# Longitudinal Space Charge Dynamics in Photoguns

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Nov 16, 2013 (4 years and 7 months ago)

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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
𝐿𝑃
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
𝑟𝑟

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

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

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

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