for the case with aligned drive and witness beams (a)–(c) and for misaligned drive and witness beams with offsets of $X_{d,0}=X_{w,0}=0.05k_p^{-1}$ (d)–(f). As shown in (f), an offset of the drive beam of $X_{d,0}>0$ results in a wake centroid of $⟨W⟩<0$.

Figure 2

(a) Difference between witness beam centroid $X_w$ and focusing wake centroid $⟨W⟩$ for different initial witness and/or drive beam offsets as a function of the propagation distance. The witness beam centroid quickly converges to the wake centroid within a few damped oscillations, demonstrating the stability of the scheme versus initial offsets. The cases of a misaligned driver (b) and both a misaligned driver and misaligned witness beam (c) are also shown for higher witness energies of 5 and 10 GeV, respectively. Inset in (c): $X_w$ along the propagation axis. Despite an increased damping length, the evolution is still stable, i.e., $X_w$ converges to $⟨W⟩$.

Figure 3

Distribution of betatron wavenumbers $k_{\beta }/k_p$ along the comoving variable $\zeta$. The rms wave number spread per slice ${\sigma }_{k_{\beta }}$ is depicted by the red bars. The head-to-tail wave number spread, defined as the difference between the mean wave number at the head of the bunch (located at $+1{\sigma }_z$) and the tail (located at $-1{\sigma }_z$), is depicted by the black bar. The head-to-tail spread is larger than the average of the intraslice spread.

Figure 4

(a)–(c) Emittance, energy gain, and relative energy spread as a function of the propagation distance. Depending on the offset, emittance growth can be observed, which saturates as soon as the beam is aligned with the wake centroid. Only marginal differences in energy gain and energy spread are observed.

Figure 5

Phase-space of an unperturbed (solid gray line) KV beamlet and of a KV beamlet with an initial offset $X_{w,0}>0$ (solid blue-red-black line). The KV beamlet with an initial offset is not an equilibrium distribution anymore: the particles that are initially on the blue ($C^{+}$) and red ($C^{-}$) arch continue their trajectories on the blue and red dashed lines, respectively. Thus, they are effectively part of KV beamlets with sizes $X_0+X_{w,0}$ (blue) and $X_0-X_{w,0}$ (red), respectively. The particles that are initially on the black arches ($C^0$) fill trajectories in between the red and blue orbits (filamentation).

Figure 6

Damping in a steplike transverse focusing field during propagation time $s$. The numerical solution of Eq. (a25) agrees well with the reduced modeling of an exponential beam and with an exponential decay assuming the damping length $S_{\mathrm{damp}}$. The damping of a Gaussian beam in the reduced model takes slightly longer but the physical scaling was found to be the same.