Quasi-phase-matched acceleration of electrons in a corrugated plasma channel

A laser pulse propagating in a corrugated plasma channel is composed of spatial harmonics whose phase velocities can be subluminal. The phase velocity of a spatial harmonic can be matched to the speed of a relativistic electron resulting in direct acceleration by the guided laser field in a plasma waveguide and linear energy gain over the interaction length. Here we examine the fully self-consistent interaction of the laser pulse and electron beam using particle-in-cell (PIC) simulations. For low electron beam densities, we find that the ponderomotive force of the laser pulse pushes plasma channel electrons towards the propagation axis, which deflects the beam electrons. When the beam density is high, the space charge force of the beam drives the channel electrons off axis, providing collimation of the beam. In addition, we consider a ramped density profile for lowering the threshold energy for trapping in a subluminal spatial harmonic. By using a density ramp, the trapping energy for a normalized vector potential of $a_0=0.1$ is reduced from a relativistic factor ${\gamma }_0=170$ to ${\gamma }_0=20$.

Figure 1

(a) Fourier transform of the longitudinal electric field ($E_z$) in time ($t$) and space ($z$) at a laser wavelength ${\lambda }_L=800\mathrm{nm}$, normalized vector potential $a_0=0.01$, modulation period $d=20\mu \mathrm{m}$, and modulation amplitude $\Gamma =0.9$. The diagonal lines represent the spatial harmonics. The fundamental spatial harmonic is the central diagonal line. The diagonals to the left and right of the fundamental are $\pm 1\mathrm{st}$ spatial harmonics, respectively. (b) Phase of the on-axis longitudinal electric field at a fixed $\xi$ point. The period of the phase oscillation corresponds to the density modulation period.

Figure 2

On-axis longitudinal electric field (blue) and time integral of the on-axis longitudinal electric field (red) as a function of acceleration time for a fixed $\xi$ point. In (a) the modulation period matches the dephasing length, $L_d=356\mu \mathrm{m}$, while in (b) the modulation period is $d=350\mu \mathrm{m}$. (c) Self-consistent energy gain as a function of acceleration for three different modulation periods: $350\mu \mathrm{m}$, $353\mu \mathrm{m}$, and $356\mu \mathrm{m}$.

Figure 3

Energy gain as a function of acceleration time for different initial electron energies. Here the modulation period is equal to the dephasing length. (a) ${\gamma }_0=50$, 100, and 200 for $a_0=0.1$ (b) ${\gamma }_0=30$, 50, 100, and 200 for $a_0=0.25$.

Figure 4

Transverse position-longitudinal momentum phase space of the beam electrons after 9 mm acceleration for a beam density $n_b=3.5\times {10}^{16}{\mathrm{cm}}^{-3}$, (a) $a_0=0.25$ and ${\gamma }_0=100$, and (b) $a_0=0.1$ and ${\gamma }_0=200$.

Figure 5

Transverse position-longitudinal momentum phase space of the beam electrons after 9 mm acceleration for $a_0=0.1$ and${\gamma }_0=200$ (a) low beam density, $n_b=7\times {10}^{10}{\mathrm{cm}}^{-3}$, and (b) high beam density, $n_b=3.5\times {10}^{16}{\mathrm{cm}}^{-3}$.

Figure 6

On-axis charge density after 4.2 ps of acceleration with $a_0=0.1$. (b) Vertically magnified image of (a). The blue line is the on-axis charge density for high beam density, $n_b=3.5\times {10}^{16}{\mathrm{cm}}^{-3}$, and the red line is for low beam density, $n_b=7\times {10}^{10}{\mathrm{cm}}^{-3}$. The black line in (b) indicates the initial beam electron profile.

Figure 7

Energy spectra of beam electrons for different initial energies: ${\gamma }_0=100$, 200, and 500 after 9 mm of acceleration, are the red line, black line, and blue line, respectively, while the green line is ${\gamma }_0=200$ after 18 mm acceleration. In all cases the normalized vector potential was $a_0=0.1$.

Figure 8

Transverse position-longitudinal momentum phase space of the beam electrons after 18 mm of acceleration for a beam density, $n_b=3.5\times {10}^{16}{\mathrm{cm}}^{-3}$, normalized vector potential $a_0=0.1$ and initial energy ${\gamma }_0=200$.

Figure 9

Energy spectrum as a function of time for $n_b=3.5\times {10}^{16}{\mathrm{cm}}^{-3}$, $a_0=0.1$, and ${\gamma }_0=200$. For clarity the spectrum is normalized to its maximum at each time.

Figure 10

(a) On-axis electron density for a plasma waveguide with a density ramp. The ramp allows trapping of lower energy electrons in this case ${\gamma }_0=20$ for a normalized vector potential of $a_0=0.1$. (b) Energy gain of ${\gamma }_0=20$ electrons with (blue) and without (red) the density ramp pictured in (a). The energy gain of ${\gamma }_0=10$ electrons is the black line in (b).