U. IrisoECLOUD’04 – 21 April 2004 1

ECLOUD’04April 19-23 2004, Napa, CA

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.

U. IrisoECLOUD’04 – 21 April 2004 2

Outline

1) Motivation: the bunch to bunch evolution

2) Can the Electron Cloud be represented by maps?

2.1. The first N=N and N=0.

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 (->maximize 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 m+1 is m and m+1 . That is… !

• Plot m+1 vs m :

imim a ·1

– Looks like a parabola that gets to the line y=x for saturation.

– The EC build up using 3rd order fits look quite accurate…

Note: I don't show (m, m+1)

corresponding to the first N=0 (first “no-bunch” in the abort gap). I will...

and ai(N)!!

; i > 1

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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:

● The first N=0 (first “no bunch” in the abort gap after a bunch train of M bunches with bunch charge N) is determined by another polynomial, and it is independent of N. This point in (rho_m+1, rho_m) is out of the N=0 line due to duration of space charge effects.

ECLOUD (Thanks G. Rumolo!)CSEC

SEY from Furman & Pivi SEY from Cimino & Collins

N=0 curve (decay)

First N=0 curveN=0 curve (decay)

First N=0 curve

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2. Can the EC be represented by maps?

• Once we have ai (i=1,2,3) as a f(N), we just need an algorithm depending on Nm, being m the bunch number in the bunch train

33

2211 ··· mmmm aaa

N=N build up

First N=0

N=0 decay (gap)

• Much faster than following ns-to-ns using “typical” EC simulation codes (~1h vs ~1ms)

Question: What’s the best way to distribute 68 bunches? Let’s see:

We have quite a few possibilities… 110!/(110-68)!68! ~ 10^30

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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

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: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

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

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2. Can the EC be represented by maps?

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

The first N=N is needed!!

Similarly to what happens with the first N=0, doesn’t jump from N=0 to N=N in only one bunch.

N=0: Decay curve

N=N: Build up curve

First N=0 curve

First N=N curve

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

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2. Can the EC be represented by maps?

● Complete algorithm then, requires:

33

2211 ··· mmmm aaa

N=N build up (N,N)

First N=0 (0,N)

N=0 gap (0,0)

First N=N!! (N,0) Evaluating Maps for Electron Cloud (MEC) vs “usual” EC simulations codes (in this case, CSEC) gives now very good agreement. See next slides...

Note: MEC requires an initial 0 (seed).

(Nm , Nm-1 )

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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 N=N INCLUDED!! => is overestimated

FIRST N=N INCLUDED!!=> Good agreement

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m+1(m ) evolution for BP (3,2,0)(6,4,0)

m

m+1

(0,0): linear coefficient a00 < 1 (< a01)

(0,N): linear coefficient a01 < 1

(N,0): linear coefficient a10 >1 (< a11)

(N,N): linear coefficient a11 > 1

Bunch Number1 2 3 4 5 6 7 9 108

Nm

(N,N) (N,0)

(0,N)

(0,0)

(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

δmax =2.3

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3. N exploration of parameter space: a map application

Suppose the map: ...··· 321 mmmm cba

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:

We have seen we need four sets of parameters, depending on

(N, N)

(0 , N)(0 , 0)

(N, 0)

, where F is:0)·( NFHm

, full bunch follows a full bunch a11, b11, c11

, full bunch follows an empty one a10, b10, c10

, empty bunch follows a full one a01, b01, c01

, empty bunch follows an empty one a00, b00, c00

iMHiMi aaaaF 00110110 )(

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3. N exploration of parameter space: a map application

H

Mi

aa

a

aa

aaF 00

00

11

0011

0110

If F > 1; will increase (up to a saturated value, out of linear regime)If F < 1; the EC disappears.

This factor is written as:

Minimum F requires

i

aa

aa

0011

0110 < 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

For a given M, does not blow up if (a10·a01)/(a11·a00) < 1

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4. EC phase transitions at RHICA

u 79

+ x

109

P (

Tor

r)

10-9

10-10

10-9

10-11

0

50

25 Sudden pressure drop, while beam decays “adiabatically”.Do simulations reproduce this kind of “1st order phase transition”?

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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 RHICA

u 79

+ x

109

P (

Tor

r)

10-10

10-9

10-11

0

50

25

Not all places show 1st order phase transitions behavior. 2nd order types are also present for the same beam.

IR10: 1st order

IR12: 2nd order

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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:

2nd order behavior, analogy with Type II superconductors)

Similar EC behaviors:

-D. Schulte P(W/m) vs δmax

(in ECLOUD’04)

-M. Furman

(LHC-Project Report 180)

Are the 1st order phase transitions reproducible with some code?

sat= (N-Nc)

= 0.509 +/- 0.017

Nc = 7.398 +/- 0.005

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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 N=0”, and “first N=N), 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.