Probing atoms by periodically modulated electron bunches

Abstract

When passing through an undulator in a Free Electron Laser, dense bunches of relativistic electrons split into micro-bunches, attaining a periodic space-time structure. We show that the field of such periodically modulated bunches is tremendously influenced by coherence effects, resulting in a novel type of beam-atom interaction. Our results indicate that employing such bunches (alone or in combinations with the radiation they emit) offers a multitude of new opportunities for exploring atomic dynamics on a femtosecond time scale.

Figures (4)

• Figure 1: Energy spectrum of electrons emitted in ionization of H(1s) atoms by a bunch of $1.35$ GeV electrons passed through an undulator. $N_t = 1.6 \times 10^{9}$, $L = 30$$\mu$m, $a_0 = 50$$\mu$m, $\lambda_U = 3.5$ cm, $\mathcal{ K } = 3.8$ and $l_0 = 0.005$$\mu$m. Dotted curve: all bunch electrons act incoherently (multipled by $10$). Dashed curve: coherence within a micro-bunch is taken into account but the micro-bunches act incoherently. Solid curve: coherences within a single micro-bunch and of different micro-bunches are taken into account. The cross sections are given per bunch.
• Figure 2: The energy spectrum of equivalent photons carried by $1.35$ GeV (solid curve) and $14$ GeV (dash curve) electron bunches (for each bunch only the first two high-frequency lines are shown). The spectrum of equivalent photons, carried by the corresponding unmodulated bunches, are shown by squares. For more explanations see text.
• Figure 3: The number of CE photons in the line centered at $\hbar \omega_1 \approx 60$ eV as a function of the bunch radius $a_0$. The other parameters are $N_t = 1.6 \times 10^9$, $1.35$ GeV, $L = 30$$\mu$m, $\lambda_U = 3.5$ cm, $\mathcal{ K } = 3.8$ and $l_0 = 0.005$$\mu$m.
• Figure 4: Ionization of H(1s) by $14$ GeV electron bunch as a function of the bunch radius. $N_t = 1.6 \times 10^9$, $L = 10$$\mu$m, $\lambda_U = 6.8$ cm, $\mathcal{ K } = 7.2$. Solid curve: tunneling ionization. Dashed curve: ionization by $N_t$ individual electrons. Dotted curve: ionization via absorption of a CE photon from the first high-frequency line.