macroparticle model predictions Frank Zimmermann UFO study meeting 23 June 2011 with contributions from Massimo Giovannozzi, Athanasia Xagkoni (NTU Athens), Zhao Yang (EPFL),

References: C. Sagan, “Mass and Charge Measurements of Trapped Dust in the CESR Storage Ring,'‘ NIM A330 371 (1993). F. Zimmermann, ``Trapped Dust in HERA and DORIS,'' DESY HERA 93-08 (1993) F. Zimmermann, ``Trapped Dust in HERA and Prospects for PEP-II,'' PEP-II AP Note No.: 8-94 (1994) F. Zimmermann, J.T. Seeman, M. Zolotorev, W. Stoeffl, “Trapped Macroparticles in Electron Storage Rings,'' IEEE PAC'95 Dallas (1995). V. Baglin, “Can we optimise the cleanup process further?,’’ Proc. LHC Performance Workshop Chamonix 2010, 25-29 January 2010. F. Caspers, private communication (2008). Wolfram Research, Mathematica 7. M. Brugger, F. Cerutti, A. Ferrari, V. Vlachoudis, “FLUKA Estimations Concerning Obstacles in the LHC Magnets,'‘ CERN-AB-Note-2007-018 ATB (2007). The FLUKA Team, “Summary of FLUKA Estimations for Obstacles in the LHC Magnets,” private communication by G. Arduini, 24.02.2009 M. Giovannozzi, F. Zimmermann, A. Xagkoni, “Interaction of Macro-Particles with LHC p Beam,” IPAC’10 Kyoto Z. Yang, “Simulation of the interaction of macro-particles with the LHC proton beam,” EPFL TP VI Reports, 8 January and 4 June 2011

Macro-Particle Dynamics equations of motion: electric field of beam electric image force gravity

Beam Loss Rate beam loss rate for a macro-particle with mass loss rate corresponding to quench limit for SC magnets simulated by FLUKA ~ 1-2x107/s at top energy, and 15x more at injection beam loss rate for a macro-particle with mass A = 1013 as a function of vertical distance y from the beam center, at x = 0.

From (5), we can define a charging cross section scharging = preAatomR/|Q|, in analogy to the nuclear interaction cross section sint of (7). The initial charging cross section is of order Gbarn or about 9 orders of magnitude larger than the nuclear cross section, which explains why the macro-particles rapidly charge in the periphery of the beam without causing any serious beam loss.

charging rate dQ/dt for a macro-particle with mass A = 1013 and initial charge Q = −1 as a function of vertical distance y from the beam center, at x = 0.

Parameters

total vertical acceleration at the upper (red) or lower (dark blue) chamber wall due to the beam force, image force and gravity as a function of the mass of a singly charged [Q=−1] dust particle, for the nominal LHC beam current (bold) and for ten times this current (thin).

The LHC beam, even at nominal current, is not able to pick up (round) charged dust particles from the bottom of a metallic vacuum chamber. However, sufficiently heavy dust particles could fall into the beam from above, or they could start to move towards the beam as a result of mechanical vibration or of eddy currents induced while the magnetic field is ramped. We next study the motion and charge state of such maroparticles as well as the associated beam loss.

Vertical and horizontal position of macro-particles with three different masses, as indicated, and initial charge Q = −1, launched at x = +1 mm above the beam, as a function of time (top); the same trajectories in the x−y plane, and associated charge evolutions (bottom).

“dust” particles falling into the LHC beam trajectory in x-y space round Al object; A=1014 → R~2.5 mm, A=1016 → R~11 mm design beam current, Ntot=3.2x1014 present beam current, Ntot=2.3x1012 particles heavier than A=1016 proton masses continue to fall down even particles of mass A=1018 proton masses are charging up to be repelled upwards resulting loss rates (compare with quench threshold ~a few 107 p/s) longer and higher losses for present beam current! total loss duration ~a few ms design beam current

“dust” particles falling into the LHC beam round Al object; A=1014 → R~2.5 mm, A=1016 → R~11 mm medium beam current, Ntot=4.6x1013, 3.5 TeV medium beam current, Ntot=4.6x1013, 0.45 TeV

quench threshold nominal beam current, Ntot=3.2x1014, 7 TeV quench threshold high beam current, Ntot=7.0x1014, 7 TeV

indications from the simulations: for large enough particle mass (A≥1016) simulated peak loss rate above quench threshold simulated loss duration of order 1 ms loss duration gets shorter at higher beam energy loss duration gets shorter at higher beam current losses are below quench limit at high current at 7 TeV

“second crossing” & magnetic field Z. Yang A=1012 A=1014 B =0 T, 8.33 T and 80 T (Blue, red and green)

log(loss rate) versus time “second crossing” & magnetic field log(loss rate) versus time Z. Yang A=1012 A=1014 B =0 T, 8.33 T and 80 T (Blue, red and green)

particle trajectory of A=1012, B=8.33 T Np=1.15*1011*2808 0.060703 s 0.064946 s 0.13530 s 0.14275 s

loss duration & total loss for Al particle 1.15*1011* 400 1600 2808 1012 0.00097 0.00055 0.00036 1014 0.00199 0.00155 0.00139 1016 0.00295 0.00242 0.00224 Loss duration for varying values of mass and Np in units of second (B=8.33 T). 1.15*1011* 400 1600 2808 1012 0.01817 0.00185 0.00064 1014 24.208 2.82042 1.13349 1016 29039.1 3894.48 1629.73 Total # of lost protons for varying values of mass and Np (B=8.33 T).

loss duration & total loss for Cu particle 1.15*1011*400 1.15*1011*1600 1.15*1011*2808 1012 0.00094 0.00051 0.00030 1014 0.00198 0.00154 0.00138 1016 0.00297 0.00243 0.00224 The loss duration is almost independent of the material of the macro-particle. The total number of lost protons for a copper particle is smaller than that for an aluminum particle. Loss duration [in s] for varying mass A and total proton intensity Np (B=8.33 T). 1.15*1011*400 1.15*1011*1600 1.15*1011*2808 1012 0.01424 0.00141 0.00045 1014 18.7440 2.21784 0.89563 1016 22099.9 3030.90 1276.52 Total # of lost protons for varying value of mass A and total proton intensity Np (B=8.33 T).

Findings of Yao Zhang: Time separation between 1st and 2nd crossing is consistent with some beam observations of multiple successive events. However, losses at 2nd crossing always much lower than for 1st crossing, which is different from observations. Effect of magnetic force on the macro-particle motion is weak and can be neglected, even for a field of 8.33 T. The loss duration and the number of lost protons decrease with higher total beam intensity; the losses roughly in inverse proportion. Increasing the beam size by a factor of 5 reduces the total # of lost protons by about a factor of 3. This might be part of the explanation why events have not been important at LHC injection. [This dependence might not be monotonic; why else would 7 TeV be much better?]