macroparticle model predictions
Frank Zimmermann
UFO study meeting
23 June 2011
with contributions from
Massimo Giovannozzi, Athanasia Xagkoni
(NTU Athens), Zhao Yang (EPFL),
References:
1)
C. Sagan, “Mass and Charge Measurements of Trapped Dust in the CESR Storage
Ring,'‘ NIM A330 371 (1993).
2) F. Zimmermann, ``Trapped Dust in HERA and DORIS,'' DESY HERA 93-08 (1993)
3) F. Zimmermann, ``Trapped Dust in HERA and Prospects for PEP-II,'' PEP-II AP Note
No.: 8-94 (1994)
4) F. Zimmermann, J.T. Seeman, M. Zolotorev, W. Stoeffl, “Trapped Macroparticles in
Electron Storage Rings,'' IEEE PAC'95 Dallas (1995).
5) V. Baglin, “Can we optimise the cleanup process further?,’’
6) Proc. LHC Performance Workshop Chamonix 2010, 25-29 January 2010.
7) F. Caspers, private communication (2008).
8) Wolfram Research, Mathematica 7.
9) M. Brugger, F. Cerutti, A. Ferrari, V. Vlachoudis, “FLUKA Estimations Concerning
Obstacles in the LHC Magnets,'‘ CERN-AB-Note-2007-018 ATB (2007).
10) The FLUKA Team, “Summary of FLUKA Estimations for Obstacles in the LHC
Magnets,” private communication by G. Arduini, 24.02.2009
11) M. Giovannozzi, F. Zimmermann, A. Xagkoni, “Interaction of Macro-Particles with
LHC p Beam,” IPAC’10 Kyoto
12) 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
electric field of beam
electric image force
gravity
equations of motion:
Beam Loss Rate
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
even particles of mass
A=1018 proton masses
are charging up to be
repelled upwards
present beam current, Ntot=2.3x1012
particles heavier than
A=1016 proton masses
continue to fall down
resulting loss rates (compare with quench threshold ~a few 107 p/s)
design beam
current
longer and higher
losses for present
beam current!
total loss duration
~a few ms
“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
nominal beam current,
Ntot=3.2x1014, 7 TeV
quench
threshold
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
Y co ordinate m
0.02
Y co ordinate m
0.02
0.01
0.01
X co ordinate m
0.02
0.01
0.01
0.02
A=1012
X co ordinate m
0.02
0.01
0.01
A=1014
0.01
0.01
0.02
0.02
0.02
B =0 T, 8.33 T and 80 T (Blue, red and green)
“second crossing” & magnetic field
log(loss rate) versus time
Z. Yang
log beamlossrate
log beamlossrate
0
time s
0.02
0.04
0.06
0.08
0.10
0.12
0
time s
0.02
0.14
0.04
0.06
0.08
0.10
0.12
0.14
10
50
20
100
30
40
50
60
A=1012
A=1014
150
200
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
0.064946 s
Y co ordinate m
0.02
y co ordinate m
0.02
0.01
0.01
0.060703 s
0.00
Time s
0.02
0.04
0.06
0.08
0.10
0.12
0.14
x co ordinate m
0.02
0.01
0.01
0.01
Y co
ordinate m
0.0005
0.01
0.0004
0.02
0.13530 s
0.0003
0.02
0.0002
0.0001
0.0000
0.130
0.14275 s
Time s
0.132
0.134
0.136
0.138
0.140
0.142
0.144
0.02
loss duration & total loss for Al particle
1012
1014
1016
1.15*1011*
400
0.00097
0.00199
0.00295
1.15*1011*
1600
0.00055
0.00155
0.00242
1.15*1011*
2808
0.00036
0.00139
0.00224
Loss duration for varying values of mass and Np in units of second
(B=8.33 T).
1.15*1011*
1.15*1011*
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 1.15*1011 1.15*1011
*400
*1600
*2808
1012
0.00094 0.00051 0.00030
1014
0.00198 0.00154 0.00138
1016
0.00297 0.00243 0.00224
Loss duration [in s] for varying mass
A and total proton intensity Np
(B=8.33 T).
1.15*1011 1.15*1011 1.15*1011
*400
*1600
*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).
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.
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?]