Systematic studies of the microbunching instability at very low bunch charges

At KARA, the Karlsruhe Research Accelerator of the Karlsruhe Institute of Technology synchrotron, the so-called short-bunch operation mode allows the reduction of the bunch length down to a few picoseconds. The microbunching instability resulting from the high degree of longitudinal compression leads to fluctuations in the emitted terahertz radiation, referred to as bursting. For extremely compressed bunches at KARA, bursting occurs not only in one but in two different bunch-current ranges that are separated by a stable region. This work presents measurements of the thresholds and bursting frequencies in both regimes. Good agreement is found between the data and numerical solutions of the Vlasov-Fokker-Planck equation.

Figure 1

Spectrogram of the fluctuations of the THz intensity as a function of the decaying bunch current, showing the microbunching instability. It was obtained in a measurement lasting several hours while the bunch current decreased. No short-bunch-length bursting occurs, as the bunch was not compressed strongly enough. The measurement was taken for settings resulting in a shielding of $\mathrm{\Pi }\approx 1.41$ ($f_{\mathrm{s}}=9.4\mathrm{kHz}$, $V_{\mathrm{rf}}=1048\mathrm{kV}$, ${\tau }_d=10.6\mathrm{ms}$).

Figure 2

Snapshot spectrogram of the fluctuations of the THz intensity as a function of the bunch current for a synchrotron frequency of 6.55 kHz ($\mathrm{\Pi }\approx 0.74$, $V_{\mathrm{rf}}=1400\mathrm{kV}$, ${\tau }_d=10.6\mathrm{ms}$). Below the end of the microbunching instability (main bursting threshold) around 0.052 mA, a second unstable region is clearly visible between 0.038 and 0.016 mA. The current bins were chosen such that a high bunch-current resolution in the region of the short-bunch-length bursting was achieved. For this measurement, approximately 115 bunches were filled.

Figure 3

CSR strength vs shielding of thresholds from snapshot measurements at different settings of the machine parameters compared to the linear scaling law given by Eq. (1) (line). The lower bound (orange disks) as well as the upper bound (blue triangles) of the SBB are shown. The main bursting threshold is shown in red (squares) for machine settings where short-bunch-length bursting occurred and in green (diamonds) for settings where it did not occur. The purple stars represent thresholds and bounds which were obtained from a full decay of a single bunch and not from snapshot measurements. The error bars display the one standard deviation uncertainties calculated from the measurement errors.

Figure 4

Simulated spectrogram showing the end of the microbunching instability (main bursting threshold) around $54\mu \mathrm{A}$ as well as the short-bunch-length bursting between 36 and $22\mu \mathrm{A}$. The frequencies are directly below 2 and 4 times the synchrotron frequency, similar to the frequencies observed in the corresponding measurements (see Fig. 2) [21].

Figure 5

CSR strength at the bursting thresholds as a function of the shielding parameter for measurements and VFP solver calculations for different machine settings. The measured area of instability is indicated as a light blue area and confined by the measured thresholds (blue disks, already shown in Fig. 3) with the error bars displaying the standard deviation error of each measurement. The red triangles show the results from the VFP solver calculations at the corresponding machine settings (red line to guide the eye). The gray line indicates the linear scaling law for the main bursting threshold given by Eq. (3).