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

2. References:
C. Sagan, “Mass and Charge Measurements of Trapped Dust in the CESR Storage Ring,'‘ NIM A (1993).
F. Zimmermann, ``Trapped Dust in HERA and DORIS,'' DESY HERA (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, 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 ATB (2007).
The FLUKA Team, “Summary of FLUKA Estimations for Obstacles in the LHC Magnets,” private communication by G. Arduini,
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

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

4. 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.

5. 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.

6. 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.

7. Parameters

8. 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).

9. 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.

10. 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).

11. “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

12. “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

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

14. 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

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

16. 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)

17. particle trajectory of A=1012, B=8.33 T Np=1.15*1011*2808s s s s

18. loss duration & total loss for Al particle
1.15*1011*
400
1600
2808
1012
1014
1016
Loss duration for varying values of mass and Np in units of second (B=8.33 T).
1.15*1011*
400
1600
2808
1012
1014
24.208
1016
Total # of lost protons for varying values of mass and Np (B=8.33 T).

19. loss duration & total loss for Cu particle
1.15*1011*400
1.15*1011*1600
1.15*1011*2808
1012
1014
1016
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
1014
1016
Total # of lost protons for varying value of mass A and total proton intensity Np (B=8.33 T).

20. 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?]