Longitudinal Space Charge Dynamics
in
Photoguns
Accelerator Physics Seminar,
11/1/2013
Jared
Maxson
eRHIC
(~1nC)
•
Many applications of CW photoemission sources (RF,
DC,
etc
) need large charge per bunch:
•
And the Cornell ERL (~100pC)?
•
Interplay between gun Energy, photocathode field,
and max. charge extractable. What is the maximum?
Motivation
LCLS II high charge
mode (~
0.3
nC
)
•
Transverse Limits:
–
Space charge force damped as
→
𝛾
2
, want
higher voltage for smaller
emittance
•
Longitudinal Limit:
–
Long. space charge overwhelms acceleration
force, charge extraction ceases
–
Simple case of fully filled planar diode:
Naïve Limits
Max supportable current is given
by the Child

Langmuir Law:
𝐽
𝑎
=
4
𝜖
0
9
2
𝑉
0
3
2
2
•
What if the bunch is short, it not filling whole
diode region (like a laser pulse)?
–
Bazarov
, Dunham, Sinclair 2009: If bunch is a
“pancake”,
A
=
𝜎
𝑋
𝜎
𝑧
≫
1
, then:
–
Valfells
et. al. 2001: Short pulse, but 1D:
Naïve Limits
𝐽
𝐿𝑃
𝐽
𝐿
=
2
1
−
1
−
3
4
𝑇
𝜏
2
𝑇
𝜏
3
≥
1
!
Factor of two incl. for
image charge
•
Koh,
Ang
, and Kwan 2005: A full 3D CL limit!
–
Utilize the short pulse result for long. dimension
–
Current enhancement from 3D effects:
–
Presume first that
𝐽
𝑎
,
3
(
𝑟
,
𝑧
)
=
𝑧
𝑣
𝑧
∝
𝑧
𝜙
𝑧
+
0
=
𝐽
𝑃 𝐿
–
Consider change in the
on

axis longitudinal field
from
off axis particles:
Δ
=
𝑟
,
0
𝑟𝑟
4𝜋
𝜖
0
𝑟
2
+
2
3
/
2
–
Integrate over whole volume for
(
3
)
.
–
0
~
0
,
=
𝐽
3
𝐽
𝑆𝑃 𝐿
=
𝜙
3
𝜙
𝐿
=
𝑧
3
𝑧
(
𝐿
)
~
2
!
For A~1
Full 3D Limit
•
Exceeding the max current in the 1D CL case:
•
For a short 3D pulse:
–
Re

emission occurs when:
•
SC expansion drops density of head
beamlet
•
Beamlet
travels far enough away:
=
𝜎
2
𝜖
0
(
1
−
2
+
2
1
/
2
)
Above the limit
A bit later:
•
Dave Dowell (1997) measured this beam
breakup in the ELSA injector
•
Only took projections of phase space:
Previous Measurement
Only took projections of the
longitudinal phase space!
Physics of Plasmas
4
, 3369 (1997);
doi
:
10.1063/1.872477
•
Using quadratic and cubic aberration terms, fit
the full long. phase space:
Previous Measurement
•
The 3D relations of
Koh
, et al. have not been
experimentally verified to date.
•
Dowell’s measurement was only indirect. Can we
measure the real virtual cathode phase space?
•
Can we reproduce
Koh’s
results in simulation?
–
Track beam of various pulse lengths of given radius
through ERL
photogun
.
–
Increase bunch charge until some particles are
reflected back toward cathode
—
this is the critical
current!
Current Standing
`
What does the phase space actually look like above the limit?
What about the transverse distribution? How does the
emittance
change?
Exit of 500kV ERL gun
A “normal” bunch at gun exit
virtual cathode instability
virtual cathode instability
Virtual Cathode Instability
Transverse Distribution
×
1000
Y (mm)
×
1000
Z(m)
Thanks
I
gal
!
Full Phase Space Measurement in R128
•
EMS system measures vertical phase space,
via two horizontal 30um slits, and box
correctors (4 total).
•
Deflector cavity converts time position to
vertical position

> allows measurement of
longitudinal profile (bunch length)
•
Vertical slits make resolution better.
•
A collimating slit (120 um vertical slit) and
dipole magnet measures energy spread
Beamline
Overview
Gun
Anode
https://wiki.lepp.cornell.edu/ERL/Private
/R128Beamline
L0
Sol.
Corr.
Mag.
Laser in
EMS
Slits
Def
Cav
Coll.
Slit
F.cup
R128
Sol.
Spec.
Dipole
Wire
Scanner
Full Phase Space Measurement
×
1000
Y (mm)
EMS Cor. 1
EMS Cor. 2
Time (
ps
)
d
E
/E
All slits in, deflector on, through dipole,
On final
viewscreen
:
•
Transmission through slits
>1e

5.
–
Quads and R128 solenoids allow the squeezing of the
beam through the slits, while still forming a good image.
Updated
Beamline
Design
Sol 1
Slits
quad1
R128 Sol
•
ERL laser pulses exit the final amplifier around
~2.5 ps. Too small! Use pulse stacking to
lengthen:
•
Can remove a crystals to shorten. Allows for a
pulse length scan.
•
Can rotate second crystal away from 45 degrees
to give head/tail slope.
Pulse length
45
deg
45
deg
45
deg
Pulse length
Changing the
p
ulse shape
Shorten:
Modulate:
•
CW sources continue to demand charges at
the space charge limit.
•
The onset of the limit has not been fully
measured.
–
The virtual cathode instability has only been
measured indirectly
–
The 3D modifications of CL have not been verified
in experiment.
•
We’re all set up in R128 to do it. Stay tuned!
Conclusions
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