Cavity voltage phase modulation to reduce the high-luminosity Large Hadron Collider rf power requirements

The Large Hadron Collider (LHC) radio frequency (rf) and low-level rf (LLRF) systems are currently configured for constant rf voltage to minimize transient beam loading effects. The present scheme cannot be extended beyond nominal LHC beam current (0.55 A dc) and cannot be sustained for the high-luminosity (HL-LHC) beam current (1.1 A dc), since the demanded power would exceed the peak klystron power. A new scheme has therefore been proposed: for beam currents above nominal (and possibly earlier), the voltage reference will reproduce the modulation driven by the beam (transient beam loading), but the strong rf feedback and one-turn delay feedback will still be active for loop and beam stability. To achieve this, the voltage reference will be adapted for each bunch. This paper includes a theoretical derivation of the optimal cavity modulation, introduces the implemented algorithm, summarizes simulation runs that tested the algorithm performance, and presents results from a short LHC physics fill with the proposed implementation.

Figure 1

Cavity voltage with 2244 bunches, $1.2\times {10}^{11}$ protons/bunch, 25 ns spacing, 6.5 TeV.

Figure 2

Klystron power with 2244 bunches, $1.2\times {10}^{11}$ protons/bunch, 25 ns spacing, 6.5 TeV.

Figure 3

Cavity voltage with 654 bunches, 50 ns spacing, 450 GeV.

Figure 4

Klystron power with 654 bunches, 50 ns spacing, 450 GeV.

Figure 5

Calculated cavity phase modulation for HL-LHC filling pattern and beam parameters. 2748 bunches, $2.2\times {10}^{11}$ protons per bunch, 7 TeV, 16 MV rf voltage, $4.4\mu \mathrm{s}$ long abort gap. The phase is reported in ps with respect to the 400 MHz rf clock.

Figure 6

Simulation of the algorithm with half-full ring. Optimal phase modulation.

Figure 7

Peak power reduction as the algorithm optimizes the phase modulation.

Figure 8

Average klystron forward power. 204 bunches, beam 1.

Figure 9

Average klystron forward power. 1164 bunches, beam 2.

Figure 10

Average klystron forward power. 204 bunches, beam 1.

Figure 11

Average klystron forward power. 1164 bunches, beam 2.

Figure 12

Klystron forward power per turn. 204 bunches, beam 1.

Figure 13

Klystron forward power per turn. 1164 bunches, beam 2.

Figure 14

Beam 2 abort gap population and klystron 1B2 forward power. The yellow line indicates when the algorithm is on/off. The blue line shows the abort gap population and the red line the klystron power.

Figure 15

Beam 2 bunch length and klystron 1B2 forward power. The yellow line indicates when the algorithm is on/off. The blue line shows the bunch length and the red line the klystron power.

Figure 16

Phase modulation for all cavities. 204 bunches, beam 1.

Figure 17

Phase modulation for all cavities. 1164 bunches, beam 2.

Figure 18

Average klystron forward power. 2220 bunches, beam 1.

Figure 19

Average klystron forward power. 2220 bunches, beam 2.

Figure 20

ATLAS and CMS instantaneous luminosity.

Figure 21

ALICE and LHCb instantaneous luminosity. ALICE was switched off during the algorithm deployment (15:50–16:20).

Figure 22

Collision point time shift for the ATLAS detector.

Figure 23

Collision point longitudinal shift for ATLAS. Data and theoretical estimation.

Figure 24

Collision point time shift for the ALICE detector.

Figure 25

Collision point longitudinal shift for ALICE. Data and theoretical estimation.