1

Experimental Observations of a Multi-

Stream in a Long Intense Beam

B. Beaudoin, S. Bernal, I. Haber, R.A. Kishek, T. Koeth

Institute for Research in Electronics & Applied Physics

Energy Research Facility

College Park, MD, USA

May 15, 2013

2

1. Motivation behind this work

2. The University of Maryland Electron Ring (UMER), a tool to study

intense beams on a small scale using low energy electrons

3. Bunch wrapping and onset condition

• Longitudinal erosion (debunching) of long beams due to space

charge

• PIC simulations of bunch wrapping

• Calculation of the onset

• Comparison between theory, measurements and simulations

4. Extending to multi-bunch trains (still within the long wavelength limit)

5. Conclude

Outline

Background

1000 1000000 1000000000 1E+121 keV 1 MeV 1 GeV 1 TeV

e-

p

HI

electrons

protons

heavy ions

UMER

1000 1000000 1000000000 1E+121000 1000000 1000000000 1E+121 keV 1 MeV 1 GeV 1 TeV

e-

p

HI

e-

p

HI

electrons

protons

heavy ions

UMER

APERTURE PLATE

UMER spans a broad range of intensities

through the use of the aperture plate

/o

cs/vo

4 4

FULL LATTICE PERIODS: 0.32 m

3.66 m

University of Maryland Electron Ring

Single turn injection at 60 Hz

Ring Diagnostics:

14 Fast, Capacitive BPMs

1 Wall Current Monitors

RF-Knockout

Slow and Fast Fl. Screens

OTR Screens

Circulation Time 197 ns

FULL LATTICE PERIODS: 0.32 m

BPM

3.66 m

University of Maryland Electron Ring

Single turn injection at 60 Hz

Ring Diagnostics:

14 Fast, Capacitive BPMs

1 Wall Current Monitors

RF-Knockout

Slow and Fast Fl. Screens

OTR Screens

Circulation Time 197 ns

4

FULL LATTICE PERIODS: 0.32 m

WCM

BPM

3.66 m

University of Maryland Electron Ring

Single turn injection at 60 Hz

Ring Diagnostics:

14 Fast, Capacitive BPMs

1 Wall Current Monitors

RF-Knockout

Slow and Fast Fl. Screens

OTR Screens

Circulation Time 197 ns

4

FULL LATTICE PERIODS: 0.32 m

WCM

BPM

3.66 m

University of Maryland Electron Ring

Single turn injection at 60 Hz

I-Cell

Ring Diagnostics:

14 Fast, Capacitive BPMs

1 Wall Current Monitors

RF-Knockout

Slow and Fast Fl. Screens

OTR Screens

Circulation Time 197 ns

4

FULL LATTICE PERIODS: 0.32 m

WCM

BPM

3.66 m

University of Maryland Electron Ring

Single turn injection at 60 Hz

I-Cell

Ring Diagnostics:

14 Fast, Capacitive BPMs

1 Wall Current Monitors

RF-Knockout

Slow and Fast Fl. Screens

OTR Screens

Circulation Time 197 ns

4

0 2 4 6 8 10 12 14 16 18 20-0.8

-0.6

-0.4

-0.2

0.0

0.2

Beam

Cu

rren

t (m

A)

Time (s)

Longitudinal Bunch Erosion of Bunch Current

AC component of RC10 wall current monitor signal (Negative going signal)

Injected Turn

5c

4

os

o o

qg

m

The 0.6 mA beam

sc0.0049

vo

5

0 2 4 6 8 10 12 14 16 18 20-0.8

-0.6

-0.4

-0.2

0.0

0.2

Beam

Cu

rren

t (m

A)

Time (s)

10

Longitudinal Bunch Erosion of Bunch Current

AC component of RC10 wall current monitor signal (Negative going signal)

Injected Turn

5c

4

os

o o

qg

m

Eroding

(mA)

Head

Tail

Normalized

The 0.6 mA beam

sc0.0049

vo

z

dE

dz

0zE

Tail

Dv = 2cs

Head

z

0zE

Line-charge

density

Longitudinal Space-Charge Physics

-CERN 77-13, 19 July 1977,

“Theoretical Aspects of the Behavior of Beams in Accelerators and Storage Rings

-A. Faltens, E.P. Lee, and S.S. Rosenblum, Journal of Applied Physics, 61, 5219, (1987).

Velocity

One - Dimensional

0zE

vo

Dv = -2cs

1wkr

Long wavelength limit

cs is the longitudinal wave

speed of a perturbation on the

bunch.

rw is the pipe radius

5c

4

os

o o

qg

m

Inter Spacing Shrinks as the Bunch wraps

DL = Bunch length

C = Ring

circumference

Injected length

DL = 0.5C

Beam propagated 23 m

DL > 0.56C

h = fill factor =

injected pulse

length / ring lap-

time

6 mA beam

h = 0.50

Simulated Phase Space

7

Inter Spacing Shrinks as the Bunch wraps

DL = Bunch length

C = Ring

circumference

Injected length

DL = 0.5C

>2cs

Beam propagated 23 m

DL > 0.56C Beam propagated 310.5 m

DL = 2C

h = fill factor =

injected pulse

length / ring lap-

time

6 mA beam

h = 0.50

Simulated Phase Space

7

Inter Spacing Shrinks as the Bunch wraps

DL = Bunch length

C = Ring

circumference

Injected length

DL = 0.5C

>2cs

>cs

Beam propagated 23 m

DL > 0.56C

Beam propagated 713 m

DL > 4C

Beam propagated 310.5 m

DL = 2C

h = fill factor =

injected pulse

length / ring lap-

time

6 mA beam

h = 0.50

Simulated Phase Space

7

Inter Spacing Shrinks as the Bunch wraps

<cs

DL = Bunch length

C = Ring

circumference

Injected length

DL = 0.5C

>2cs

>cs

Beam propagated 23 m

DL > 0.56C

Beam propagated 713 m

DL > 4C

Beam propagated 908.5 m

DL = 5C

Beam propagated 310.5 m

DL = 2C

h = fill factor =

injected pulse

length / ring lap-

time

6 mA beam

h = 0.50

Simulated Phase Space

7

Signature of the Onset in the Current Profiles

16

Current Profiles from the RC 10 Wall Current Monitor

Beam becomes “DC”

6 mA beam

h = 0.50

Experimental

sc0.013

vo

Simulation

Onset

No charge loss in simulation

Condition required for the Onset

z

2c𝑠 + v𝑜

c𝑠 + v𝑜

v𝑜 − 2c𝑠

v𝑜 − c𝑠

𝜂𝐶 2 2c𝑠 𝑠 v𝑜 + 𝜂𝐶 2

−c𝑠 𝑠 v𝑜 + 𝜂𝐶 2

𝐶 + c𝑠 𝑠 v𝑜 − 𝜂𝐶 2 𝐶 − 𝜂𝐶 2 𝐶 − 2c𝑠(𝑠 v𝑜 ) − 𝜂𝐶 2

v(z,s)

Wrapped around

beam end in ring

geometry

Assume the filament

separation is a cs

sonset = Onset of

instability

Δv = vℎ𝑒𝑎𝑑 𝑧, 𝑠 − v𝑡𝑎𝑖𝑙 𝑧, 𝑠 = 4cs 3 − (2v𝑜𝐶 3 𝑠) 𝜂 − 1

Δv = cs = 4c𝑠 3 − (2v𝑜𝐶 3 𝑠𝑜𝑛𝑠𝑒𝑡) 𝜂 − 1

𝑠𝑜𝑛𝑠𝑒𝑡 = (2v𝑜𝐶 cs ) 𝜂 − 1

Filament Separation is = cs

v𝑡𝑎𝑖𝑙 𝑧, 𝑠 = v𝑜 − (2v𝑜 3 𝑠) 𝐶 − 𝑧 + 𝑐𝑠 𝑠 v𝑜 − 𝜂𝐶 2

vℎ𝑒𝑎𝑑(𝑧, 𝑠) = v𝑜 + (2v𝑜 3 𝑠) 𝑧 + 𝑐𝑠 𝑠 v𝑜 − 𝜂𝐶 2

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Fill Factor and Current Dependence on the Onset

10

Experiment

Simulation (WARP)

Theory

Onset of Instability

h s

21

co

onset

v Cs

1/ 2

s 5

0 0

c4

oqg

m

onsetonset

sturns

C

B.L. Beaudoin, R.A. Kishek, I. Haber, T.W. Koeth, submitted (2012).

6mA

104mA

11

Current loss delays the

longitudinal wave velocity, cs and

thus delays the onset of the

instability

Incorporating Transverse Current Loss into the

Simulation Model

time

Avg C

urr

ent

(mA

)

- No Loss

- Current Loss

- Measurement

- Simulation

Normalized

Fill Factor Dependence on the Number of

Filamentations

𝑀𝑡ℎ𝑟 = Δ𝐿𝑜𝑛𝑠𝑒𝑡 𝐶 = 8𝐶 𝜂 − 1 + 𝜂𝐶 𝐶

h = 0.35

130 ns long bunch

𝑀𝑡ℎ𝑟 = 8 𝜂 − 1 + 𝜂

h = 0.66

70 ns long bunch

DL > 3.5C DL > 7C

The growth rate of the modulations

in phase space is also dependent

on the fill factor

Phase Space (6 mA beam) 100 ns long bunch

h = 0.50 DL > 5C

12

Extending to Multi-Short-Bunch Trains

sc0.0164

vo

7.7 mA beam

3 pulse bunch train at 50 MHz

Experimental Observation

Onset of instability

sonset = 132.7 m

turnsonset = 11.5

C (20 )v 1.167ons m

For multiple bunch

trains, C is the pulse

to pulse spacing

C C

…

12.570.0636

197.39

ns

nsh

Multi-Bunch Train

h s

21

co

onset

v Cs

131.2onsets m

Preliminary

13

Summary and Concluding Remarks

22

• Longitudinal space-charge causes the beam to wrap the machine several

times.

• The onset of the instability occurs when the separation between the

innermost filaments is a longitudinal wave velocity, cs.

• Comparisons between theory, measurements and PIC simulations have

shown good agreement.

• Future Activities

– Measure growth rates and amplitudes as a function of line-charge density and fill factor

– Continue to work on multi-bunch trains to characterize parameter space for multiple

bunches.

– Inject shorter and shorter bunches until we approach the short wavelength limit where

krw >> 1

Thank you

15

Extra Slides

16

Fitting to Determine the Onset

h 0.38

To go from 𝑒𝑥𝑝−3.5 to 𝑒𝑥𝑝0, for this

particular case, the growth is about

~3.5 s or 17.7 turns.

Time Time

Beam current 6.0 mA

17