Multi-pass Beam Breakup (BBU) in energy recovery linacs (ERL)

Eduard Pozdeyev, BNL

E. Pozdeyev, BNL 2/15

Instability mechanism and threshold

B

'12xmx x E

Beam establishes a feedback that can become unstable. The threshold is approximately

)sin()/(

2

*rL

bth

TmQQR

c

VI

)(sin)cos()sin()()(cos 2343214

212

* mmmmm

1 accel.-1 decel., 2D

N accel.-N decel., 1D

*)/(

2

MQQR

c

VI

L

bth

i ijij

ij TmM )sin(* 12

E. Pozdeyev, BNL 3/15

Experimental observation of BBU at JLab FEL

IR wiggler

-0.01 -0.005 0 0.005 10

-2

10-1

100

t(sec)

P(m

W)

3.6 mA4.2 mA5.0 mA

y = 631.24x - 1645.2

0

400

800

1200

1600

2000

0 1 2 3 4 5 6

I (mA)

1/t

(1/s

ec)

th

bth

L I

II

QtVV

2exp0

II

I

th

theff

0

E. Pozdeyev, BNL 4/15

Beam behavior below the threshold: Q(I)

II

IQQ

th

thLeff

th

bth

L I

II

QtVV

2exp0

-1000 -500 0 500 100010

-4

10-3

10-2

10-1

dF(Hz)

S2

1

2.5 mA2.0 mA1.5 mA1.0 mA0.5 mA

y = -0.0583x + 0.167

0

0.05

0.1

0.15

0.2

0 0.5 1 1.5 2 2.5 3

I (mA)

1/Q

-2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500-95

-90

-85

-80

-75

-70

-65

-60

-55

-50

dF(Hz)

S2

1

0.0 mA0.5 mA1.0 mA1.5 mA

y = 0.0467x + 0.1512

0

0.05

0.1

0.15

0.2

0.25

0 0.5 1 1.5 2

I (mA)

1/Q

F=2116.584 MHz, m12sin(Tr)>0 F=2106.0 MHz, m12sin(Tr)<0

Also valid for Ith<0!

E. Pozdeyev, BNL 5/15

Formula, BBU codes benchmarking: Comparison to experiments

Method Threshold (mA)

Simplified formula 2.0

Simulations* (TDBBU, MATBBU, New Code, BI)

2.1

Direct Measurement 2.3

E. Pozdeyev, BNL 6/15

Multi-pass BBU codes

Multi-pass BBU code can be separated in two groups according to their algorithm: TRACKING or EIGENVALUE

Name TDBBU New Code bi BBU-R MATBBU

Developer Lab JLab JLab/BNL Cornell U. JAERI JLab

Algorithm tracking tracking tracking tracking eigenvalue

# Dimensions 2D 2D 2D 1D 1D

# Recirculation unlimited unlimited ?unlimited? 2 unlimited

Cumulative BBU yes yes yes & no ? no

Input elements/mat. elements/mat. matrices ? elements/mats.

ProgrammingLanguage

Fortran/C C++/Java C++ C Fortran/C

E. Pozdeyev, BNL 7/15

Mitigation techniques: development of low-QHOM, high-gradient cavities

• Design of multi-cell cavities with low-Q (~104), low-R/Q HOMs seems to be the most reliable way to increase the BBU threshold

• The work is under way at BNL, JLAB, Cornell U…

BNL JLAB

E. Pozdeyev, BNL 8/15

Mitigation techniques: HOM frequency spread (large-scale

machines)

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5

BB

U th

resh

old

curr

ent (

mA

)

amplitude of HOM randomization (MHz)

f_HOM (MHz) Ith (mA)

0 25.8

1.3 280

10 418

Cornell ERLQ=2.1E4, Ncav=320

(Hoffstaetter, Bazarov, Song)

6-GeV JAERI ERLCav./HOM parameters - ?

(M. Sawamura, R. Hajima)

E. Pozdeyev, BNL 9/15

Optical BBU suppression methods: n-phase advance, rotation

• Adjustment of m12 and/or m34 was effectively used at JLAb FEL (D. Douglas). Effective for small machines. Provides a suppression factor of a few.

• Strong coupling (rotation or reflection) promises to suppress BBU significantly in a two-pass machine if x-y modes are degenerate and well –separated (R. Rand, T. Smith). Effective for small, two-pass machines. Easily provides suppression by a factor of a few. Its effectiveness reduces for a large number of cavities. Its effect on multi-pass machines has not been properly studied.

E. Pozdeyev, BNL 10/15

Enhancement of rotation: double elliptical cavities

S21

f

b

a

ba

f

S21

70 MHz

Larger mode degeneracy can be achieved via axially asymmetric design of accelerating cavities.

d

d

f

f 5

6

±d is the variation of the transverse cavity size

For a square cavity

a/b ≈1.05-1.07

E. Pozdeyev, BNL 11/15

Narrow (limited) band feedback, broad band feedback

• Narrow (limited) band feedback can be used to mitigate effect of a few modes in a small machine

• Broad band (Bunch-by-Bunch) feedback can be used in large scale machines. Complexity: Bunch passes through a machine only once or a few times. Instability growth rates can be of the order of a few tens of microseconds.

BPF

V

V e i

E. Pozdeyev, BNL 12/15

Prediction of BBU threshold at eRHIC Linac based on CEBAF experience

CEBAF: QHOM=3.2e4, R/Q=50, R/Q·Q=1.6e6, Ncav=320, Npass=5

eRHIC(LR): QHOM=892, R/Q=57, R/Q·Q=4.2e4, Ncav=200, Npass=3

• Ith, CEBAF=20 mA

• Scaling:– Ith 1/sqrt(Q) (J. Bisognano).

– Ith 1/N2pass

– Ith 1/Ncav

• All numbers plugged in, the projection is Ith,eRHIC=530 mA

E. Pozdeyev, BNL 13/15

Simulation of BBU threshold at eRHIC linac (very preliminary)

• eRHIC Linac Parameters: – 200 16MeV/pass cavities, measured Cu-model

HOMspectrum– 50 foc. and 50 defoc. quadrupoles, G=1.262 T/m– 3 acel.-decel. passes, each is 1.3 km long– 28 MHz bunch rep.rate

E. Pozdeyev, BNL 14/15

Other effects that require accurate consideration

• Cumulative (single-pass) BBU• Short-range transverse wakes (“banana-

effect”). 1cm-long bunch can be long enough to be affected by short range wakes. It can be of important for applications requiring “good emittance”.

• CSR• Fast ion instability• …

E. Pozdeyev, BNL 15/15

Acknowledgements

• BNL: V. Ptitsyn, V. Litvinenko, R. Calaga• JLab: L. Merminga, G. Krafft, B. Yunn, C.

Tennant, S. Benson , D. Douglas, K. Jordan, G. Neil, H. Wang, C. Hovater, R. Rimmer

• Stanford: Todd Smith• Cornell: I. Bazarov, G. Hoffstaetter• DESY: Stefan Simrock• JAERI: M. Sawamura, R. Hajima