Terahertz coherent radiation from steady-state microbunching in storage rings with $X$-band radio-frequency system

The mechanism of steady-state microbunching (SSMB) has been proposed [D. F. Ratner and A. W. Chao, Phys. Rev. Lett. 105, 154801 (2010)] to produce steady-state microbunched beams by using laser modulations in a storage ring for generating coherent radiation with high repetition rate at wavelengths from the submillimeter to extreme ultraviolet range. In the present paper, we analyze the dynamics of the SSMB system with a Hamiltonian and Jacobi matrix approach and identify the original proposal of SSMB as a mechanism with period-1 fixed point in phase space. We then propose an alternative SSMB mechanism with period-2 fixed point, which is able to produce microbunched beams with shorter bunch length and, hence, higher harmonic. Taking the SPEAR3 storage ring as an example, we illustrate the application of the period-2 SSMB to generate terahertz (THz) steady-state coherent radiation in a storage ring using an $X$-band radio-frequency (rf) system instead of a more technically demanding laser system. Issues covered include choice of rf parameters, system errors, beam lifetime, collective effects, and radiation power evaluation. Compared to the more traditional low-momentum-compaction operation mode, the proposed SSMB scheme potentially promises higher beam current, larger bunching factor, and hence brightness increase of at least 1 order of magnitude.

Figure 1

Period-1 SSMB with $H=9$, left figures show evenly distributed microbunches within one modulation wavelength, and right figures show three microbunches with separation of ${\lambda }_{\mathrm{mod}}/H$. Both cases generate coherent radiation of wavelength ${\lambda }_r={\lambda }_{\mathrm{mod}}/H$.

Figure 2

One-stage modulation SSMB system. The green box indicates the modulation source. OP1 and OP2 indicate the observation points at the entrance and the opposite of the modulation source, respectively.

Figure 3

The motions described by Eq. (2.3) in phase space with $K=0.5,1,2,2.5,3,3.5,4,5,5.5$, and 6.2, and with observation point at the entrance of the modulation (OP1 in Fig. 2).

Figure 4

The motions described by Eq. (2.3) in phase space with $K=3.5$ and 5, and with observation point on the opposite of the modulation (OP2 in Fig. 2).

Figure 5

Variation of $v_s$ and ${\theta }_0$ (or ${\theta }_1$) with respect to modulation amplitude $K$.

Figure 6

Shrinkage of the stable integer resonance island due to resonance overlapping between the adjacent integer and half integer resonance islands. The green dashed lines and red dotted lines indicate the separatrices of the half integer and integer resonance islands in a single resonance approach, respectively. The red solid line indicates the boundary of the integer resonance island stable area.

Figure 7

SSMB in the SPEAR3 storage ring after ${10}^6$ turns’ tracking while including the existing 476.3 MHz rf cavity, radiation damping, and quantum excitation, with the beam distribution at the $X$-band rf cavity (top left), and the beam distribution (top right), density profile (bottom left) and Fourier component $b_f^2$ (bottom right) at the radiator, with $b_f$ the bunching factor.

Figure 8

Normalized surviving particles in the cases of with $X$-band rf and existing 476.3 MHz rf system (red solid), with only $X$-band rf (green dashed) and with only existing 476.3 MHz rf (blue dotted). The curves in the first 5000 turns are expanded on the image inset.

Figure 9

Model for one discontinuity on the perfectly conducting vacuum chamber (left) and wake potential calculated with ECHO code (right), $\Delta z=1\mathrm{mm}$, $\Delta r=5\mathrm{mm}$, and pipe radius $b\approx 17\mathrm{mm}$.

Figure 10

Square of the bunching factor $b_f^2$ at the radiator, with $X$-band rf cavity for both injection and modulation.