BEAM STABILITY REQUIREMENTS

Specific requirements for beam stability for synchrotron radiation experiments vary considerably, depending on the sensitivity of photon-sample interaction and experimental setup to beam parameter fluctuations. This sensitivity is a function of the beam line component configuration, detector and measurement method, sample characteristics and photon beam properties. Nevertheless generic stability specifications can be estimated from stability criteria for measurement parameters common to a majority of experiments (see Table 1).

Table 1: Typical stability requirements for selected measurement parameters common to a majority of experiments (adapted from [1])

Measurement parameter	Stability requirement
Intensity variation $\Delta I/I$	$<$0.1 % of normalized $I$
Position and angle accuracy	$<$1 % of beam $\sigma$ and $\sigma'$
Energy resolution $\Delta E/E$	$<$0.01 %
Timing jitter	$<$10 % of critical $t$ scale
Data acquisition rate	$\approx$10$^{-3}$-10$^{5}$ Hz
Stability period	10$^{-2(3)}$-10$^{5}$ sec

As a result the electron beam motion has to be stabilized in its 6-dimensional phase space such that the above stability requirements for the photon beam parameters are met. Experiment sensitivity to electron beam instability can be characterized in phase space where the photon beam is represented by a spectral flux density distribution (flux per unit of photon frequency bandwidth). The beam line and experimental sample are represented as a system of apertures forming an acceptance volume within this space [2]. If the measurement signal is defined as the total flux within the acceptance volume, then measurement noise is caused by fluctuations of the beam density distribution in this volume. Figure 1 depicts the displacement of the photon beam with emittance $\epsilon_0$ by centroid motion resulting in $\epsilon_{\rm cm}$ projected to the vertical phase space at an aperture located at a certain distance from the source point.

Figure 1: Emittance growth caused by centroid motion [1].

The effect of beam instability on flux transmitted through a phase space aperture depends on the time scale of the fluctuation relative to the detector sampling and data integration times. For fluctuation frequencies much larger than sampling and integration rates, the beam distribution is effectively "smeared out" in phase space, increasing its area but not introducing any new noise. The effective beam emittance is thus given by $\epsilon_{\rm eff}=\epsilon_{0}+\epsilon_{\rm cm}$. Centroid motion of $\approx$30 % of the beam size $\sigma$ and divergence $\sigma'$ causes only a 10 % increase in $\epsilon_{\rm eff}$ ignoring possible aliasing effects. Fluctuation frequencies in the range of or less than data integration rates are more harmful. In this case, the beam can move relative to the aperture on a sample-by-sample or scan-by-scan basis, introducing new measurement noise and $\epsilon_{\rm eff}$ is represented by the envelope of emittance ellipse displacements $\epsilon_{\rm eff}\approx\epsilon_{0}+2\sqrt{\epsilon_{0}\epsilon_{\rm cm}}+\epsilon_{\rm cm}$ [1] as shown in Figure 1. Centroid motion of $\approx$5 % causes a 10 % increase in $\epsilon_{\rm eff}$. Beam motion occurring over periods much longer than measurement times may have no effect on data quality since the beam is essentially stable. This is especially true if the experiment can be realigned or recalibrated between measurements. The most demanding beam stability requirements arise for a fluctuation frequency interval approximately bounded at the high end by data sampling rates and at the low end by data integration and sample scan times, so that beam noise is not averaged out. Noise spikes or infrequent jumps that do not contribute significantly to the RMS noise floor can be harmful for experiments, particularly those employing difference measurements. Since most 3rd generation light sources feature low beta ($\approx$1 m) straights in order to allow for low gap ($<$10 mm) insertion devices (IDs), and operate at very small emittance coupling ($<$1 %) values with horizontal design emittances of just a few nm$\cdot$rad, the requirements compiled in Table 1 lead to sub-micron tolerances for the vertical positional and angular stability of the electron beam at the ID source points ( $\sigma_{\rm cm}$ $<$1$\mu$m, $\sigma_{\rm cm}'$ $<$1$\mu$rad) over a large frequency range 10$^{-5}$-10$^{2(3)}$ Hz.