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The LHC RF

The LHC RF. OP shutdown lectures 2012 P. Baudrenghien CERN-BE-RF. Many thanks to T. Mastoridis and J. Tuckmantel for their contribution . Content. A bit of theory: Synchrotron Longitudinal Dynamics RF through the LHC cycle Filling Ramping Physics RF malfunctioning Power RF

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The LHC RF

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  1. The LHC RF OP shutdown lectures 2012 P. Baudrenghien CERN-BE-RF Many thanks to T. Mastoridis and J. Tuckmantel for their contribution LHC RF

  2. Content • A bit of theory: Synchrotron Longitudinal Dynamics • RF through the LHC cycle • Filling • Ramping • Physics • RF malfunctioning • Power RF • Debunching incidents • The hardware behind the scene • Annex • References. Further reading. LHC RF

  3. Synchrotron longitudinal dynamics This part will be covered quickly as there is much overlap with Rende’slecture “Longitudinal” LHC RF

  4. A synchrotron is a circular accelerator whose RF varies during acceleration, in phase with the magnetic field, to keep the particles on a centered orbit LHC RF

  5. The synchronous particle • Consider a reference particle that stays on the centered orbit turn after turn. It is called the synchronous particle • The fRF must be locked to the revolution frequency to have coherent effect turn after turn. The ratio h is called the harmonic number LHC RF

  6. In order for the synchronous particle to stay exactly on the centred orbit, the radial component of the magnetic force must compensate the centrifugal force. Let r be the magnet bending radius, and q the particle charge, we have • Using the relations between b, pand gwe get (see annex 1) • With the RF frequency at infinite energy LHC RF

  7. Using the linear relation between the momentum and the dipole field, we get • The above equation is a characteristic of synchrotrons: • It links the RF frequency and the magnetic field • It saturates (asymptotic behavior when the particle approaches the speed of light) • It depends on the particle’s mass over charge ratio E0/q. That ratio will be different for Lead than protons. As ions are less relativistic, the RF frequency swing will be larger than for protons, for the same magnetic ramp • We will use the above results in the section on ramping LHC RF

  8. Synchronous (or stable) phase • Let fs be the phase of the RF in the cavity when the particle crosses. The energy increase per turn is • Now going to time derivative • or, from the relation between momentum and energy • The LHS is defined by the machine momentum ramp. That, in turn, defines the product V.sinfs • In the LHCdp/dt=0 and the stable phase is 180 degrees except during the ramp where it reaches 176.5 degrees Synchrotron above transition: stable phase between 90 and 180 degrees Stable phase during the LHC ramp LHC RF

  9. We have a description for the synchronous particle motion: The magnetic field will keep it exactly centered and the RF will keep it at the exact center of the bucket (in non-accelerating conditions). If all particles were synchronous, the bunch length, momentum spread and emittance would all be zero…To talk about these collective characteristics, we must now consider the motion of particles that are not strictly synchronous LHC RF

  10. Single-particle Longitudinal Dynamics • Let (ps,fs) refer to the Synchronous particle. Consider another particle P with a slightly different (p,f) . Given the small momentum difference P has also a different revolution frequency we have a minus sign because f is the RF phase when P crosses the cavity. This relation is kinematic only.The superscript ~ represents deviations with respect to the synchronous particle while the subscript s refers to the synchronous particle • Dynamics: Crossing the cavity at a different RF phase, the momentum increase is different for P and for the Synchronous particle LHC RF

  11. The revolution frequency error can be related to the momentum error via the slippage factor h • Differentiating the kinematic relation and using the above, we get • With we derive a second-order non-linear equation describing the synchrotron motion. Notice the non-linearity (sine) LHC RF

  12. Small amplitude oscillations: We can linearize the previous equation and we get • This synchrotron equation represents an undamped resonator with resonant frequency Ws called the synchrotron frequency • Given a phase or momentum error as initial conditions, the particle will oscillate endlessly around the stable phase, exchanging longitudinal displacement with momentum offset • The period of the synchrotron frequency is the characteristic time-response of the beam. We will call “adiabatic” the evolutions that are slow with respect to this period • Periodic motion is possible only if h.cos(fs) > 0 • In the LHC the gt is 53. We inject with g above 450. We are above transition from injection on. Acceleration below transition Acceleration above transition LHC RF

  13. After integration, the equation of synchrotron motion becomes • For each value of the constant C we have a different trajectory • For small deviations from the stable phase the trajectories are ~ circular in phase space • For larger deviations the trajectories are deformed, but still closed (stable) • Above some excursion the trajectories are not closed any more and these particles are not controlled by the RF • The limiting closed trajectory is called the separatrix. The enclosed surface in phase space is called bucket, and its area is called bucket area Trajectories in normalized phase space (f, 1/Wsdf/dt) above transition for synchronous phase 180 degrees (top,left), 170 (top, right), 160 (bottom, left) and 150 degrees (bottom, right). The Separatrix is in red. Stable trajectories are shown in blue, unstable motion appears in green. The particles move on the trajectories clockwise. LHC RF

  14. The previous phase space plots are in normalized (f, 1/Ws (df/dt)) units. The trajectories are similar if the horizontal axis is in time, and the vertical axis in Dp or DE (momentum or energy deviation) • The bucket area A is usually expressed in physical Energy.Time unit (eVs) • The function a(fs) is a non-linear function describing the rapid reduction of bucket area with the stable phase. It is equal to 1 for 0 or 180 degrees and drops to 0.3 for 30 or 150 degrees • The particles will occupy an area inside the bucket. We call this area the bunch longitudinal emittance • The RF voltage must be dimensioned to allow for capture and acceleration without loss. The bucket area must always be significantly larger than the bunch emittance. The ratio is called the filling factor. Energy dependent RF parameters Constant LHC RF

  15. A few additional useful formulas • The bucket half height in momentum • and in energy • For the case of a stationary bucket (fs = 0 or p), we get Accelerating bucket Stationary bucket LHC RF

  16. Adiabatic evolution • During the acceleration ramp, the RF voltage and the Energy vary, thereby changing the synchrotron frequency and the trajectories in Energy-Time phase space • The longitudinal evolution is said to be adiabatic if the relative change of synchrotron frequency in one synchrotron period is small (say less than 10%) • For adiabatic evolution, the trajectory in phase space will evolve, but the area encircled by the trajectory remains constant LHC RF

  17. Trajectory of the 2-s bunch edge at start ramp (1.2 ns 4-s length). The area 4psEst = 0.54 eVs Trajectory of the 2-s bunch edge at 3.5 TeV. Same area but halved bunch length (0.6 ns 4-s length). Evolution during an hypothetic adiabatic LHC ramp • Applying the reasoning to the particle at the 2-s edge of the bunch, we get formulas for adiabatic evolution of 4-s bunch length and 2-s momentum spread NO GOOD! That short bunch would be unstable LHC RF

  18. Filling LHC RF

  19. The SPS arrives at 450 GeV/c. 57 Hz difference at 400 MHz Rephasing • The SPS beam, at 450 GeV/c, must first be locked onto the LHC RF • The trace below shows the phase difference between the SPS RF (multiplied by two to bring it at 400 MHz) and the LHC RF • The horizontal axis in SPS turn. Full span (18000) corresponds to 420 ms Step 1: The SPS frequency is trimmed to be exactly half the LHC frequency Step 2: We apply a frequency bump to the SPS RF to align SPS bucket 1 with the LHC injection bucket reference (fc). This step can be repeated once Extraction: is visible as a transient in the trace. (No extraction in this cycle) Step 3: We close the Phase Locked Loop that reduces the phase error to zero LHC RF

  20. Coming improvement: The rephasing hardware in the SPS is not fully PPM yet. An upgrade is ongoing LHC RF

  21. Capture. High intensity protons. • At injection, the RF parameters are defined with respect to the SPS bunch • 1.5 ns bunch length (4st) • 4.5 10-4 momentum spread Dp/p (2sp) • 4p sEstemittance 0.48 eVs (~ 0.5 eVs as quoted by the SPS) • 95 % population within the 6p sEstcontour 0.72 eVs (Gaussian approximation) • The situation is not favourable • The longitudinal emittance cannot be reduced (instabilities in the SPS) • The SPS RF cannot be increased above 7.2 MV, resulting in a 1.5-1.6 ns bunch length, that is large for capture in a 400 MHz bucket (2.5 ns RF period) • In addition the SPS bucket area is much larger than the bunch emittance (3 eVs vs. 0.5 eVs, bucket half height Dp/p=10-3) providing much space for the development of tails before extraction to the LHC • The original LHC RF design included a series of 200 MHz cavities (ACN) to ease capture. These were not installed LHC RF

  22. 95% intensity contour (0.72 eVs area) Contours correspond to steps of 5% in integrated intensity SPS scraping: contour at SPS extraction with same area as at the end of blow-up in the SPS ramp (1.05 eVs) • In 2010, we captured with 3.5 MV. This is closed to the matched voltage (2.5-3 MV) that would induce no bunch shape oscillations at injection. The LHC bucket has • 0.94 eVs bucket area • 6.6 10-4Dp/p bucket half height • Although sufficient, there is not much tolerance to phase error (horizontal bunch vs. bucket displacement) and energy errors (vertical) Losses: 3.2 % if the bunch distribution is Gaussian with infinite tails 1.4 % if the distribution is a Gaussian truncated by the 1.05 eVs contour Analysis by T. Mastoridis LHC RF

  23. Contours correspond to steps of 5% in integrated intensity 95% intensity contour SPS scraping: contour at SPS extraction with same area as at the end of blow-up in the SPS ramp (1.05 eVs) • Capture with 3.5 MV, in presence of 200 ps and 10-4Dp/p injection errors Losses: 5.7 % if the bunch distribution Gaussian with infinite tails 3.2 % if the distribution is a Gaussian truncated by the 1.05 eVs contour Analysis by T. Mastoridis LHC RF

  24. Contours correspond to steps of 5% in integrated intensity 95% intensity contour SPS scraping: contour at SPS extraction with same area as at the end of blow-up in the SPS ramp (1.05 eVs) • In 2011, we increased the capture voltage to 6 MV. The LHC bucket has • 1.23 eVs bucket area • 8.6 10-4 bucket half height Losses: 1.14 % if the bunch distribution is Gaussian with infinite tails 0.02 % if the distribution is a Gaussian truncated by the 1.05 eVs contour Analysis by T. Mastoridis LHC RF

  25. Contours correspond to steps of 5% in integrated intensity 95% intensity contour SPS scraping: contour at SPS extraction with same area as at the end of blow-up in the SPS ramp (1.05 eVs) • Capture with 6 MV, in presence of 200 ps and 10-4Dp/p injection errors Losses: 2.47 % if the bunch distribution is Gaussian with infinite tails 0.6 % if the distribution is a Gaussian truncated by the 1.05 eVs contour Analysis by T. Mastoridis LHC RF

  26. With 6 MV, the capture is strongly mismatched resulting in strong quadrupole oscillations Bunch length is ~ 1.4 ns at injection Reduced to 1.1 ns after 4 seconds Mountain range display of the bunch profile at injection with a mismatched capture voltage (voltage too high). Observe the quadrupole oscillations, resulting in strong modulation of bunch length. For illustration only: The figure is not the LHC (it is the SPS). LHC RF

  27. The quadrupole oscillations are visible on the bunch length measurement on a short timescale (period around 10 ms). After a few seconds, filamentation has taken place and the bunch has re-arranged its distribution to the LHC bucket, resulting in a reduction of the Full Width at Half Max (FWHM) bunch length • In transfer between machines, one generally wishes to avoid these oscillations. In the LHC we will later blow-up the emittance to 2 eVs in the ramp, and that will erase the consequences of the mismatched capture Bunch length is ~ 1.4 ns at injection Reduced to 1.1 ns after 4 seconds LHC RF

  28. The OP crew must make sure that the injection phase error (horizontal offset of the bunch w-r-t- the bucket) and injection frequency error (vertical bunch/bucket offset) are minimized to optimize capture LHC RF

  29. LHC Capture Transients -30 deg in 60 turns -> -15 Hz @ 400 MHz Dp/p ~ 10-4 Phase loop is fast: “jumps” the RF on the beam at injection Synchro loop is slow. No reaction in first 100 turns. Slope gives frequency (energy) error at injection Inj Phase Error 35 deg/45 deg Synchro loop brings RF (and beam) back to Freq Prgm reference Cavity field “jumps” on the beam in ~ 10 turns Phase Loop Error: Beam PU-Cav Sum Synchro Loop Error: VCXO-Freq Prgm -15 deg in 80 turns -> -6 Hz @ 400 MHz LHC RF

  30. Correction of the injection phase is done from a measurement on the first turn • From the observation, we should correct the LSA setting by -35 degrees (B1) and -45 degrees (B2) • The measurement averages over all bunches, that is the ones just injected and the circulating ones (if any). It should be adjusted with the first pilot injection (no other circulating bunch) and checked/re-adjusted with the first batch injection (typically 12b in protons – there will be a small unwanted contribution from the circulating pilot if we do not over inject) • As filling proceeds, more bunches are circulating and the average reflects the injection transient less and less • Adjustment of injection phase has no side-effect on other equipment. Should always be done Inj Phase Error 35 deg/45 deg Phase Loop Error: Beam PU-Cav Sum Synchro Loop Error: VCXO-Freq Prgm LHC RF

  31. If the measured phase error is positive, increase the LSA phase by the measured error (in degrees) NON_MULTIPLEXED Injection Phase Phase A for B1, phase B for B2 • The injection phase is trimmed in LSA LHC RF

  32. The frequency error is related to the slope of the synchro error signal at injection -30 deg in 60 turns -> -15 Hz @ 400 MHz Dp/p ~ 10-4 • During the first ~50 turns after injection, the synchro error shows the phase slippage between the injected bunch(es) and the RF. The corresponding frequency error Df can be deduced from the slope. Assume a phase slip Df (30 degrees) over N (60) turns, the frequency error is 15 Hz at 400 MHz • Caution: changing the injection frequency changes the orbit (after capture) and the SPS extraction momentum. It will require at least one SPS cycle for the rephasing to work -15 deg in 80 turns -> -6 Hz @ 400 MHz Synchro Loop Error: VCXO-Freq Prgm LHC RF

  33. 400.788863 MHz. We measure a -20 degrees phase slip in 100 turns, or -6 Hz. We add 10 Hz • Example: July 27, 2010 400.788873 MHz. We measure a -12 degrees phase slip in 200 turns, or -2 Hz. We add 2 Hz 400.788875 MHz. Good enough. Frequency error below 1 Hz • Note that the effect is always less than expected. This is explained by the change in revolution frequency caused by the change of momentum at SPS extraction, following the change of frequency. Synchro Loop Error: VCXO-Freq Prgm LHC RF

  34. The corresponding momentum error can be computed • With gt=53, we get Dp/p = 10-4 for 15 Hz • The LHC bucket half height is 8E-4 Dp/p (6 MV). A 5 Hz error corresponds to 3.3 10-5Dp/p, that is 4% of the half height. ACCEPTABLE We have a project to automate these adjustments, suggesting trims to the operators…Will be implemented in 2012 LHC RF

  35. The setting is the frequency offset (in Hz) from 400 MHz. If the measured error is positive, decrease the LSA frequency by the measured error (in Hz). Should be between 788855 and 788865 (p-p) Use FREQUENCY_PROGRAM The Hierarchy will update dependent settings. Beam Process dependent The two rings are locked (except p-Pb). Use Beam Control B1 • The injection frequency is trimmed in LSA LHC RF

  36. Caution 1: Ralph vs. Phil… • The radial loop should be off during filling. If enabled, it will correct the RF frequency to center the beam after capture. The injection frequency for the rest of the filling will be different from the one observed in the capture transients • But…it is political issue. Without touching the magnetic field, the injection frequency is the only knob to minimize frequency errors on first turn and center the beam after capture • After filling, and before starting the ramp, the radial loop should be switched on LHC RF

  37. Then click on CONFIGURE INJECTION FIXED DISPAY First select BEAM CONTROL • Caution 2: If the traces are flat at zero it can be that • You have injected a pilot of too low an intensity. The settings are adjusted to deal with 2E11 p/bunch (proton runs). Anything below 1E10 p/bunch is invisible. So ask the SPS for a fatter pilot (or improve injection steering…) • The RF has been playing with the acquisition memory. You must reload the default settings via the RF CONTROL application LHC RF

  38. Coming improvement: In 2012 we will commission a Longitudinal Damper that will damp the phase/energy error of the incoming batch before loss appears. Adjustment of capture will become much more relaxed… LHC RF

  39. Filling is the only phase in the LHC cycle when the OP crew must make routine adjustments to the RF parameters LHC RF

  40. Ramping LHC RF

  41. 400.788860 MHz -> 400.789715 MHz (p in ring 1) 400.784216 MHz -> 400.789639 MHz (Pb in ring 2) Fast BCT p RF p Fast BCT Pb RF Pb LHC RF

  42. During the ramp, the energy is supplied by the RF at a rate that must follow the momentum ramp • In fast cycling machines, this sets the minimum voltage through the ramp as the bucket area decreases quickly with the stable phase • The LHC ramp is very slow. We have captured with 6 MV and collide with 12 MV (for IBS, to be discussed later). We ramp the voltage linearly, but that is not very critical • Given the long ramp, the stable phase remains close to 180 degrees • The maximum energy gain per turn is 500 keV only Stable phase during the LHC ramp Trajectories in (f, df/dt/Ws) phase space for phase 176.5 degrees LHC RF

  43. We ramp the RF voltage linearly from 6 MV to 12 MV (p-p), from 8 MV to 12 MV (Pb-Pb) LHC RF

  44. Longitudinal stability and Longitudinal blow-up LHC RF

  45. Without blow-up, the longitudinal emittance is preserved during the acceleration: The bunch length shrinks and the energy spread increases in the same proportion so that the area encircled by the trajectory in Energy-Time phase space is constant (adiabatic evolution) • The longitudinal blow-up will keep the bunch length constant. It is armed by the sequencer and triggered by the timing. It requires no OP intervention • If it is disabled (in the sequencer), the nominal intensity bunch will become unstable in the ramp May 15th, 2010. First attempt to ramp nominal intensity single bunch. Bunch length during ramp, starting at 1.2 ns. The bunch becomes unstable when the length falls below 700 ps. No blow-up at the time… LHC RF

  46. The culprit for the instability is the 0.06 W inductive impedance of the LHC (pumping slots, shielded bellows, experimental chambers, RF cavities) • It is a broadband impedance: The wakefield vanishes between the passage of successive bunches so that the limit is on the single bunch intensity • Similar instabilities in the transverse plane can be cured by octopolesthat create non-linearities in the betatron motion, resulting in betatron tune spread and so-called Landau damping: The particles do not all resonate at the same frequency anymore • In the longitudinal plane, the non-linearity is built into the synchrotron motion: The force is proportional to the sine of the phase deviation LHC RF

  47. With the non-linearity, the frequency of the synchrotron oscillations decreases with their peak amplitude • Frequency spread can therefore be achieved by controlling the bunch length. The blow-up injects phase noise in the RF cavity to fight the adiabatic bunch shortening during the ramp, and keep length at a set value Ws/Ws0 as a function of the maximum phase deviation in radian. Exact formula (bottom trace, blue) and parabolic approximation. Non-accelerating bucket (fs = 0). • Mathematically, the stability criteria is • Thanks to the blow-up that keeps bunch length t constant, the threshold is independent of the energy. It is proportional to the voltage and the stability therefore improves through the ramp as the voltage is increased from 6 to 12 MV LHC RF

  48. Trajectory of the 2-s bunch edge at 3.5 TeV. Without blowup. UNSTABLE Trajectory of the 2-s bunch edge at 3.5 TeV with blowup keeping the 4-s length at 1.2 ns. The area 4psEst = 2.12 eVs Trajectory of the 2-s bunch edge at start ramp (1.2 ns 4-s length). The area 4psEst = 0.54 eVs Evolution during a real LHC ramp GOOD! The large emittance bunch is stable LHC RF

  49. Practical info for OP • The blow-up is sequencer driven. No OP intervention needed • You should just check the bunch length evolution through the ramp. The length should settle at 1.2 ns Notice the slow bunch lengthening at 3.5 TeV compared to 450 GeV. IBS in physics will be discussed later Fast bunch lengthening at 450 GeV, caused by IBS Last injection Ramp starts. Adiabatic bunch shortening Flat top. Length stabilized at 1.2 ns Blow-up: RF phase noise counteracts the bunch shortening LHC RF

  50. Practical info for OP (2) • You should not use it for pilots. It is not needed (low bunch intensity) and does not work well… (we work on improving it…) • It is used with the ion bunch (2E10 charges/bunch). It is not strictly needed as that bunch intensity is stable but it helps for IBS caused transverse emittance blow-up (see later) • All settings are in LSA,but if it fails while properly armed in the sequencer,…call the RF expert LHC RF

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