Use of Maps for exploration of Electron Cloud parameter space

1
Use of Maps for exploration of Electron Cloud
parameter space
Ubaldo Iriso and Steve Peggs
M. Blaskiewicz, A. Drees, W. Fischer, H.C. Hseuh,
G. Rumolo, L. Smart, D. Trbojevic, S.Y. Zhang.
ECLOUD04 April 19-23 2004, Napa, CA
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Outline
1) Motivation the bunch to bunch evolution 2)
Can the Electron Cloud be represented by
maps? 2.1. The first NN and N0. 2.2. Examples
for the RHIC case
3) N exploration of parameter space 4) Electron
Cloud phase transitions at RHIC 5) Conclusion
and outlook
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1. Motivation the bunch to bunch evolution
After experimental observations at RHIC during
Run-3, the use of gaps along the bunch train is
chosen to minimize the detrimental effects of
Electron Cloud (EC)

• If EC density does not produce beam
  instabilities,
• If the flux into the wall does not produce
  pressure rises above harmful limits,
• If we are below heat load limit,
• then... who cares if EC is there?

QUESTION How do we evaluate the bunch pattern
that minimizes EC density (-gtmaximize luminosity?
BNL C-A/AP/118
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1. Motivation the bunch to bunch evolution

• For a given surface and beam pipe dimensions and
  an initial electron cloud density (? ), what is
  the ? evolution after a bunch m passes by?

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2. Can the EC be represented by maps?

• For a given surface, for the EC build up the only
  thing changing between the bunch m and bunch m1
  is ?m and ?m1 . That is ?!
• Plot ?m1 vs ?m

• Looks like a parabola that gets to the line yx
  for saturation.
• The EC build up using 3rd order fits look quite
  accurate

i gt 1
and ai(N)!!
Note I don't show (?m, ?m1) corresponding to
the first N0 (first no-bunch in the abort
gap). I will...
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2. Can the EC be represented by maps?

• Results for different N using CSEC (M.
  Blaskiewicz), and ECLOUD (F. Zimmermann). This
  is, results using different SEY parameterization

ECLOUD (Thanks G. Rumolo!)
CSEC
First N0 curve
First N0 curve
N0 curve (decay)
N0 curve (decay)
SEY from Furman Pivi
SEY from Cimino Collins
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2. Can the EC be represented by maps?

• Once we have ai (i1,2,3) as a f(N), we just need
  an algorithm depending on Nm, being m the bunch
  number in the bunch train

• Question Whats the best way to distribute 68
  bunches? Lets see

We have quite a few possibilities
110!/(110-68)!68! 1030
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Example the RHIC application

• At RHIC, a given bunch pattern is determined by
  the triplet (Ks, Kb, Kg), where
• Ks bucket spacing (multiple of 3 due to kicker
  limitations)
• Kb number of consecutive bunches with this
  bucket spacing
• Kg bunches not filled with this bucket spacing

• Unless otherwise noted, this is structure is
  repeated until the abort gap

Example (3,2,0)(6,4,0) 3 bunches with 3
buckets spacing, followed by 4 bunches with 6
buckets spacing Some parameters to know about
RHIC Harmonic number, 360. Abort gap 30
buckets. Bucket length 35.6 ns. Bunch harmonic
number 120. Abort gap, 10 bunches
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2. Can the EC be represented by maps?

• ? evolution from CSEC for the BP (3,2,0)(6,4,0)

• The first NN is needed!!
• Similarly to what happens with the first N0, ?
  doesnt jump from N0 to NN in only one bunch.

• When many successive bunches are filled, this
  misalignment is not significant.

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2. Can the EC be represented by maps?

• Complete algorithm then, requires

NN build up (N,N)
First N0 (0,N)
N0 gap (0,0)
First NN!! (N,0)
(Nm , Nm-1 )

• Note MEC requires an initial ?0 (seed).

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2. Can the EC be represented by maps?
Bunch pattern (3,12,8)
Bunch pattern(3,2,0)(6,4,0)
1st turn
2nd turn
3rd turn
1st turn
2nd turn
3rd turn
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2. Can the EC be represented by maps?
Bunch pattern (3,4,0)(6,8,0)
Bunch pattern (3,4,0)(6,8,0)
NO FIRST NN INCLUDED!! gt ? is overestimated
FIRST NN INCLUDED!! gt Good agreement
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?m1(?m ) evolution for BP (3,2,0)(6,4,0)
Nm
Bunch Number
1
2
3
4
5
6
7
9
10
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(N,0)
(N,N)
(N,N) linear coefficient ? a11 gt 1
(0,N)
(N,0) linear coefficient ? a10 gt1 (lt a11)
(0,N) linear coefficient ? a01 lt 1
(0,0)
(0,0) linear coefficient ? a00 lt 1 (lt a01)
(Nm, Nm-1)
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3. N exploration of parameter space

• All the information for the EC build up can for
  a regularly distributed bunch train can be
  determined by ai coefficients.

ECLOUD (Thanks G. Rumolo!)
CSEC
dmax 2.3
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3. N exploration of parameter space a map
application

• Suppose the map

We have seen we need four sets of parameters,
depending on
, full bunch follows a full bunch ? a11, b11,
c11
(N, N)
, full bunch follows an empty one ? a10, b10, c10
(N, 0)
, empty bunch follows a full one ? a01, b01, c01
(0 , 0)
, empty bunch follows an empty one ? a00, b00,
c00
(0 , N)
If ?, remains always small enough, we can use
linear approximation. After H possible bunches,
having filled up to M bunches and i transitions
(from 0 to N, and vice versa), the linear
approximation says
, where F is
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3. N exploration of parameter space a map
application
If F gt 1 ? will increase (up to a saturated
value, out of linear regime) If F lt 1 the EC
disappears.
This factor is written as
For a given M, ? does not blow up if
(a10a01)/(a11a00) lt 1
Minimum F requires ?
lt 1 ? large values of i !!
That is, maximum number of transitions, that is,
the most sparse distribution of bunches minimizes
EC. ? Current way to distribute bunches at RHIC
to minimize EC
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4. EC phase transitions at RHIC
50
Au 79 x 109
25
Sudden pressure drop, while beam decays
adiabatically. Do simulations reproduce this
kind of 1st order phase transition?
0
10-9
10-9
P (Torr)
10-10
10-11
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4. EC phase transitions at RHIC

• (P, N) diagram for the previous case

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4. EC phase transitions at RHIC
50
Not all places show 1st order phase transitions
behavior. 2nd order types are also present for
the same beam.
Au 79 x 109
25
0
10-9
IR10 1st order
P (Torr)
10-10
IR12 2nd order
10-11
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4. EC phase transitions at RHIC

• (P, N) diagram for the previous case

IR10 1st order behavior
IR12 2nd order behavior
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4. EC phase transitions at RHIC
Simulation results using CSEC for fine ?N
?sat ? (N-Nc) ?
2nd order behavior, analogy with Type II
superconductors) Similar EC behaviors -D.
Schulte P(W/m) vs dmax (in ECLOUD04) -M. Furman
(LHC-Project Report 180)
? 0.509 /- 0.017 Nc 7.398 /- 0.005
Are the 1st order phase transitions reproducible
with some code?
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5. Conclusions

• From the EC simulation codes (CSEC), the
  multi-bunch EC build up for RHIC has been
  determined using a 3rd order polinomial map.
  Preliminary results from ECLOUD are promising.
• A memory of two bunches both for the decay as
  for the build-up is found. With this effect taken
  into account (first N0, and first NN),
  agreement between MEC and CSEC is very good.
• Given a machine limitation ?limit (due to heat
  load, pressure rise, instabilities), MEC is
  useful for RHIC to find out the best way to live
  with EC by changing the bunch pattern
• Using maps, exploration of (?,N) is done, and
  standard maths are used to justify sparse
  distribution for bunches along a bunch train.
• 1st order and 2nd order phase transitions are
  seen at RHIC, but only 2nd order phase
  transitions seems to be reproducible with the
  codes.

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and outlook

• How do coefficients vary with SEY, R, etc
  follows. Can we find some few parameters to
  describe EC (sic).
• Can we map EC from experimental data?
• Does it work for your machine with your code?
  
• Is it an artefact due to long RHIC bunch spacing?
  Can we go to shorter bunch spacings? B-factories?
• Are the 1st order phase transitions reproducible
  with EC codes?

and acknowledgements
M. Blaskiewicz, A. Drees, W. Fischer, H.C. Hseuh,
R. Lee, N. Luciano, G. Rumolo, L. Smart, R.
Tomás, D. Trbojevic, L. Wang, S.Y. Zhang.