Proof-of-Principle Direct Measurement of Landau Damping Strength at the Large Hadron Collider with an Antidamper

Landau damping is an essential mechanism for ensuring collective beam stability in particle accelerators. Precise knowledge of the strength of Landau damping is key to making accurate predictions on beam stability for state-of-the-art high-energy colliders. In this Letter, we demonstrate an experimental procedure that would allow quantifying the strength of Landau damping and the limits of beam stability using an active transverse feedback as a controllable source of beam coupling impedance. In a proof-of-principle test performed at the Large Hadron Collider, stability diagrams for a range of Landau octupole strengths have been measured. In the future, the procedure could become an accurate way of measuring stability diagrams throughout the machine cycle.

Figure 1

Schematic of the LHC transverse feedback system (a) and its impact on a collective mode within the LHC stability diagram (b) for a 450 GeV Gaussian beam with $4\times {10}^{-5}\mathrm{rms}$ tune spread generated by the LHC octupole system.

Figure 2

The instability growth rate scales linearly with the damper gain, allowing one to calibrate the feedback strength. The nonzero gain required to start an instability is caused by natural nonlinearities of the machine. Overall, experimental data (diamonds) are in good agreement with numerical simulations with SC taken into account (filled circles). For comparison, the simulation data for the no-SC case is also shown (empty circles). Dashed and dash-dotted lines represent linear fits of the data above the instability threshold.

Figure 3

Stability region observed in particle tracking for the assumed natural nonlinearities in the LHC ($E=450\mathrm{GeV}$, rms tune spread ${10}^{-5}$) including space charge: The color of the dots depicts the maximum beam excursion. The blue squares and line show the measured limit of stability; the solid black line shows a SD prediction for a Gaussian beam.

Figure 4

The measured height of the stability diagrams at 450 GeV scales linearly with the octupole current with the negative octupole polarity providing around 30% larger coverage of negative mode frequency shifts, which are relevant for coherent beam stability in the LHC. Solid lines, $Q^{\prime }=14$; dashed line, $Q^{\prime }=3$.