Nonlinear Thomson scattering with ponderomotive control

In nonlinear Thomson scattering, a relativistic electron reradiates the photons of a laser pulse, converting optical light to x rays or beyond. While this extreme frequency conversion offers a promising source for probing high-energy-density materials and driving uncharted regimes of nonlinear quantum electrodynamics, conventional nonlinear Thomson scattering has inherent trade-offs in its scaling with laser intensity. Here we discover that the ponderomotive control afforded by spatiotemporal pulse shaping enables regimes of nonlinear Thomson scattering that substantially enhance the scaling of the radiated power, emission angle, and frequency with laser intensity. By appropriately setting the velocity of the intensity peak, a spatiotemporally shaped pulse can increase the power radiated by orders of magnitude. The enhanced scaling with laser intensity allows for operation at significantly lower electron energies or intensities.

Figure 1

(a) A conventional NLTS configuration in which the intensity peak and phase fronts of a laser pulse travel in the opposite direction as the electron. At the rising edge of the intensity peak, the ponderomotive force decelerates the electron, redshifting the emitted frequencies and widening their emission angle (purple cone). (b) NLTS with ponderomotive control aligns the velocities of the intensity peak and the electron. Here the ponderomotive force increases or maintains the electron velocity, allowing for higher-frequency emission into a smaller angle. The electron trajectory in its average rest frame (figure eight) is depicted to the left of each case.

Figure 2

Cycle-averaged radiated power as a function of the ponderomotive velocity ${\beta }_I$ and the vector potential $a$ normalized to power radiated in conventional NLTS $\langle P_C\rangle$. Here ${\gamma }_0=5$, and for the purpose of calculating $\langle P_C\rangle$, ${\beta }_I=-1$. The dashed lines indicate the matched and drift-free conditions. Within the gray region, the ponderomotive force accelerates the electron to a velocity greater than ${\beta }_I$, and the electron outruns the intensity peak [49]. The insets depict the cycle-averaged electron trajectories (black lines) relative to the motion of the intensity peak (contours).

Figure 3

Left: Power radiated per steradian as a function of the angle with respect to the initial electron velocity $\theta$ and the angle coplanar with the laser polarization $\varphi$ for ${\gamma }_0=5$ and $a_0=3$. Right: The projection of the radiated power on a plane located a distance $r_0$ from the source. Each plot has been normalized to its maximum value: 0.016, 0.50, 204 $\mathrm{MeV}{\mathrm{sr}}^{-1}{\mathrm{ps}}^{-1}$ for conventional, drift-free, and matched NLTS, respectively.

Figure 4

Spectrum of emitted radiation from a collection of electrons with ${\gamma }_0=5$ and $a_0=3$. Left: No energy spread; right: $\mathrm{\Delta }\gamma /{\gamma }_0=5\%$ all in the longitudinal momentum. The quantity $U_r$ has units of energy, and each plot is normalized to its maximum value. For matched NLTS, the horizontal axis is scaled to $4{\gamma }_I^2{\omega }_0$, not $4{\gamma }_0^2{\omega }_0$, and therefore extends to much higher frequencies.

Figure 5

Example of a practical flying focus design for drift-free NLTS. (a)–(c) Evolution of the propagation invariant intensity profile across the interaction region $L$. The flying focus pulse travels from right to left, while its intensity peak travels from left to right. The intensity peak counterpropagates with respect to the phase fronts and maintains a stationary profile in the frame $\xi =z-v_{I}t$. (d) The bowl-shaped transverse intensity profile formed by the orthogonally polarized Laguerre-Gaussian modes. (e) The on-axis ($r=0$) temporal profile of the intensity peak. (f) On-axis intensity as a function of $z$ and $\eta$. The dashed line illustrates the slope of the expected trajectory. Note that the abscissa is $\eta /c=t+z/c$ and that a laboratory frame trajectory $z=v_{I}t$ is equivalent to $z=v_g{v}_I\eta /c(v_g-v_I)$.