2. Crab Cavities Failure Mode: Machine Protection Matrix Goals: Identify the most critical failure cases Design mitigation methods Make machine protection experiments on the SPS ring Method: Determine realistic hardware failure mode Model the effect on the field Derive the effect of each failure mode on the beam Track the particles along the machine during a failure scenario with nominal HL-LHC beam parameters and collimator settings Obtain time-dependent loss maps Check the effect of combined failures Estimate (and measure) occurrence frequency Propose experiments to verify effects of failures and mitigations in SPS or LHC

3. Failure modeTime constants (µs) Maximum amplitude (degrees, MV, Hz, …) Beam kick (mrad) Bunch angle and rotation (θ­ yz, θ­ yz ’) … Phase jump Voltage drop Frequency shift (phase slip) Quench Loss-induced multiple Quench Phase feedback failure Klystron failure Coupler failure LLRF failure... … Failure modeTime constants (µs) Maximum amplitude (degrees, MV, Hz, …) Beam kick (mrad) Bunch angle and rotation (θ­ yz, θ­ yz ’) … Phase jump Voltage drop Frequency shift (phase slip) Quench Loss-induced multiple Quench Phase feedback failure Klystron failure Coupler failure LLRF failure... … -Determine realistic hardware failure mode -Model the effect on the field and then the beam (some can be the sum of others)

4. Failure mode…After 1 turn: Beam displ. (σ) Head-Tail oscillations (θ­ yz ) Particles lost (%) …After 3 turns: … … Phase jump Voltage drop Frequency shift (phase slip) Quench Loss-induced multiple Quench Phase feedback failure Klystron failure Coupler failure LLRF failure... … Track the particles along the machine during a failure scenario Obtain time-dependent loss maps Failure mode…After 1 turn: Beam displ. (σ) Head-Tail oscillations (θ­ yz ) Particles lost (%) …After 3 turns: … … Phase jump Voltage drop Frequency shift (phase slip) Quench Loss-induced multiple Quench Phase feedback failure Klystron failure Coupler failure LLRF failure... …

5. Failure mode…After 3 turns: Beam displ. (σ) Head-Tail oscillations (θ­ yz ) Particles lost (%) …After 10 turns: … … Phase jump Voltage drop Frequency shift (phase slip) Quench Loss-induced multiple Quench Phase feedback failure Klystron failure Coupler failure LLRF failure... … Track the particles along the machine during a failure scenario Obtain time-dependent loss maps

6. Failure mode…After 10 turns: … Combined failure effect Est. frequency (cavity -1 s -1 ) Meas. frequency (cavity -1 s -1 ) Phase jump Voltage drop Frequency shift (phase slip) Quench Loss-induced multiple Quench Phase feedback failure Klystron failure Coupler failure LLRF failure... … Check the effect of combined failures Estimate (and measure) occurrence frequency Failure mode…After 10 turns: … Combined failure effect Est. frequency (cavity -1 s -1 ) Meas. frequency (cavity -1 s -1 ) Phase jump Voltage drop Frequency shift (phase slip) Quench Loss-induced multiple Quench Phase feedback failure Klystron failure Coupler failure LLRF failure... …