Cerdanyola del Vallès, 10th October 2018. A prompt measurement of the beam energy in the storage ring is inferred from the magnetic field of the bending dipole using the well-known Lorentz Force with a precision of 0.1%. In order to improve the beam energy measurement, a more precise technique called Resonant Spin Depolarization providing a precision of around 0.001% has been implemented and worked at ALBA during the last years.
The spin is a property of elemental particles related with its angular momentum. The electrons spin can only have two orientations, and when the majority of a bunch of electrons has a dominant direction, we say that the beam is polarized. The Resonant Spin Depolarization method first tries to polarize the beam electrons, and then detect its sudden spin depolarization, which depends on the particle’s energy.
The orbiting electrons emit synchrotron radiation as they pass through the dipole magnets. A small fraction of this radiation produces an electron spin flip, but the flip that leads to a smaller magnetic energy state is slightly more favorable. In the case of electrons, the spin pointing against the main dipole field direction is more probable. So even if a "fresh injected" beam in the storage ring starts with a polarization of 50% (meaning, half of the beam electrons spin pointing in one direction, and the other half in the opposite one), for probability reasons after a certain time the beam electrons will slowly start to point towards the more favorable direction. In the equilibrium state, the ALBA electron beam can reach a polarization of around 92.38% (i.e., 92.38% of the electrons spin has the same direction).
The beam polarization has a direct impact on the beam Touschek lifetime since electrons with the same spin direction have a slightly smaller cross-section. This means a smaller probability to hit each other and consequently, a smaller probability of being lost: in short, the beam lifetime is larger for a polarized electron beam. This effect is appreciated in Fig. 1 where the beam lifetime after a fresh injection has been recorded. As the beam circulates freely in the ALBA storage ring for around 1h, the beam electrons start to align in the same direction (against the main dipole field direction), and the beam lifetime increases by about 7%.
Figure 1. The lifetime product increases just after an injection of 100mA in the storage ring as a consequence of the electron beam polarization.
While the beam polarization occurs naturally and in a time scale of ~1h, the beam depolarization can be externally induced by exciting the beam electrons with an electromagnetic field at the appropriate frequency. At this moment, the beam particles will depolarize resonantly in few seconds and consequently, the beam lifetime will suddenly decrease. An example of this process is shown in Fig. 2, which shows the lifetime product as the vertical excitation goes from 7.541 to 7.538 MHz. In this case, the depolarization frequency is found at 7.53957 MHz, when the beam lifetime decreases again by about a 7%.
The depolarization frequency is linearly proportional to the beam energy: fdep = a · γ · frev, where "a" is the anomalous magnetic moment, "frev" is the beam revolution frequency, and γ = E / mc^2 the Lorentz factor (with "m" the eletron mass and "c" the speed of light). Since these parameters are all known with great accuracy, the beam energy is therefore inferred with very good precision. For the case in Fig. 2, the beam energy is E=2.97891 ±0.00001 GeV, where the error bars are given by the margins of the step shown in the plot.
Figure 2. Frequency scan of the electromagnetic kick looking for the depolarization frequency. The equivalent energy is shown in the top horizontal axis.
Can we then say that the ALBA beam energy is 2.97891 GeV? Well… not always. The Accelerator Division has been doing precise energy measurements every run during the last 3 years. Figure 3 shows that the beam energy is on average 2.9789 and has small jumps up to +/- 0.5 MeV peak to peak (that is to say, 0.015%). This is arguably related to the small changes produced in the beam orbit between measurements carried out at different times. Unfortunately, we still have not found an accurate explanation to this phenomenon. Therefore, if one wants to be really precise (or picky?) about the energy of the ALBA electron beam, one should say that “ALBA is a Synchrotron Light Source, whose energy is 2.979 GeV and varies with time within a range of +/-0.5 MeV… ”. Certainly, shorter forms and approximations of this sentence are indeed valid.
Figure 3. Energy measurements at the ALBA Storage Ring since 2015 using the Resonant Spin Depolarization technique.
