Steady-State Microbunching in a Storage Ring for Generating Coherent Radiation

Synchrotrons and storage rings deliver radiation across the electromagnetic spectrum at high repetition rates, and free electron lasers produce radiation pulses with high peak brightness. However, at present few light sources can generate both high repetition rates and high brightness outside the optical range. We propose to create steady-state microbunching (SSMB) in a storage ring to produce coherent radiation at a high repetition rate or in continuous wave mode. In this Letter we describe a general mechanism for producing SSMB and give sample parameters for extreme ultraviolet lithography and submillimeter sources. We also describe a similar arrangement to produce two pulses with variable spacing for pump-probe experiments. With technological advances, SSMB could reach the soft x-ray range ($<10\mathrm{nm}$).

Figure 1

An illustration of harmonic SSMB for $H=3$. At top, we show particles in phase space at the modulator. Each turn around the ring, particles slip forward or backward from dispersion, but the distribution is stationary for a periodic modulation. At bottom, at an intermediate point in the ring ($1/H$ the way around), the microbunches are spaced by ${\lambda }_{\mathrm{in}}/H$, i.e., the beam is microbunched with ${\lambda }_{\mathrm{out}}={\lambda }_{\mathrm{in}}/H$.

Figure 2

Example schematic for a two-stage system. A laser cavity and two undulators of length $L_u$ and $1.9L_u$ modulate the electron beam at opposite ends of a storage ring. SSMB from the modulation and dispersion produces coherent light in a radiator. rf modules could replace the laser modulation to produce long wavelengths, and an additional radiator could be placed at the same distance in front of $L_u$.

Figure 3

Phase space for harmonic SSMB at left and frequency beating at right (with $b=10$), with two-stage modulations on top and one-stage modulations below. For harmonic SSMB, two-stage modulations provide a cleaner phase space with shorter stable regions. For frequency beating, the one-stage phase space has stable islands throughout ${\lambda }_{\mathrm{out}}=b{\lambda }_{\mathrm{in}}$, but radiative energy loss removes the side islands.

Figure 4

Simulation of a two-stage manipulation to produce SSMB. After $10\times {10}^6$ revolutions, we find bunches stacked at steady state in energy space (top left). After an additional dispersive section of $R_{56}/15$, we find SSMB at the 15th harmonic (top right). The density profile is shown bottom left, with the Fourier transform bottom right.