FlatBeams and Emittance Exchange

1
Flat-Beams andEmittance Exchange
P. Emma1, Z. Huang1, K.-J. Kim2, Ph. Piot3 June
23, 2006

• Flat-beam gun can produce gt1001 emittance ratio
• Smaller emittance (ey) might approach 0.1 mm
• Longitudinal emittance may also approach 0.1 mm
• Larger ez is useful to Landau damp m-bunching
• Can we exchange ez ? ex and produce
  g(ex , ey , ez) (0.1 , 0.1 , 10) mm, or better?

1 SLAC, 2 ANL, 3 FNAL
2
FEL needs very bright electron beam
transverse emittance
eN ? 0.2 mm at 1 Å, 15 GeV
energy spread
sd ? 0.01 at Ipk 4 kA, K ? 3.5, lu ? 3 cm,
Long. emittance requirement is ??z?? ? ??z ? 60
?m
RF gun produces both ??x ??z few mm
Can we reduce ??x at the expense of ??z ?
3
Gain Length vs. K of FEL at 0.4 Å
gex,y ? 1 mm, Ipk ? 3.5 kA, sd ? 0.01
gex,y ? 0.1 mm, Ipk ? 1 kA, sd ? 0.01
assume that the beta function in the undulator is
optimized to produce the shortest gain length
4
Intrinsic energy spread is too small to be a
benefit for x-ray SASE FEL
A beam heater is required, which Landau damps the
CSR/LSC micro-bunching instability
Final long. phase space at 14 GeV for initial
modulation of 1 at l 15 mm
beam blows up with no heater
heated beam stays cool
5
Very Small Energy Spread is Wasted
LCLS Parameters
without heater
with heater
Ming Xie scaling
6
How cold is the photo-injector beam?
Parmela Simulation
TTF measurement
H. Schlarb, M. Huening
3 keV
DE/E
simulation
measured
Dt (sec)
3 keV, accelerated to 14 GeV, and compressed ?36 ?
3/14?106?36 lt 1?10-5
Too small to be useful in FEL (no effect on FEL
gain when lt1?10-4)
7
Generating a Flat Beam (Y. Derbenev), (R.
Brinkmann, Y. Derbenev, K. Flöttmann), (D.
Edwards ), (Y.-E Sun)
UV light
skew quads
rf gun
booster cavity
gex ? 0.4 mm gey ? 40 mm
X3
X4
X5
X6
X7
X8
experiment
simulation
Ph. Piot, Y.-E Sun, and K.-J. Kim, Phys. Rev.
ST Accel. Beams 9, 031001 (2006)
8
Injector Simulation (Astra, Impact-T)

• 2.6-GHz, 1.5-cell RF gun
• 138 MV/m peak E-field in gun
• 8 TESLA SC-cavities at 1.3 GHz (216 MeV)
• round-to-flat converter of 3 skew quads
• 3D oblate ellipsoid laser pulse
• 0.6 mm per mm radius thermal emittance
• 36 MV/m peak E-field in TESLA cavities
• 300 mm rms laser spot size on cathode
• 50 mm rms bunch length (80 fs laser pulse)
• 20 pC bunch charge (34 A)

9
Emittance Levels from Simulation

• Thermal 2D (0.6 mm/mm)?(0.3 mm) ? 0.23 mm
• Transverse 4D (0.23 mm)2 ? 0.053 mm2
• After skew 4D (9.9 mm)?(0.0054 mm) ? 0.053 mm2
• Longitudinal 2D 0.080 mm

10
Space-Charge Effects on Emittance
Is the small longitudinal emittance consistent
with the space charge force?
sx ? 300 mm, sz ? 50 mm, I ? 34 A, E0 ? 138 MV/m,
j0 ? 45
gez ? 0.13 mm
not so different than 0.08 mm seen in simulation
K.-J. Kim, NIM, A275, 201, (1989)
11
Evolution of Transverse Emittances Along
Photo-Injector Beamline (to 216 MeV)
gex
9.9 mm
coupled values
intrinsic gex,y ? 0.23 mm
gez
0.084 mm
gey
rf gun
0.0054 mm
acc. cavities
skew quads
12
Longitudinal Distributions After Photo-Injector
slice energy spread (rms ? 4?10-6, 0.9 keV)
E0 216 MeV
gez 0.080 mm gey 0.0054 mm gex 9.92 mm
13
Transverse Distributions After Photo-Injector
E0 216 MeV
gez 0.080 mm gey 0.0054 mm gex 9.92 mm
?
14
Emittance Exchange Concept (2002)
Electric and magnetic fields
k
h

• Particle at position x in cavity gets
  acceleration DE/E ? d ? kx

• This energy deviation d in chicane causes
  position change Dx -hd

Must include magnetic field and calculate
emittance in both planes
Cornacchia, Emma, PRST AB 5, 084001 (2002)
15
Improved Emittance Exchanger (2005)
2L
Rk
h
R1
k
h
R1
rectangular RF deflecting cavity
x ? R56 of dog-leg
x, z mapping (ignore y coordinate here)
System modified by K.-J. Kim, 2005
16
Full Emittance Exchange
If RF deflector voltage is set to k -1/h
and transverse (bend-plane) and longitudinal
emittances are completely exchanged.
17
Emittance Exchange Limitations
4x4 transfer matrix is four 2x2 blocks1
Equal emittances remain equal. (If ex0 ez0 then
ex ez.)
2
Equal, uncoupled emittances cannot be generated
from unequal, uncoupled emittances3. (Setting
A  ½ produces equal emittances, but then they
are highly coupled with ?2 ? 0.)
1 K.L. Brown, SLAC-PUB-2370, August 1980.
2 Thanks to Bill Spence.
3 E. Courant, in Perspectives in Modern
Physics..., R.E. Marshak, ed., Interscience
Publishers, 1966.
18
Emittance Exchanger Parameters
19
CSR Suppression with Large Beam Size
, bx 100 m
CSR also reduced when horizontal beam size
exceeds transverse coherence length
With this large bx and large ex, the CSR
emittance growth is estimated (1D, elegant) at
0.08 mm ? 0.16 mm.
20
Cavity Thick-Lens Effect
tail
Thin-lens gives no x-offset in cavity
head
Thick-lens By kick, and then x-offset changes d
add chirp to compensate no mean x-offset
21
Control of Second-Order Dispersive Aberration

• Energy spread is induced in T-cav due to
  transverse beam extent (d kx)
• Second-order dispersion is generated in last two
  bends, which dilutes bend plane (x) emittance
• The right initial energy chirp minimizes the
  divergence, g, after the last bend, which
  minimizes emittance growth

d kx
Tcav
q
Dx? qd2
h
x? kz
Dx hd2
22
The Effect of Initial Chirp ? Small g at System
Exit

• The final divergence, g, is decreased by the
  initial chirp ? shorter bunch in cavity ? less
  kick, x? kz, after cavity...
• For large g (left) and small g (right), the same
  Dx increase produces much larger area increase
  (emittance growth) when g is large (g is Twiss
  parameter, 1a2/b, not energy)

x?
x?
much bigger area increase when large g
much smaller area increase when small g
(ge0)1/2
(gmine0)1/2
x
x
?Dx2?1/2
?Dx2?1/2
(be0)1/2
(be0)1/2
23
Longitudinal Distributions After Exchanger (no
CSR)
slice energy spread (rms ? 6?10-5, 13 keV)
E0 216 MeV
gez 9.92 mm gey 0.0054 mm gex 0.084 mm
24
Transverse Distributions After Exchanger (no CSR)
sx
x
x
y
sy
E0 216 MeV
gez 9.92 mm gey 0.0054 mm gex 0.084 mm
y
25
Transverse phase space (left two plots) and
longitudinal phase space (right two plots) before
(top) and after (bottom) emittance exchange.
BEFORE EXCHANGER
AFTER EXCHANGER
sz ? 500 mm!
26
Operating parameters and achieved beam
parameters at photo-injector end
27
Flat Beam FEL at 0.4 Å
Assume ?und 3 cm, K 1.34, gex ? 0.16 mm, ?x,y
20 m Ipk ? 1 kA, sd ? 0.024 at 13.6 GeV
(hence gez ? 10 mm)
Round beam gex gey ? 0.16 mm
Emittance-exchanged beam
confirmed with Genesis 1.3
Ming Xie, NIMA507, 450 (2003)
28
Unusual System Characteristics
Need extremely stable energy (0.5?10-6 rms jitter
? 10 x-beam size jitter)
29
Summary

• Simulations of flat-beam gun with emittance
  exchanger suggest possible levels of
• gez ? 9.9 mm, gey ? 0.0054 mm, gex ? 0.16 mm
• Large z-emittance should Landau-damp
  micro-bunching instabilities
• Bunch gets longer (50 ? 500 mm) and will need to
  be compressed by ?250 to achieve 1 kA
• CSR needs much closer look
• Sensitivity to energy jitter may be Achilles heel